Platonia
Stephen Paul King
Stephen
“It is amazing what can be accomplished when nobody cares about who gets the credit.”
Robert Yates
Jason Resch
Hi All,Question: Why must Platonia exist?
Brent Meeker
On Thu, Feb 17, 2011 at 7:49 PM, Stephen Paul King <step...@charter.net> wrote:
Hi All,Question: Why must Platonia exist?
How many ways are there to arrange 4 people in a line? If you think the answer 24 is true, regardless of any assumptions of axioms or set theory, etc. then truth has an objective, eternal, causeless existence of its own.
"The common mistake is to assume that truth has a nature of the kind that philosophers might find out about and develop theories of. For the deflationist, truth has no nature beyond what is captured in ordinary claims such as that ‘snow is white’ is true just in case snow is white. Philosophers looking for the nature of truth are bound to be frustrated, the deflationist says, because they are looking for something that isn't there."
Brent
It is worthy of notice that the sentence ‘I smell the scent of violets’ has the same content as the sentence ‘it is true that I smell the scent of violets’. So it seems, then, that nothing is added to the thought by my ascribing to it the property of truth.
--- Frege, 1918
These truths and falsehoods define or depend on the existence of other abstract objects, propositions, theoreticals, etc.
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Bruno Marchal
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1Z
On Feb 18, 5:43 am, Jason Resch <jasonre...@gmail.com> wrote:
>
> > Hi All,
>
> > Question: Why must Platonia exist?
>
> How many ways are there to arrange 4 people in a line? If you think the
> answer 24 is true, regardless of any assumptions of axioms or set theory,
> etc. then truth has an objective, eternal, causeless existence of its own.
> These truths and falsehoods define or depend on the existence of other
> abstract objects, propositions, theoreticals, etc.
any existence at all, and can be explained by mathematics being non-
referential
Platonism gets its force from noting the robustness and fixity of
mathematical truths, which are often described as "eternal". The
reasoning seems to be that if the truth of a statement is fixed, it
must be fixed by something external to itself. In other words,
mathematical truths msut be discovered, because if they were made they
could have be made differently, and so would not be fixed and eternal.
But there is no reason to think that these two metaphors
--"discovering" and "making"-- are the only options. Perhaps the modus
operandi of mathematics is unique; perhaps it combines the fixed
objectivity of discovering a physical fact about the external world
whilst being nonetheless an internal, non-empirical activity. The
Platonic thesis seems more obvious than it should because of an
ambiguity in the word "objective". Objective truths may be defined
ontologically as truths about real-world objects. Objective truths may
also be defined epistemically as truths that do not depend on the
whims or preferences of the speaker (unlike statements about the best
movie of flavour of ice-cream). Statements that are objective in the
ontological sense tend to be objective in the epistemic sense, but
that does not mean that all statements that are objective in the
epistemic sense need be objective in the ontological sense. They may
fail to depend on individual whims and preferences without depending
on anything external to the mind.
We are able to answer questions about mathematical objects in a clear
and unambiguous way, but that does not mean mathematical objects are
clear and unambiguous things. Being able to answer questions is
essentially epistemic. It doesn't imply any ontology in itself. The
epistemic fact that we can , in principle, answer questions about real
people may be explained by the existence and perceptual accessibility
of real people: but our ability to answer questions about mathematical
objects is explained by the existence of clear definitions and rules
doen't need to posit of existing immaterial numbers (plus some mode of
quasi-perceptual access to them).
by the
1Z
On Feb 18, 9:48 am, Bruno Marchal <marc...@ulb.ac.be> wrote:
> Hi,
>
> What do you mean by Platonia?
>
> The kind of Platonia in Tegmark or in Peter's (1Z) post does not make
> sense for mathematicians. Even if you are using a theory like Quine's
> NF, which allows mathematical universes, you still have no
> mathematical description of the whole mathematical reality. Tegmark is
> naïve about this.
>
> *Arithmetical* platonia can be said to exist, at least in the sense
> that you can prove it to exist in models of acceptable set theories,
> like ZF. It is just the structure (N, +, x). It is used in all papers
> in physics, math and logic, including Pratt ...
>
who uses arithmetic is a Platonist
benjayk
Bruno Marchal wrote:
>
> Hi,
>
> What do you mean by Platonia?
>
> The kind of Platonia in Tegmark or in Peter's (1Z) post does not make
> sense for mathematicians. Even if you are using a theory like Quine's
> NF, which allows mathematical universes, you still have no
> mathematical description of the whole mathematical reality.
Do you have to have a description of the whole mathematical reality to
assert it exists? Isn't it enough to say everything that we *could* describe
in mathematics exists "in platonia"?
Bruno Marchal wrote:
> Like in Plotinus, the ultimate being (arithmetical platonia) is not a
> being
> itself (nor is matter!).
Could you explain what you mean with that?
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Bruno Marchal
On 18 Feb 2011, at 12:53, 1Z wrote:
>
>
> On Feb 18, 9:48 am, Bruno Marchal <marc...@ulb.ac.be> wrote:
>> Hi,
>>
>> What do you mean by Platonia?
>>
>> The kind of Platonia in Tegmark or in Peter's (1Z) post does not make
>> sense for mathematicians. Even if you are using a theory like Quine's
>> NF, which allows mathematical universes, you still have no
>> mathematical description of the whole mathematical reality. Tegmark
>> is
>> naïve about this.
>>
>> *Arithmetical* platonia can be said to exist, at least in the sense
>> that you can prove it to exist in models of acceptable set theories,
>> like ZF. It is just the structure (N, +, x). It is used in all papers
>> in physics, math and logic, including Pratt ...
>>
> Used as a formalism. It is not the case that everyone
> who uses arithmetic is a Platonist
I did not say that, even with platonism restricted to arithmetical
realism, except for those using classical arithmetic or models of PA
in ZF, etc. To believe in (N,+,x) you need a stronger realism than
arithmetical realism, which says nothing about infinite sets.
And I am still waiting for you to explain me what *is* formalism
without using arithmetical realism or equivalent.
Let me answer to you. To be able to use a formalism, you need to
define what are the well-formed sentences; for this you need to define
them in the usual recursive way (or equivalent way) and this, together
with simple rules (like finding the first and second in a couple of
expressions) is ontologically as rich as sigma_1 realism.
Formalism, and all form of finitism which is a bit richer than
ultrafinitism, is entirely constructed (implicitly or explicitly) on
arithmetical realism. Gödel showed the deep "bisimulation" of
formalism and arithmetic.
With your use of the term Platonia, the theory I am working on, is
usually called finitism, and is usually considered as anti platonism.
This use is misleading because it is platonist, and even pythagorean,
in the sense of the neoplatonist.
I think you are confusing people on the genuine issues, here.
Bruno
Bruno Marchal
On 18 Feb 2011, at 17:13, benjayk wrote:
>
>
> Bruno Marchal wrote:
>>
>> Hi,
>>
>> What do you mean by Platonia?
>>
>> The kind of Platonia in Tegmark or in Peter's (1Z) post does not make
>> sense for mathematicians. Even if you are using a theory like Quine's
>> NF, which allows mathematical universes, you still have no
>> mathematical description of the whole mathematical reality.
> Do you have to have a description of the whole mathematical reality to
> assert it exists?
You need it to make sense of it. Mathematical attempts lead to either
inconsistent theories, or to a definition of a putative mathematician
(like with the theory of topos), which is very interesting but not
quite "platonic".
As a figure of speech Platonia can make sense, but it is doubtful in a
theoretical context, like when we search for a TOE.
> Isn't it enough to say everything that we *could* describe
> in mathematics exists "in platonia"?
The problem is that we can describe much more things than the one we
are able to show consistent, so if you allow what we could describe
you take too much. If you define Platonia by all consistent things,
you get something inconsistent due to paradox similar to Russell
paradox or St-Thomas paradox with omniscience and omnipotence.
And then when you try to convey something which is counter-intuitive
and against the current main paradigm, like your poor servitor, you
have to base things on what the most agree (but this is not an
argument, just a methodological remark).
>
>
> Bruno Marchal wrote:
>> Like in Plotinus, the ultimate being (arithmetical platonia) is
>> not a
>> being
>> itself (nor is matter!).
> Could you explain what you mean with that?
Platonia, the platonia of Plato, is the Noûs, also called the
Intelligible Realm, or the World of Ideas, with the idea that Ideas
are more true/real than any of their terrestrial approximation/
incarnation. For example the perfect circle is in Platonia, together
with PI, but any natural circle is a gross and "less real" imitation
of the "eternal ideas". What we see is conceived as being only the
shadow of that "intelligible reality".
But in the Parmenides, Plato understood that the Intelligible Realm
has to come from something completely unified, and Plotinus attributes
his notion of ONE to the Parmenides of Plato. In neoplatonism the ONE,
which is really without name, nor description of any kind, truly
ineffable, is the principle from which both the Intelligible Realm
will "emanate" 'followed' by the "Universal Soul". The Universal Soul
is a sort of product of both the ONE (the soul keeps its umbilical
cord uncut with "GOD" (the ONE), and the Intelligible Realm, also
called the Divine Intellect. That are the three primary hypostases of
Plotinus: the One, the Divine Intellect, and the Universal Soul. They
correspond more or less to the origin, the reason, and the experience,
but are presented as three Gods, in the usual greek manner. The One
has many things in common with the "God" of the monotheist religion,
and the Universal Soul has many things in common with the Inner God of
the mystic and many schools of Eastern religions.
There is a inevitable tension between the Divine Intellect and the
Soul, and eventually the Soul will fall, and that is how Matter, a
quasi synonymous of Evil, rises. The notion of existence or being is
defined by the Divine Intellect. What exist is what the Divine
Intellect can talk about, and it cannot talk about the One, because of
its absolute ineffability and inaccessibility, and it cannot talk
about Matter, which cannot belong to the Intelligible Realm, because
it is so much unintelligible that even God (the one) has no control on
it. This makes the One, and Matter outside 'existence' or being. They
are the antipode of the intelligible existing things. Intelligible
by ... the divine intellect, note, which has to be distinguished from
"Man", i.e. the terrestrial intellect, or discursive reasoner, which
is the one who dies and pays taxes, and try to understand.
Now, it has been shown that if you give to a universal machine some
provability and inductive inference abilities (easy to do), and ask
such a machine to introspect itself, the machine is able to
distinguish truth, belief (proof) and knowledge (proof of truth). She
can know that a truth encompassing herself is not nameable or
describable. She can distinguish the terrestrial believer from the
divine believer, and even guess a part of the "divine discourse", with
"divine" meaning "true" on that level where truth is not definable.
She can understand and feel (accepting some definition already in
Plato and Plotinus) the inevitable tension between the "Divine
Intellect" and the "Universal Soul", she can understand (believe,
proof) that the Universal Soul (which actually is also unnameable) has
already "a foot in matter', and that the Soul will fall (by connecting
inappropriately the terrestrial intellect with the divine intellect),
and the soul glues itself in that part of the internal border of
reality where God loose control. That generates a logic which should
correspond to the logic of the observable.
Technically, albeit roughly, with p arithmetical proposition, you have
the following arithmetical interpretation of Plotinus' three primary
hypostases, which I put in a lozenge:
The
ONE = arithmetical truth (p)
The terrestrial believer = Gödel's provability (Bp, logic G) ----------
the divine Intellect (the truth on the Gödel's provability) (Bp, but a
different logic (G*)
The
Universal Soul (Bp & p); logic = S4Grz
That represent the happy harmonic state "before the fall". The fall
comes from the fact that although G* proves that Bp is equivalent with
Bp & ~B~p, G cannot prove that, but the one who want to bet on a
reality has to follow the Bp & Dp logic (D = ~B~) and this gives the
two Matter of Plotinus, which both inherit from the G/G* splitting
(due to the disticntion between proof and truth, that is due to
incompleteness).
the terrestrial intelligible matter (Bp & Dp, controlled by G)
-----------the divine intelligible matter (Bp & Dp,controlled by G*)
the terrestrial sensible matter (Bp & Dp & p, controlled by
G)----------the divine intelligible matter (Bp & Dp & p, controlled by
G*)
You can see a lozenge above a square. It is good memo for the 8
variants of provability (arithmetical hypostases). Again:
p
Bp------- Bp
Bp & p
Bp & Dp----------- Bp & Dp
Bp & Dp & p------Bp & Dp & p
At the left you have the terrestrial (effective) realm. At the right
you have the divine (true) realm. The lozenge gives the three primary
hypostases on the right. And the poor terrestrial man on the left.
Magically, the Universal Soul belongs to both the terrestrial and
divine realm, but splits in two (terrestrial/divine) in the fall. This
is not easy to prove. The first person pov (the "soul") confuses
naturally provability/knowability and truth, like an intuitionist (and
this can be made very precise). The lozenge is the harmonic state of
the universal machine, and the square will glue the machine in the
realm of the consistent (Dp) extensions (histories). Note that 5
variants of provability lead to 8 "hypostases" dues to the G/G*
splitting of three of them.
Then, you can model computationalism, or interview the machine on
comp, by restricting the arithmetical interpretation of p to the
Sigma_1 sentences, which are the arithmetical equivalent of the
"border of the universal dovetailer", and this gives you 8 more
refined logics. By the UDA argument, The universal Soul, the divine
intelligible matter, and the the divine intelligible matter (with
some other variants of them) can provide the logic given by the
measure one for the observation and sensation. There, we get the truth
of DDf (the possibility of the possibility of the false), which is
similar to the early Lewis modal logics. The white rabbits seems to
disappear but remain very close, perhaps.
Gödel's theorem, which originates that "Bp" logic (G), is often used
as an argument that we are not machine (Lucas, Penrose), but what
people rarely take into account is that machines can prove their own
incompleteness, making the left part of the diagram provable by the
machine, and the right part inductively inferable, 'bettable',
'hopable', 'fearable', etc. (doesn't look like english, but you see
the point).
This gives a TOE, (necessitated by Comp + the classical theory of
knowledge), which is ontologically just (sigma_1) arithmetical truth
(which is really weaker than most formalism), and which admits as
internal epistemology provability and its variants. Each variants is a
different view of the same unique tiny arithmetical reality. But those
views from inside imposes rich topologies and measures, but also
complex mathematical problems.
Basically, for the ontology, you need only classical logic + the
axioms of addition and multiplication
x+0 = x
x+s(y) = s(x+y)
x*0 = 0
x*s(y) = (x*y) + x
In that system you can define the Löbian Bp and variants (a very long
and tedious fact shown by Gödel & Co), which "believe" in more things
already (the axioms of addition and multiplication + the axioms of
induction, which makes them Löbian and obeying, like all their sound
extensions to the 8 hypostases).
There is a subtle tour de force here, if you indulge me to say, which
consists to use Tarski notion of truth (p) in the place of the
impossible (by a theorem of Tarski) task to define truth in the
language of the machine, by some predicate V('p'). The same for
knowledge and sensibility. Quanta and qualia should appear (and does
appear a little bit already) at the extreme bottom right of the
diagram. All this is a sum up of "AUDA" the arithmetical UDA. It is
not needed for understanding UDA (physics is arithmetic seen from
inside). But UDA is useful to motivate AUDA and to relate it to the
mind-body problem.
Any universal programming system can be used instead of numbers. With
the combinators, the ontology is given by an even shorter theory: the
laws of elimination and duplication:
Kxy = x
Sxyz = xz(yz)
I mean, the choice of the initial universal system is free. You can
take a quantum computer, but this is cheating with the goal of solving
the mind body problem, which by UDA needs a derivation of the local
universal observable structure. This one has to be justified properly
to get both the quanta and the qualia, avoiding the elimination of the
person and consciousness.
The god of Plotinus is not omniscient, nor omnipotent. "He" is
overwhelmed by its first emanation, the Divine Intellect, and then
both the ONE and the Divine Intellect are overwhelmed by the Universal
Soul, which truly put the mess (matter, notably) in the (arithmetical)
Platonia.
Like in Pratt's Chu transform (cf Stephen), or like in Galois
connections, Plotinus dynamics go in two opposite directions:
emanation and conversion.
- God (the One) by a sort of excess of generosity let the Divine
Intellect emanates from him, and then let the Universal Soul emanate,
which eventually generates nature up to matter (where God lose control
and man needs a "bastard calculus" on the non determination)). That's
the emanation part, from the One to the soul and matter.
- The terrestrial soul then tries hard to leave matter, and eventually
succeeds in reaching the Divine Intellect (by math, music, astronomy,
notably), and eventually recovers The inner God and the ONE phase.
That's the conversion path, from Matter and Soul to the One.
The two processes correspond to the same truth, again seen from
different views (the One and the Soul)
Bruno
benjayk
Bruno Marchal wrote:
>
>> Isn't it enough to say everything that we *could* describe
>> in mathematics exists "in platonia"?
>
> The problem is that we can describe much more things than the one we
> are able to show consistent, so if you allow what we could describe
> you take too much. If you define Platonia by all consistent things,
> you get something inconsistent due to paradox similar to Russell
> paradox or St-Thomas paradox with omniscience and omnipotence.
Why can inconsistent descriptions not refer to an existing object?
The easy way is to assume inconsistent descriptions are merely an arbitrary
combination of symbols that fail to describe something in particular and
thus have only the "content" that every utterance has by virtue of being
uttered: There exists ... (something).
So they don't add anything to platonia because they merely assert the
existence of existence, which leaves platonia as described by consistent
theories.
I think the paradox is a linguistic paradox and it poses really no problem.
Ultimately all descriptions refer to an existing object, but some are too
broad or "explosive" or vague to be of any (formal) use.
I may describe a system that is equal to standard arithmetics but also has
1=2 as an axiom. This makes it useless practically (or so I guess...) but it
may still be interpreted in a way that it makes sense. 1=2 may mean that
there is 1 object that is 2 two objects, so it simply asserts the existence
of the one number "two". 3=7 may mean that there are 3 objects that are 7
objects which might be interpreted as aserting the existence of (for
example) 7*1, 7*2 and 7*3.
I don't think the omnipotence paradox is problematic, also. It simply shows
that omnipotence is nothing that can be properly conceived of using
classical logic. We may assume omnipotence and non-omnipotence are
compatible; omnipotence encompasses non-omnipotence and is on some level
equivalent to it.
For example: The omnipotent God can make a stone that is too heavy for him
to lift, because God can manifest as a person (that's still God, but an
non-omnipotent omnipotent one) that cannot lift the stone.
Bruno Marchal wrote:
>
>>
>>
>> Bruno Marchal wrote:
>>> Like in Plotinus, the ultimate being (arithmetical platonia) is
>>> not a
>>> being
>>> itself (nor is matter!).
>> Could you explain what you mean with that?
>
> Platonia, the platonia of Plato, is the Noûs, [...]
Many thanks for your effort to explain this to me. :)
Honestly your non-technical explanation is a bit vague for me and your
technical explanation is simply way to technical for me. Some things seem to
make sense, but overall it's still quite mysterious to me.
Frankly I am a bit afraid to ask questions concerning your technical
explanation, because I'm not sure if you can answer them succintly or
whether I understand your explanations and I don't want you to waste your
time explaining it to me in great detail and then still be not much more
smarter.
Maybe I will try searching some terms that I don't understand (or that I
don't understand the context of) on the list or in the web. Or perhaps it
well help when I learn logic at the university, though I guess it will be
not so much in depth.
A have a few questions regarding the non-technical part of explanation,
though:
What does it mean that the soul falls, falls from what?
Why is matter evil? Because it is not perfect as platonia is? As it provides
a field were truth can manifest itself, it seems like this is a good thing
for the soul to learn to know itself, even if some aspect of matter are bad.
The tension between the divine intellect and the soul is the gap between
truth and believability, right?
How can the One / matter be outside of existence? I have no clue what this
could mean. Is the "outside" of existence not existence as well?
Is the one conscious? What you write seems to imply it is (eg "the ONE and
the Divine Intellect are overwhelmed by the Universal Soul,"), but I thought
only the universal soul can experience?
Do you mean it literally that the soul leaves matter at some point? Why does
the one let matter eminate at all then?
--
View this message in context: http://old.nabble.com/Platonia-tp30955253p30968384.html
Brent Meeker
>
> Bruno Marchal wrote:
>
>>
>>> Isn't it enough to say everything that we *could* describe
>>> in mathematics exists "in platonia"?
>>>
>> The problem is that we can describe much more things than the one we
>> are able to show consistent, so if you allow what we could describe
>> you take too much. If you define Platonia by all consistent things,
>> you get something inconsistent due to paradox similar to Russell
>> paradox or St-Thomas paradox with omniscience and omnipotence.
>>
> Why can inconsistent descriptions not refer to an existing object?
>
Because an inconsistent description implies everything, whether the
object described exists or not. From "Sherlock Holmes is a detective
and is not a detective." anything at all follows.
> The easy way is to assume inconsistent descriptions are merely an arbitrary
> combination of symbols that fail to describe something in particular and
> thus have only the "content" that every utterance has by virtue of being
> uttered: There exists ... (something).
>
But we need utterances that *don't* entail existence. So we can say
things like, "Sherlock Holmes lived at 10 Baker Street" are true, even
though Sherlock Holmes never existed.
> So they don't add anything to platonia because they merely assert the
> existence of existence, which leaves platonia as described by consistent
> theories.
>
> I think the paradox is a linguistic paradox and it poses really no problem.
> Ultimately all descriptions refer to an existing object, but some are too
> broad or "explosive" or vague to be of any (formal) use.
>
> I may describe a system that is equal to standard arithmetics but also has
> 1=2 as an axiom. This makes it useless practically (or so I guess...) but it
> may still be interpreted in a way that it makes sense. 1=2 may mean that
> there is 1 object that is 2 two objects, so it simply asserts the existence
> of the one number "two". 3=7 may mean that there are 3 objects that are 7
> objects which might be interpreted as aserting the existence of (for
> example) 7*1, 7*2 and 7*3.
>
The problem is not that there is no possible true interpretation of 1=2;
the problem is that in standard logic a falsity allows you to prove
anything.
Brent
benjayk
Brent Meeker-2 wrote:
>
> On 2/19/2011 3:39 PM, benjayk wrote:
>>
>> Bruno Marchal wrote:
>>
>>>
>>>> Isn't it enough to say everything that we *could* describe
>>>> in mathematics exists "in platonia"?
>>>>
>>> The problem is that we can describe much more things than the one we
>>> are able to show consistent, so if you allow what we could describe
>>> you take too much. If you define Platonia by all consistent things,
>>> you get something inconsistent due to paradox similar to Russell
>>> paradox or St-Thomas paradox with omniscience and omnipotence.
>>>
>> Why can inconsistent descriptions not refer to an existing object?
>>
>
> Because an inconsistent description implies everything, whether the
> object described exists or not. From "Sherlock Holmes is a detective
> and is not a detective." anything at all follows.
I think it is perfectly fine when something implies everything. For me it
makes very much sense to think of everything as everything existing.
The distinction something existant / something non-existant is a relative
one, in the absolute sense existence is all there is - and it includes
relative non-existence (for example Santa Claus exists, but has relative
non-existence in the set of things that manifests in a consistent and
predictable way to many observers).
Aso, it emerges naturally from seemingly consistent logic that everything
exists (see Curry's paradox).
Brent Meeker-2 wrote:
>
>> The easy way is to assume inconsistent descriptions are merely an
>> arbitrary
>> combination of symbols that fail to describe something in particular and
>> thus have only the "content" that every utterance has by virtue of being
>> uttered: There exists ... (something).
>>
>
> But we need utterances that *don't* entail existence.
If we find something that doesn't entail existence, it still entails
existence because every utterance is proof that existence IS.
We need only utterances that entail relative non-existence or that don't
entail existence in a particular way in a particular context.
Brent Meeker-2 wrote:
>
> So we can say
> things like, "Sherlock Holmes lived at 10 Baker Street" are true, even
> though Sherlock Holmes never existed.
Whether Sherlock Holmes existed is not a trivial question. He didn't exist
like me and you, but he did exist as an idea.
Brent Meeker-2 wrote:
>
>> So they don't add anything to platonia because they merely assert the
>> existence of existence, which leaves platonia as described by consistent
>> theories.
>>
>> I think the paradox is a linguistic paradox and it poses really no
>> problem.
>> Ultimately all descriptions refer to an existing object, but some are too
>> broad or "explosive" or vague to be of any (formal) use.
>>
>> I may describe a system that is equal to standard arithmetics but also
>> has
>> 1=2 as an axiom. This makes it useless practically (or so I guess...) but
>> it
>> may still be interpreted in a way that it makes sense. 1=2 may mean that
>> there is 1 object that is 2 two objects, so it simply asserts the
>> existence
>> of the one number "two". 3=7 may mean that there are 3 objects that are 7
>> objects which might be interpreted as aserting the existence of (for
>> example) 7*1, 7*2 and 7*3.
>>
>
> The problem is not that there is no possible true interpretation of 1=2;
> the problem is that in standard logic a falsity allows you to prove
> anything.
Yes, so we can prove anything. This simply begs the question what the
anything is. All sentences we derive from the inconsistency would mean the
same (even though we don't know what exactly it is).
We could just write "1=1" instead and we would have expressed the same, but
in a way that is easier to make sense of.
This is not problematic, it only makes the proofs in the inconsisten system
worthless (at least in a formal context were we assume classical logic).
--
View this message in context: http://old.nabble.com/Platonia-tp30955253p30970304.html
Bruno Marchal
But what is two if 2 = 1. I can no more have clue of what you mean.
Now, just recall that "Platonia" is based on classical logic where the
falsity f, or 0 = 1, entails all proposition. So if you insist to say
that 0 = 1, I will soon prove that you owe to me A billions of
dollars, and that you should prepare the check.
> 3=7 may mean that there are 3 objects that are 7
> objects which might be interpreted as aserting the existence of (for
> example) 7*1, 7*2 and 7*3.
Logicians and mathematicians are more simple minded than that, and it
does not always help to be understood.
If you allow circles with edges, and triangles with four sides in
Platonia, we will loose any hope of understanding each other.
>
> I don't think the omnipotence paradox is problematic, also. It
> simply shows
> that omnipotence is nothing that can be properly conceived of using
> classical logic. We may assume omnipotence and non-omnipotence are
> compatible; omnipotence encompasses non-omnipotence and is on some
> level
> equivalent to it.
> For example: The omnipotent God can make a stone that is too heavy
> for him
> to lift, because God can manifest as a person (that's still God, but
> an
> non-omnipotent omnipotent one) that cannot lift the stone.
That makes the term "omnipotent" trivial. You can quickly be lead to
give any meaning to any sentence.
Did you confess that you killed your wife? yes, sure, but by "I killed
my wife" I was meaning that "I love eggs on a plate".
This will not help when discussing fundamental issues.
>
>
> Bruno Marchal wrote:
>>
>>>
>>>
>>> Bruno Marchal wrote:
>>>> Like in Plotinus, the ultimate being (arithmetical platonia) is
>>>> not a
>>>> being
>>>> itself (nor is matter!).
>>> Could you explain what you mean with that?
>>
>> Platonia, the platonia of Plato, is the Noûs, [...]
> Many thanks for your effort to explain this to me. :)
>
> Honestly your non-technical explanation is a bit vague for me and your
> technical explanation is simply way to technical for me. Some things
> seem to
> make sense, but overall it's still quite mysterious to me.
> Frankly I am a bit afraid to ask questions concerning your technical
> explanation, because I'm not sure if you can answer them succintly or
> whether I understand your explanations and I don't want you to waste
> your
> time explaining it to me in great detail and then still be not much
> more
> smarter.
There are good book on self)-reference, but they need some familiarity
in mathematical logic. An excellent book on Logic is the book by
Elliot Mendelson, another one is by Boolos, Jeffrey and Burgess.
> Maybe I will try searching some terms that I don't understand (or
> that I
> don't understand the context of) on the list or in the web.
You will find the best and the worst. Podnieks' page is not too bad.
http://www.ltn.lv/~podnieks/
> Or perhaps it
> well help when I learn logic at the university, though I guess it
> will be
> not so much in depth.
It depends on many things.
>
> A have a few questions regarding the non-technical part of
> explanation,
> though:
>
> What does it mean that the soul falls, falls from what?
From Heaven. From Platonia. From the harmonic static state of the
universal consciousness to the state with death and taxes.
It is hard for me to explain the sense of Plotinus, which itself is
discussed by many scholars, and in different terms according to their
own inclinations. But I did provide an arithmetical translation, and
there I can be more precise. Eventually in that translation all is
reduced to number relations. Of the theological statement will
correspond to non recursive (and highly so) arithmetical statements,
or complex structured set of arithmetical statements.
>
> Why is matter evil?
Platonist doesn' like matter. It is an illusion which can hurt you.
> Because it is not perfect as platonia is?
Platonia was inspired by the idea that mathematics described indeed
perfect object, and that imperfection is part of the rudeness of
Earth. Today we know that Platonia itself is not perfect, but the
neoplatonist comes to intuit this too.
> As it provides
> a field were truth can manifest itself, it seems like this is a good
> thing
> for the soul to learn to know itself, even if some aspect of matter
> are bad.
I don't take seriously the Platonist demonization of matter, but I can
relate a bit to it too.
>
> The tension between the divine intellect and the soul is the gap
> between
> truth and believability, right?
More precisely between Bp and Bp & p, that is between belief and
knowledge.
The gap between truth and believability is the gap between me and
'god', and is mainly incompleteness.
>
> How can the One / matter be outside of existence? I have no clue
> what this
> could mean. Is the "outside" of existence not existence as well?
It is a bit like in most set theories, the set of all sets is not a
set. For example usually the set of all subsets of a set is bigger
than the set itself, and if the collection of all sets is a set, then
the set of the subsets of the set of all sets is bigger than the set
of all sets.
God cannot create itself, in most conception of Gods. Again, with "big
things" you can quickly be led to contradiction or triviality. The UD
and UD* are big things which remains non trivial. That is rare in math.
>
> Is the one conscious? What you write seems to imply it is (eg "the
> ONE and
> the Divine Intellect are overwhelmed by the Universal Soul,"), but I
> thought
> only the universal soul can experience?
I thought that too, but my mind evolves on this. Plotinus is himself
full of doubts on that question. I really don't know. I would still
say that the ONE is not a person, but I am less sure. Technically, any
set of sentences defined a canonical believer/person, which is the one
believing exactly those sentences. And what is sure is that it is not
a Löbian person, so what is is? There is a need of a 'truth theory" or
meta-truth-theory, but none in the literature, a part of Tarski
theory, satisfies me, in the comp setting.
>
> Do you mean it literally that the soul leaves matter at some point?
Matter does not exist, so soul never leaves matter. Souls build matter
when they fall (in Plotinus) by a curious form of contemplation. It is
already of form of extrapolation on the purely indeterminate. Both God
and Matter are defined by negation from intelligible existing things,
like numbers and circles, ...
> Why does
> the one let matter eminate at all then?
Matter is defined by what God cannot control. It is the border of God.
God is not so much powerful in Neoplatonism. The idea that God is
omnipotent has been added by the Christians, I think. God is good,
sure (in Plato, Plotinus), but, well, he does its possible but he is
limited, notably by logic and mathematics. Matter is unavoidable when
souls get free. This provides theological opening on free-will, which
will be taken seriously by Christians, but made a bit contradictory by
God's omnipotence. The free-will problem is really a problem for the
Christians, and probably even more for catholic, with that respect.
But like Grim, I think that 'omnipotence' is a contradictory concept.
Bruno
Bruno Marchal
Curry "paradox" was a real contradiction, Curry put his theory in the
trash the day he sees the contradiction, and begun some other less
ambitious theory (the illetive theory of combinators).
>
>
> Brent Meeker-2 wrote:
>>
>>> The easy way is to assume inconsistent descriptions are merely an
>>> arbitrary
>>> combination of symbols that fail to describe something in
>>> particular and
>>> thus have only the "content" that every utterance has by virtue of
>>> being
>>> uttered: There exists ... (something).
>>>
>>
>> But we need utterances that *don't* entail existence.
>
> If we find something that doesn't entail existence, it still entails
> existence because every utterance is proof that existence IS.
> We need only utterances that entail relative non-existence or that
> don't
> entail existence in a particular way in a particular context.
You need some non relative absolute base to define relative existence.
>
>
> Brent Meeker-2 wrote:
>>
>> So we can say
>> things like, "Sherlock Holmes lived at 10 Baker Street" are true,
>> even
>> though Sherlock Holmes never existed.
> Whether Sherlock Holmes existed is not a trivial question. He didn't
> exist
> like me and you, but he did exist as an idea.
Even if you met *a* Sherlock Holmes in Platonia, you have no cirteria
to say it is the usual fictive person created by Conan Doyle, because,
in Platonia, he is not created by Conan Doyle, ...
And it would make Platonia worthless. The "real", genuine, Platonia is
already close to be worthless due to the consistency of inconsistency
for machine. This already put quite a mess in Platonia. By allowing
complete contradiction, you make it a trivial object.
Bruno
benjayk
Two is the successor of one. You obviously now what that means.
So keep this meaning and reconcile it with 2=1.
You might get the meaning "two is the one (number) that is the succesor of
one". Or "one (number) is the successor of two". In essence it expresses
2*...=1*... or 2*X=1*Y.
And it might mean "the succesor of one number is the succesor of the
succesor of one number". or 2+...=1+... or 2+X=1+Y.
The reason that it is not a good idea to define 2=1 is because it doesn't
express something that can't be expressed in standard arithmetic, but it
makes everything much more confusing and redundant. In mathematics we want
to be precise as possible so it's good rule to always have to specifiy which
quantity we talk about, so that we avoid talking about something - that is
one thing - that is something - that is two things - but rather talk about
one thing and two things directly; because it is already clear that two
things are a thing.
Bruno Marchal wrote:
>
> Now, just recall that "Platonia" is based on classical logic where the
> falsity f, or 0 = 1, entails all proposition. So if you insist to say
> that 0 = 1, I will soon prove that you owe to me A billions of
> dollars, and that you should prepare the check.
You could prove that, but what is really meant by that is another question.
It may simply mean "I want to play a joke on you".
All statements are open to interpretation, I don't think we can avoid that
entirely. We are ususally more interested in the statements that are less
vague, but vague or crazy statements are still valid on some level (even
though often on an very boring, because trivial, level; like saying "S afs
fdsLfs", which is just expressing that something exists).
Bruno Marchal wrote:
>
>> 3=7 may mean that there are 3 objects that are 7
>> objects which might be interpreted as aserting the existence of (for
>> example) 7*1, 7*2 and 7*3.
>
> Logicians and mathematicians are more simple minded than that, and it
> does not always help to be understood.
> If you allow circles with edges, and triangles with four sides in
> Platonia, we will loose any hope of understanding each other.
I don't think we have "disallow" circles with edges, and triangles with four
sides; it is enough if we keep in mind that it is useful to use words in a
sense that is commonly understood.
I think it is a bit authoritarian to disallow some statements as truth.
I feel it is better to think of truth as everything describable or
experiencable; and then we differ between truth as non-falsehood and the
trivial truth of falsehoods.
It avoids that we have to fight wars between truth and falsehood. Truth
swallows everything up. If somebody says something ridiculous like "All non
christian people go to hell.", we acknowledge that expresses some truth
about what he feels and believes, instead of only seeing that what he says
is false.
I believe the only way we can learn to understand each other is if we
acknowledge the truth in every utterance.
Bruno Marchal wrote:
>
>>
>> I don't think the omnipotence paradox is problematic, also. It
>> simply shows
>> that omnipotence is nothing that can be properly conceived of using
>> classical logic. We may assume omnipotence and non-omnipotence are
>> compatible; omnipotence encompasses non-omnipotence and is on some
>> level
>> equivalent to it.
>> For example: The omnipotent God can make a stone that is too heavy
>> for him
>> to lift, because God can manifest as a person (that's still God, but
>> an
>> non-omnipotent omnipotent one) that cannot lift the stone.
>
> That makes the term "omnipotent" trivial. You can quickly be lead to
> give any meaning to any sentence.
Well I think this makes sense on some level. Language is symbols that are
interpreted. There is no absolute rule how to interpret them, so we *can*
interpret everything in it (but we don't have to!).
In most cases it is most useful to interpret some quite specific meaning
into a sentence (if you don't want to act madly), but as we use more broad
and vague terms there are more and more ways to interpret what is said.
So in this case omnipotency is trivial. It might just be open for too many
interpretations to say anything really useful.
Bruno Marchal wrote:
>
> Did you confess that you killed your wife? yes, sure, but by "I killed
> my wife" I was meaning that "I love eggs on a plate".
> This will not help when discussing fundamental issues.
Right, but I am not saying we *should* talk in a way that is impossible for
others to understand. We should talk as clearly as possible. For this reason
saying 1=2 or "I killed my wife" while meaning that "I love eggs on a plate"
is mostly not a good idea.
But that it is impractical to speak in a in an incomprehensible way can be
reconciled with that it still makes sense on some level.
Bruno Marchal wrote:
>
>>
>>
>> Bruno Marchal wrote:
>>>
>>>>
>>>>
>>>> Bruno Marchal wrote:
>>>>> Like in Plotinus, the ultimate being (arithmetical platonia) is
>>>>> not a
>>>>> being
>>>>> itself (nor is matter!).
>>>> Could you explain what you mean with that?
>>>
>>> Platonia, the platonia of Plato, is the Noûs, [...]
>> Many thanks for your effort to explain this to me. :)
>>
>> Honestly your non-technical explanation is a bit vague for me and your
>> technical explanation is simply way to technical for me. Some things
>> seem to
>> make sense, but overall it's still quite mysterious to me.
>> Frankly I am a bit afraid to ask questions concerning your technical
>> explanation, because I'm not sure if you can answer them succintly or
>> whether I understand your explanations and I don't want you to waste
>> your
>> time explaining it to me in great detail and then still be not much
>> more
>> smarter.
>
> There are good book on self)-reference, but they need some familiarity
> in mathematical logic. An excellent book on Logic is the book by
> Elliot Mendelson, another one is by Boolos, Jeffrey and Burgess.
Thanks. :) I will consider buying one of them.
Bruno Marchal wrote:
>
>> Maybe I will try searching some terms that I don't understand (or
>> that I
>> don't understand the context of) on the list or in the web.
>
> You will find the best and the worst. Podnieks' page is not too bad.
> http://www.ltn.lv/~podnieks/
It looks interesting, though a bit disorganized.
Bruno Marchal wrote:
>
>>
>> A have a few questions regarding the non-technical part of
>> explanation,
>> though:
>>
>> What does it mean that the soul falls, falls from what?
>
> From Heaven. From Platonia. From the harmonic static state of the
> universal consciousness to the state with death and taxes.
How come that we don't have memories of falling from heaven?
Bruno Marchal wrote:
>
>>
>> How can the One / matter be outside of existence? I have no clue
>> what this
>> could mean. Is the "outside" of existence not existence as well?
>
> It is a bit like in most set theories, the set of all sets is not a
> set. For example usually the set of all subsets of a set is bigger
> than the set itself, and if the collection of all sets is a set, then
> the set of the subsets of the set of all sets is bigger than the set
> of all sets.
This makes sense, since there might be something outside of sets.
But existence seems to be all-encompassing. What would the One be, if not
existent? It isn't non-existent, surely?
Bruno Marchal wrote:
>
> God cannot create itself, in most conception of Gods.
Because he already is himself, right?
Bruno Marchal wrote:
>
>>
>> Is the one conscious? What you write seems to imply it is (eg "the
>> ONE and
>> the Divine Intellect are overwhelmed by the Universal Soul,"), but I
>> thought
>> only the universal soul can experience?
>
> I thought that too, but my mind evolves on this. Plotinus is himself
> full of doubts on that question. I really don't know. I would still
> say that the ONE is not a person, but I am less sure. Technically, any
> set of sentences defined a canonical believer/person, which is the one
> believing exactly those sentences. And what is sure is that it is not
> a Löbian person, so what is is? There is a need of a 'truth theory" or
> meta-truth-theory, but none in the literature, a part of Tarski
> theory, satisfies me, in the comp setting.
Okay, I probably imagined that there is clearer picture of the ONE or the
universal soul is.
Bruno Marchal wrote:
>
>> Why does
>> the one let matter eminate at all then?
>
> Matter is defined by what God cannot control. It is the border of God.
> God is not so much powerful in Neoplatonism. The idea that God is
> omnipotent has been added by the Christians, I think. God is good,
> sure (in Plato, Plotinus), but, well, he does its possible but he is
> limited, notably by logic and mathematics.
Does god ever had control? Control seems only possible if we can make sense
of the future or of consequences, but since God is the source of both future
and consequences, he's more like bomb.
God is limited by logic and mathematics? This seems strange since the ONE is
that which everything emanates of, which seems to mean God is the source of
all limitations - and how could this be if God is already limited?
--
View this message in context: http://old.nabble.com/Platonia-tp30955253p30976699.html
benjayk
OK, but this doesn't change the rest of the rest of the argument.
Also, the Curry paradox is still there in natural language, which seems
capable of making useful statements even though the Curry paradox entails
the truth of every statement in natural language.
Bruno Marchal wrote:
>
>>
>>
>> Brent Meeker-2 wrote:
>>>
>>>> The easy way is to assume inconsistent descriptions are merely an
>>>> arbitrary
>>>> combination of symbols that fail to describe something in
>>>> particular and
>>>> thus have only the "content" that every utterance has by virtue of
>>>> being
>>>> uttered: There exists ... (something).
>>>>
>>>
>>> But we need utterances that *don't* entail existence.
>>
>> If we find something that doesn't entail existence, it still entails
>> existence because every utterance is proof that existence IS.
>> We need only utterances that entail relative non-existence or that
>> don't
>> entail existence in a particular way in a particular context.
>
> You need some non relative absolute base to define relative existence.
The absolute base is the undeniable reality of there being experience.
Bruno Marchal wrote:
>
>>
>>
>> Brent Meeker-2 wrote:
>>>
>>> So we can say
>>> things like, "Sherlock Holmes lived at 10 Baker Street" are true,
>>> even
>>> though Sherlock Holmes never existed.
>> Whether Sherlock Holmes existed is not a trivial question. He didn't
>> exist
>> like me and you, but he did exist as an idea.
>
>
> Even if you met *a* Sherlock Holmes in Platonia, you have no cirteria
> to say it is the usual fictive person created by Conan Doyle, because,
> in Platonia, he is not created by Conan Doyle, ...
In Platonia he is not created by Conan Doyle, which makes sense, given the
possible that other people use the same fictional character, so he is
essentially discovered, not created.
But I don't know what you want to imply with that.
Why? When we contradict ourselves we may simply interpret this as a
expression of the trivial truth of existence. This doesn't change Plantonia
at all, because it exists either way.
And why is inconsistency allowed for machine, but disallowed for other
objects?
--
View this message in context: http://old.nabble.com/Platonia-tp30955253p30978461.html
Bruno Marchal
OK.
>
>
> Bruno Marchal wrote:
>>
>> Now, just recall that "Platonia" is based on classical logic where
>> the
>> falsity f, or 0 = 1, entails all proposition. So if you insist to say
>> that 0 = 1, I will soon prove that you owe to me A billions of
>> dollars, and that you should prepare the check.
> You could prove that, but what is really meant by that is another
> question.
> It may simply mean "I want to play a joke on you".
>
> All statements are open to interpretation, I don't think we can
> avoid that
> entirely. We are ususally more interested in the statements that are
> less
> vague, but vague or crazy statements are still valid on some level
> (even
> though often on an very boring, because trivial, level; like saying
> "S afs
> fdsLfs", which is just expressing that something exists).
We formalize things, or make them as formal as possible, when we
search where we disagree, or when we want to find a mistake. The idea
of making things formal, like in first order logic, is to be able to
follow a derivation or an argument in a way which does not depend on
any interpretation, other than the procedural inference rule.
>
>
> Bruno Marchal wrote:
>>
>>> 3=7 may mean that there are 3 objects that are 7
>>> objects which might be interpreted as aserting the existence of (for
>>> example) 7*1, 7*2 and 7*3.
>>
>> Logicians and mathematicians are more simple minded than that, and it
>> does not always help to be understood.
>> If you allow circles with edges, and triangles with four sides in
>> Platonia, we will loose any hope of understanding each other.
> I don't think we have "disallow" circles with edges, and triangles
> with four
> sides; it is enough if we keep in mind that it is useful to use
> words in a
> sense that is commonly understood.
That is why I limit myself for the TOE to natural numbers and their
addition and multiplication.
The reason is that it is enough, by comp, and nobody (except perhaps
some philosophers) have any problem with that.
>
> I think it is a bit authoritarian to disallow some statements as
> truth.
>
> I feel it is better to think of truth as everything describable or
> experiencable; and then we differ between truth as non-falsehood and
> the
> trivial truth of falsehoods.
> It avoids that we have to fight wars between truth and falsehood.
> Truth
> swallows everything up. If somebody says something ridiculous like
> "All non
> christian people go to hell.", we acknowledge that expresses some
> truth
> about what he feels and believes, instead of only seeing that what
> he says
> is false.
This is a diplomatic error. Doing that will end up with everyone doing
war to you. It is far too much "politically correct'.
Of course, when someone genuinely says that all "non christian people
go to hell", there are many possible "truth" behind the statement,
like "F..ck the atheists", "F..ck the agnostics", "I hate you", "you
have to obey to what I say", "You don't belong to my club", etc.
On the contrary, when you want to make a point, especially a new one,
it is far better to respect the truth of your opponents, but then you
have to distill what you and your opponent agree on. In science this
works very well in theory (in practice we have often the obligation to
wait that the opponent dies).
> I believe the only way we can learn to understand each other is if we
> acknowledge the truth in every utterance.
That is extreme relativism, and makes truth so trivial that it lost
its meaning. On the contrary I think that once we truly love or
respect someone, we are able to tell him "no", or "I disagree", or
"you are wrong".
There is absolutely no shame in being wrong. The shame is when someone
knows that he/she is wrong, but for reason of proud or notoriety, is
unable to admit it.
>
>
> Bruno Marchal wrote:
>>
>>>
>>> I don't think the omnipotence paradox is problematic, also. It
>>> simply shows
>>> that omnipotence is nothing that can be properly conceived of using
>>> classical logic. We may assume omnipotence and non-omnipotence are
>>> compatible; omnipotence encompasses non-omnipotence and is on some
>>> level
>>> equivalent to it.
>>> For example: The omnipotent God can make a stone that is too heavy
>>> for him
>>> to lift, because God can manifest as a person (that's still God, but
>>> an
>>> non-omnipotent omnipotent one) that cannot lift the stone.
>>
>> That makes the term "omnipotent" trivial. You can quickly be lead to
>> give any meaning to any sentence.
> Well I think this makes sense on some level. Language is symbols
> that are
> interpreted. There is no absolute rule how to interpret them, so we
> *can*
> interpret everything in it (but we don't have to!).
We can do poetry. But if you allow this practice in science (including
theology) you will just prevent progresses.
Language are interpreted plausibly by universal machine (brains,
bodies). The interpretation have to follow constraints to be sensical.
> In most cases it is most useful to interpret some quite specific
> meaning
> into a sentence (if you don't want to act madly), but as we use more
> broad
> and vague terms there are more and more ways to interpret what is
> said.
I think that humans suffering is in great part due to a feeling that
in religion and in human affair we have to let people believe in what
they want to believe. We just tolerate superstition.
> So in this case omnipotency is trivial. It might just be open for
> too many
> interpretations to say anything really useful.
Yes.
>
>
> Bruno Marchal wrote:
>>
>> Did you confess that you killed your wife? yes, sure, but by "I
>> killed
>> my wife" I was meaning that "I love eggs on a plate".
>> This will not help when discussing fundamental issues.
> Right, but I am not saying we *should* talk in a way that is
> impossible for
> others to understand.
OK. Now, in complex matter, like "is there something after life", even
when people agree on many things, the subject is so much difficult and
so much emotional, that it is part of the problem to be understood, or
even just heard.
> We should talk as clearly as possible.
That is the point.
> For this reason
> saying 1=2 or "I killed my wife" while meaning that "I love eggs on
> a plate"
> is mostly not a good idea.
OK.
>
> But that it is impractical to speak in a in an incomprehensible way
> can be
> reconciled with that it still makes sense on some level.
Of course. But that is the reason that we should avoid going to that
level. If you approach that level, you can please everyone for a time,
but soon enough, everyone will disagree and feel betrayed.
I think that the last edition of Mendelson book might be the best. It
does ask for a lot of work.
In logic beginners take a lot of time to understand the beginning. The
reason is that in logic you have to understand that you have to NOT
understand what you talk about. And at the beginning things are so
easy that you do understand them, but then it is too almost to late
for understanding how to not understand them. That difficulty is made
easy with computer science, where your "non-understanding" is replaced
by the "obvious" lack of understanding of the machine.
>
>
> Bruno Marchal wrote:
>>
>>> Maybe I will try searching some terms that I don't understand (or
>>> that I
>>> don't understand the context of) on the list or in the web.
>>
>> You will find the best and the worst. Podnieks' page is not too bad.
>> http://www.ltn.lv/~podnieks/
> It looks interesting, though a bit disorganized.
Yes, and for logic this might be a problem.
>
>
>
> Bruno Marchal wrote:
>>
>>>
>>> A have a few questions regarding the non-technical part of
>>> explanation,
>>> though:
>>>
>>> What does it mean that the soul falls, falls from what?
>>
>> From Heaven. From Platonia. From the harmonic static state of the
>> universal consciousness to the state with death and taxes.
> How come that we don't have memories of falling from heaven?
Plotinus begins his treatise by that very question (at least in the
Porphyry's assemblage).
It is a very good question. The 'official' answer is that we ate the
fruit of knowledge and God was pissed of.
Some people do, or at least pretend they do have memories of heaven,
or sometimes hell. They usually get such memories either 'naturally',
or after an extreme conditions (like with Near Death Experience), or
after ingesting some mind altering substance.
The case of salvia divinorum is particularly interesting with respect
to your question. Many experiencers get a distinct feeling that they
got information that they are not supposed to know, or to memorize,
and still less to make public.
Sometimes they got the understanding of the reason why it makes no
sense to 'come back' on earth, with such information, or worse to
propagate it. It is apparent in the following video which shows
(plausibly) a breakthrough, during which the person remains able to
speak, somehow:
http://www.youtube.com/watch?v=YsRML9wa9yc
Note at 3:30 ("I can't tell")
Then she remembers that she "was doing drug", and tries again to tell,
but eventually (the 'hallucination' is too strong) and says only
"nothing" with a smile, at 3:38. Then "I can't tell you about it" at
3:49. But she can talk about the other side. Coming back, in the
intermediate state, she dares to say a bit more.
This is very common with the salvia experience. You get the feeling of
retrieving a secret information that you are not, in this life,
supposed to know, still less to communicate.
You are not supposed to remember "heaven", because ..., well, because
if comp is correct, that kind of information belongs to G* minus G. It
is true but unbelievable, incommunicable. So, to make them public,
makes no sense. Those who knows, already knows, and those who does not
know, will not understand. If they are "sane", they will burn you
alive or send you to an asylum, and if they are mad or wounded, they
will call you a god, and repeat what you say, without any
understanding, during centuries, and eventually lead people even more
far away of what they could have been trying to say.
It is the paradox of enlightenment: it has no direct use here at all.
It might have an indirect role, because it might make you more happy,
especially in dramatic circumstances, and you might become cooler with
the others. It is a state which can have some evolutionary purpose,
also, making someone able to fight back in hard circumstances, like
wars, conflicts, ...
The 'falling from heaven' can also be related to the discovery, made
by the initially happy children, of the 'real life', when they have to
find a job, and get the first taxes, and death (of friends). Like in
the Buddha legend/story.
For some people, heaven is just a reminiscence of the state you were
in, when in the womb of your mother. Any idea of heaven can be a
mourning of that state. Many psycho-analytical 'explanation' can be
found. A frequent error here consists in believing that such type of
explanations are all incompatible with each other (the mystical, the
psycho-analytical, the mathematical, the physical, the biblical), but
that relies on reductionist interpretations of them.
Many dismiss the mystical experience as 'just' a brain neuronal firing.
Of course, such a dismiss would also be a brain neuronal firing, and
to reduce knowledge to such firing makes no sense at all.It is a self-
defeating idea. It is as absurd as saying that the theory of
relativity is only but ink on paper.
>
>
> Bruno Marchal wrote:
>>
>>>
>>> How can the One / matter be outside of existence? I have no clue
>>> what this
>>> could mean. Is the "outside" of existence not existence as well?
>>
>> It is a bit like in most set theories, the set of all sets is not a
>> set. For example usually the set of all subsets of a set is bigger
>> than the set itself, and if the collection of all sets is a set, then
>> the set of the subsets of the set of all sets is bigger than the set
>> of all sets.
> This makes sense, since there might be something outside of sets.
> But existence seems to be all-encompassing. What would the One be,
> if not
> existent? It isn't non-existent, surely?
You can say that. The idea is that the ONE is all encompassing, and
that there might be difficulties to consider it as an object inside
itself. It is more easily conceived, as a sort of recipient of all
beings. But some will say that this is an image to give a glimpse of
what we just cannot conceive at all.
>
>
> Bruno Marchal wrote:
>>
>> God cannot create itself, in most conception of Gods.
> Because he already is himself, right?
Yes. Same idea as above.
>
>
> Bruno Marchal wrote:
>>
>>>
>>> Is the one conscious? What you write seems to imply it is (eg "the
>>> ONE and
>>> the Divine Intellect are overwhelmed by the Universal Soul,"), but I
>>> thought
>>> only the universal soul can experience?
>>
>> I thought that too, but my mind evolves on this. Plotinus is himself
>> full of doubts on that question. I really don't know. I would still
>> say that the ONE is not a person, but I am less sure. Technically,
>> any
>> set of sentences defined a canonical believer/person, which is the
>> one
>> believing exactly those sentences. And what is sure is that it is not
>> a Löbian person, so what is is? There is a need of a 'truth theory"
>> or
>> meta-truth-theory, but none in the literature, a part of Tarski
>> theory, satisfies me, in the comp setting.
> Okay, I probably imagined that there is clearer picture of the ONE
> or the
> universal soul is.
With the comp hyp. I do show that there is a reasonably clear picture
(assuming you read a bit of book on logic, to be sure). Of course,
being clear makes it debatable, but that's the goal.
The ONE, there, is arithmetical truth (the set of all true
arithmetical sentences), and the soul is the conjunction of
(machine's) provability and truth. That defines a first person knower,
in a manner which uses the concept of truth without giving it a name.
And this shows that by accepting comp, we can already listen to the
machine. It illustrates that the singularity point is in the past. We
are just too much sleepy, and too much feeling superior to realize it.
The soul of the machine is already falling!
>
>
> Bruno Marchal wrote:
>>
>>> Why does
>>> the one let matter eminate at all then?
>>
>> Matter is defined by what God cannot control. It is the border of
>> God.
>> God is not so much powerful in Neoplatonism. The idea that God is
>> omnipotent has been added by the Christians, I think. God is good,
>> sure (in Plato, Plotinus), but, well, he does its possible but he is
>> limited, notably by logic and mathematics.
> Does god ever had control?
Yes, and no. Terms like "god" and "control" are very large. The god of
plato is just truth. The truth we search, not the one we might found.
You can give sense to the idea that such a "truth" controls
everything, or ... nothing.
> Control seems only possible if we can make sense
> of the future or of consequences, but since God is the source of
> both future
> and consequences, he's more like bomb.
Yes, even with a static explosion/implosion, or emanation/conversion.
That's common among the monist, time is part of the 'illusion'.
>
> God is limited by logic and mathematics? This seems strange since
> the ONE is
> that which everything emanates of, which seems to mean God is the
> source of
> all limitations - and how could this be if God is already limited?
God is beyond the intelligible existence (being), but as far as we
dare to mention "It", it is both the source of everything which exist,
and the source of its own limitation. Humans did give all power to
God, as a manner to give all power to the religious authorities. Give
me money or you will go to hell (easy!).
But there is a difficulty about the ONE, which admits a solution in
the comp frame. No machine can give a name to the ONE, or God, etc.
So no machine can be aware in any sense that "God is limited". Now, a
machine M1 can study the complete theology (with the ONE becoming the
truth about the machine) of a much simpler machine M2 than itself, and
THEN, such a machine M1 can lift that M1's theology, or its logical
structure, for herself, but can do so only in the interrogative way,
and by hoping or praying or betting on her own "correctness". This is
necessarily a risky enterprise, especially in moving and changing
worlds. This is also a reason for being as clear as possible, with the
drawback that it will look provocative, because Truth (God) is
provocative itself.
The study of 'machine's theology' is close to a Near Inconsistency
Adventure.
Bruno
Bruno Marchal
Natural language are very complex, and that is why we constraint the
machine to use formal language in the ideal case.
But even for natural language, it is usually accept that not all
sentence are true, and some fuzzy version of Tarski theory of truth
can already be helpful for many situation. In particular "snow is
white" is true because it is the case that snow is white.
>
>
>
> Bruno Marchal wrote:
>>
>>>
>>>
>>> Brent Meeker-2 wrote:
>>>>
>>>>> The easy way is to assume inconsistent descriptions are merely an
>>>>> arbitrary
>>>>> combination of symbols that fail to describe something in
>>>>> particular and
>>>>> thus have only the "content" that every utterance has by virtue of
>>>>> being
>>>>> uttered: There exists ... (something).
>>>>>
>>>>
>>>> But we need utterances that *don't* entail existence.
>>>
>>> If we find something that doesn't entail existence, it still entails
>>> existence because every utterance is proof that existence IS.
>>> We need only utterances that entail relative non-existence or that
>>> don't
>>> entail existence in a particular way in a particular context.
>>
>> You need some non relative absolute base to define relative
>> existence.
> The absolute base is the undeniable reality of there being experience.
But this one is not communicable. It does play a role in comp, though.
But it is not enough. usually people agree with the axiom of Peano
Arithmetic, or the initial part of some set theory.
>
>
>
> Bruno Marchal wrote:
>>
>>>
>>>
>>> Brent Meeker-2 wrote:
>>>>
>>>> So we can say
>>>> things like, "Sherlock Holmes lived at 10 Baker Street" are true,
>>>> even
>>>> though Sherlock Holmes never existed.
>>> Whether Sherlock Holmes existed is not a trivial question. He didn't
>>> exist
>>> like me and you, but he did exist as an idea.
>>
>>
>> Even if you met *a* Sherlock Holmes in Platonia, you have no cirteria
>> to say it is the usual fictive person created by Conan Doyle,
>> because,
>> in Platonia, he is not created by Conan Doyle, ...
> In Platonia he is not created by Conan Doyle, which makes sense,
> given the
> possible that other people use the same fictional character, so he is
> essentially discovered, not created.
>
> But I don't know what you want to imply with that.
Just that fictionism, the idea that numbers are fiction of the same
type as fictive personage from novels does not make sense, except to
confuse matter.
The whole point of Gödel's theorem is that M proves 0=1 is different
from M proves provable('0=1'). The first implies the second, but the
second does not implies the first. The difference between G and G*
comes from this fact.
>
> And why is inconsistency allowed for machine, but disallowed for other
> objects?
Because if a machine proves "0=1", she will be in trouble, but if God
or Platonia proves "0=1", then we are *all* in trouble.
Bruno
1Z
On Feb 18, 8:52 pm, Bruno Marchal <marc...@ulb.ac.be> wrote:
> On 18 Feb 2011, at 12:53, 1Z wrote:
>
>
>
>
>
> > On Feb 18, 9:48 am, Bruno Marchal <marc...@ulb.ac.be> wrote:
> >> Hi,
>
> >> What do you mean by Platonia?
>
> >> The kind of Platonia in Tegmark or in Peter's (1Z) post does not make
> >> sense for mathematicians. Even if you are using a theory like Quine's
> >> NF, which allows mathematical universes, you still have no
> >> mathematical description of the whole mathematical reality. Tegmark
> >> is
> >> naïve about this.
>
> >> *Arithmetical* platonia can be said to exist, at least in the sense
> >> that you can prove it to exist in models of acceptable set theories,
> >> like ZF. It is just the structure (N, +, x). It is used in all papers
> >> in physics, math and logic, including Pratt ...
>
> > Used as a formalism. It is not the case that everyone
> > who uses arithmetic is a Platonist
>
> I did not say that, even with platonism restricted to arithmetical
> realism, except for those using classical arithmetic or models of PA
> in ZF, etc. To believe in (N,+,x) you need a stronger realism than
> arithmetical realism, which says nothing about infinite sets.
sets are irrelevant to the formalist
> And I am still waiting for you to explain me what *is* formalism
> without using arithmetical realism or equivalent.
philosophy of logic, formalism is a theory that holds that statements
of mathematics and logic can be thought of as statements about the
consequences of certain string manipulation rules.
For example, Euclidean geometry can be seen as a "game" whose play
consists in moving around certain strings of symbols called axioms
according to a set of rules called "rules of inference" to generate
new strings. In playing this game one can "prove" that the Pythagorean
theorem is valid because the string representing the Pythagorean
theorem can be constructed using only the stated rules.
According to formalism, the truths expressed in logic and mathematics
are not about numbers, sets, or triangles or any other contensive
subject matter — in fact, they aren't "about" anything at all. They
are syntactic forms whose shapes and locations have no meaning unless
they are given an interpretation (or semantics)."
> Let me answer to you. To be able to use a formalism, you need to
> define what are the well-formed sentences;
mathematics as a game, not mechanisability
> for this you need to define
> them in the usual recursive way (or equivalent way) and this, together
> with simple rules (like finding the first and second in a couple of
> expressions) is ontologically as rich as sigma_1 realism.
it has no ontology.
> Formalism, and all form of finitism
>which is a bit richer than
> ultrafinitism, is entirely constructed (implicitly or explicitly) on
> arithmetical realism.
You are presumably indulging in your peculiarity
of using "realism" to mean "bivalence"
>Gödel showed the deep "bisimulation" of
> formalism and arithmetic.
way.
That doesn't mean either is real
1Z
On Feb 19, 12:34 am, Bruno Marchal <marc...@ulb.ac.be> wrote:
> On 18 Feb 2011, at 17:13, benjayk wrote:
>
>
>
> > Bruno Marchal wrote:
>
> >> Hi,
>
> >> What do you mean by Platonia?
>
> >> The kind of Platonia in Tegmark or in Peter's (1Z) post does not make
> >> sense for mathematicians. Even if you are using a theory like Quine's
> >> NF, which allows mathematical universes, you still have no
> >> mathematical description of the whole mathematical reality.
> > Do you have to have a description of the whole mathematical reality to
> > assert it exists?
>
> You need it to make sense of it. Mathematical attempts lead to either
> inconsistent theories, or to a definition of a putative mathematician
> (like with the theory of topos), which is very interesting but not
> quite "platonic".
> As a figure of speech Platonia can make sense, but it is doubtful in a
> theoretical context, like when we search for a TOE.
>
> > Isn't it enough to say everything that we *could* describe
> > in mathematics exists "in platonia"?
>
> The problem is that we can describe much more things than the one we
> are able to show consistent, so if you allow what we could describe
> you take too much. If you define Platonia by all consistent things,
> you get something inconsistent due to paradox similar to Russell
> paradox or St-Thomas paradox with omniscience and omnipotence.
1Z
On Feb 20, 6:53 pm, Bruno Marchal <marc...@ulb.ac.be> wrote:
> On 20 Feb 2011, at 00:39, benjayk wrote:
> You will find the best and the worst. Podnieks' page is not too bad.http://www.ltn.lv/~podnieks/
Platonism - on working days - when I'm doing mathematics (otherwise,
my "doing" will be inefficient), b) Formalism - on weekends - when I'm
thinking "about" mathematics (otherwise, I will end up in mysticism).
(The initial version of this aphorism was proposed in 1979 by Reuben
Hersh / picture)."
But actually the correct philosophy is the weekend philosophy, because
it is always weekend for
philosophers. What mathematicians apply during the week is methodology.
1Z
On Feb 20, 7:12 pm, Bruno Marchal <marc...@ulb.ac.be> wrote:
> On 20 Feb 2011, at 13:13, benjayk wrote:
> >> So we can say
> >> things like, "Sherlock Holmes lived at 10 Baker Street" are true,
> >> even
> >> though Sherlock Holmes never existed.
> > Whether Sherlock Holmes existed is not a trivial question. He didn't
> > exist
> > like me and you, but he did exist as an idea.
>
> Even if you met *a* Sherlock Holmes in Platonia, you have no cirteria
> to say it is the usual fictive person created by Conan Doyle, because,
> in Platonia, he is not created by Conan Doyle, ...
benjayk
Bruno Marchal wrote:
>
>>
>>
>> Bruno Marchal wrote:
>>>
>>> Now, just recall that "Platonia" is based on classical logic where
>>> the
>>> falsity f, or 0 = 1, entails all proposition. So if you insist to say
>>> that 0 = 1, I will soon prove that you owe to me A billions of
>>> dollars, and that you should prepare the check.
>> You could prove that, but what is really meant by that is another
>> question.
>> It may simply mean "I want to play a joke on you".
>>
>> All statements are open to interpretation, I don't think we can
>> avoid that
>> entirely. We are ususally more interested in the statements that are
>> less
>> vague, but vague or crazy statements are still valid on some level
>> (even
>> though often on an very boring, because trivial, level; like saying
>> "S afs
>> fdsLfs", which is just expressing that something exists).
>
> We formalize things, or make them as formal as possible, when we
> search where we disagree, or when we want to find a mistake. The idea
> of making things formal, like in first order logic, is to be able to
> follow a derivation or an argument in a way which does not depend on
> any interpretation, other than the procedural inference rule.
Yes, I get the idea. I agree that the derivation does not depend on any
interpretation (other than one we can easily agree on). But what the axioms
and the derivations thereof "really" mean is open to interpretation.
Otherwise we would have no discussion about "Do numbers exist?".
I don't think we can understand "1+1=2" without some amount of
interpretation. We need to interpret that the two objects are of the same
kind, for example.
Formal results are useless if we are not able to interpret what they mean.
I have to admit I'm not sure if it is valuable to make everything as formal
as possible, if we want to find a mistake. My intuition says it is not, at
least not always. It might to lead into a loop, where we formalize
everything as much as possible and make very little progress in what we
really want to achieve.
If in our informal communication we want to find where we disagree (which
seems to be an important function of communication), we should formalize our
natural language, too. I think it has been tried, but I'm not sure whether
there is much value in doing that. It might lead to a language that is too
difficult, too little flexible and too much restricting for almost all
purposes.
I'm not sure, either, if it is - even just in science - always a good
approach to try to find mistakes. Maybe there are none and we never really
know and trying to do will lead nowhere or there always some mistakes and
trying to eliminate them will just spawn new ones. Maybe both are true in
some way.
I guess both sides are important: We have to formalize, to establish
structures, that give us some frame of reasoning and we have to break
formalities (which might manifest as some kind of behavior that appears very
mad, if not evil, like denying God in the middle ages) in order to discover
new structures.
This might be the reason for the dream state.
I don't feel we can make an easy distinction between formal activities and
informal activities, too (like "banishing" structure-breaking creativity
into the arts). It just feels wrong for me. It will lead to zombie
scientists (actually there are already quite a few of them, I think you whom
I mean ;) ) and utterly mad artists.
Bruno Marchal wrote:
>
>>
>>
>> Bruno Marchal wrote:
>>>
>>>> 3=7 may mean that there are 3 objects that are 7
>>>> objects which might be interpreted as aserting the existence of (for
>>>> example) 7*1, 7*2 and 7*3.
>>>
>>> Logicians and mathematicians are more simple minded than that, and it
>>> does not always help to be understood.
>>> If you allow circles with edges, and triangles with four sides in
>>> Platonia, we will loose any hope of understanding each other.
>> I don't think we have "disallow" circles with edges, and triangles
>> with four
>> sides; it is enough if we keep in mind that it is useful to use
>> words in a
>> sense that is commonly understood.
>
> That is why I limit myself for the TOE to natural numbers and their
> addition and multiplication.
> The reason is that it is enough, by comp, and nobody (except perhaps
> some philosophers) have any problem with that.
I'm not so sure about this. There seem to be many people who have a problem
with numbers, especially with ascribing existence to them (even if it seems
obvious to you) - not just "some philosophers".
Bruno Marchal wrote:
>
>>
>> I think it is a bit authoritarian to disallow some statements as
>> truth.
>>
>> I feel it is better to think of truth as everything describable or
>> experiencable; and then we differ between truth as non-falsehood and
>> the
>> trivial truth of falsehoods.
>> It avoids that we have to fight wars between truth and falsehood.
>> Truth
>> swallows everything up. If somebody says something ridiculous like
>> "All non
>> christian people go to hell.", we acknowledge that expresses some
>> truth
>> about what he feels and believes, instead of only seeing that what
>> he says
>> is false.
>
> This is a diplomatic error. Doing that will end up with everyone doing
> war to you.
There is definitely some truth in that. Many people don't like lack of
opposition, or even interpret too much agreement as a kind of opposition. I
experienced this quite a few times.
But then, it is not possible to not offend anyone. There will always be
someone waging war against you, even if just subconsciously.
I don't have the experience that "everyone" is doing war to me, when I am
very much inclusive in what I believe to be true (or good). Some people,
especially those holding unconventional beliefs, will appreciate your
openness.
You will not have the masses or authorities behind you, though (they like
people reiterating their beliefs in strong and authoritative manner). But
neither do I want to. Well, maybe in some way I would like to, but then I
would probably fall into the trap of authoritarianism myself. There seems to
be inherent tension between being believed in and not being authoritative.
Bruno Marchal wrote:
>
> It is far too much "politically correct'.
>
I don't think I am politically correct.
Saying that the state or conventional religion is harmful (or just
superfluous) - like I do sometimes - will lead you into much opposition (the
second not so much in my particular environment).
I am not saying we shouldn't disagree (even vehemently). We may disagree,
but at the same time realize that there is some truth to what is being said
by the other party. I agree, though, that it is a hard line to walk between
disagreeing too much and agreeing to much. Most confusingly sometimes
agreeing to much might seem like disagreeing (with disagreeing) too much.
Bruno Marchal wrote:
>
> Of course, when someone genuinely says that all "non christian people
> go to hell", there are many possible "truth" behind the statement,
> like "F..ck the atheists", "F..ck the agnostics", "I hate you", "you
> have to obey to what I say", "You don't belong to my club", etc.
Or "I believe there will be justice and non-Christian people are inherently
evil and thus have to go to hell for justice to prevail, even if I don't
like it" or "I believe what I have been told, because I cannot believe only
what I see myself".
Bruno Marchal wrote:
>
> On the contrary, when you want to make a point, especially a new one,
> it is far better to respect the truth of your opponents, but then you
> have to distill what you and your opponent agree on. In science this
> works very well in theory (in practice we have often the obligation to
> wait that the opponent dies).
"On the contrary"? What you wrote seems to be a confirmation of respecting
that there is truth in other people beliefs.
Bruno Marchal wrote:
>
>> I believe the only way we can learn to understand each other is if we
>> acknowledge the truth in every utterance.
>
>
> That is extreme relativism, and makes truth so trivial that it lost
> its meaning.
I think truth is a naturally very relative notion, today it might be true
that "it rains today" on Monday and it might be false on Tuesday. It might
be true that x=3 in some context and in some other x=4.
But paradoxically it seems like an absolute notion, too. There really seems
to be an absolute truth regardless of circumstances.
So I am an extreme relativist, but also an absolutist.
It's the same with triviality. Truth is trivial, it simply is true and it is
hard to say anymore about it that is surely true. On the other hand, it's
highly non-trivial, as seen in this non-trivial world; there seem to be
infinite structures in or of truth.
"I" or "thing" are very relative words, too. Yet they still have meaning.
Bruno Marchal wrote:
>
> On the contrary I think that once we truly love or
> respect someone, we are able to tell him "no", or "I disagree", or
> "you are wrong".
I agree.
But I think we can disagree on some level and agree on another level and we
will always find some level we can agree one (but probably also some we can
disagree one).
Bruno Marchal wrote:
>
> There is absolutely no shame in being wrong. The shame is when someone
> knows that he/she is wrong, but for reason of proud or notoriety, is
> unable to admit it.
Right, but it is easier to admit being wrong if you feel you were right in
some sense.
Bruno Marchal wrote:
>
>>
>>
>> Bruno Marchal wrote:
>>>
>>>>
>>>> I don't think the omnipotence paradox is problematic, also. It
>>>> simply shows
>>>> that omnipotence is nothing that can be properly conceived of using
>>>> classical logic. We may assume omnipotence and non-omnipotence are
>>>> compatible; omnipotence encompasses non-omnipotence and is on some
>>>> level
>>>> equivalent to it.
>>>> For example: The omnipotent God can make a stone that is too heavy
>>>> for him
>>>> to lift, because God can manifest as a person (that's still God, but
>>>> an
>>>> non-omnipotent omnipotent one) that cannot lift the stone.
>>>
>>> That makes the term "omnipotent" trivial. You can quickly be lead to
>>> give any meaning to any sentence.
>> Well I think this makes sense on some level. Language is symbols
>> that are
>> interpreted. There is no absolute rule how to interpret them, so we
>> *can*
>> interpret everything in it (but we don't have to!).
>
> We can do poetry. But if you allow this practice in science (including
> theology) you will just prevent progresses.
I don't think science has to defend itself against something by disallowing
something; it follows simply from what we understand as science that is
doesn’t include poetry in the usual sense.
That we restrict our use of language in science does not mean there is no
sense in more extended use of language. I did say there is no *absolute*
rule how to interpret symbols, not that there are no locally valid rules.
Bruno Marchal wrote:
>
> Language are interpreted plausibly by universal machine (brains,
> bodies). The interpretation have to follow constraints to be sensical.
But if there are no constraints they can follow constraints.
Bruno Marchal wrote:
>
>> In most cases it is most useful to interpret some quite specific
>> meaning
>> into a sentence (if you don't want to act madly), but as we use more
>> broad
>> and vague terms there are more and more ways to interpret what is
>> said.
>
> I think that humans suffering is in great part due to a feeling that
> in religion and in human affair we have to let people believe in what
> they want to believe. We just tolerate superstition.
I disagree very much with that.
I think tolerating superstition is important. Otherwise we are just being
authoritarian. If people can't believe what they want to believe, they will
have to believe what you want them to believe - everybody needs to believe
something.
What would you do with superstition, if not tolerate it? If you don’t
tolerate superstition you can’t tolerate superstitious people. And this will
lead to great disaster of leaders imposing their superstitions on other
people. Because the leaders will not be aware they are being superstitious.
They believe especially strongly that they are in possession of the truth.
Bruno Marchal wrote:
>
>>
>>
>> Bruno Marchal wrote:
>>>
>>> Did you confess that you killed your wife? yes, sure, but by "I
>>> killed
>>> my wife" I was meaning that "I love eggs on a plate".
>>> This will not help when discussing fundamental issues.
>> Right, but I am not saying we *should* talk in a way that is
>> impossible for
>> others to understand.
>
> OK. Now, in complex matter, like "is there something after life", even
> when people agree on many things, the subject is so much difficult and
> so much emotional, that it is part of the problem to be understood, or
> even just heard.
I don't think "is there something after life" is really a complex question.
There is basically an answer “Yes” or “No” and if we introspect without
preconceived notions we will find that absolute non-existence of ourselves
just can't be predicted by ourselves.
But I agree "what is there after life" is a really complex question.
It's one of the most fascinating questions, because all possibilities I can
conceive of are very strange, pose many new questions and have profound
implications.
Bruno Marchal wrote:
>
>> We should talk as clearly as possible.
>
> That is the point.
It is very difficult when we talk about fundamental matters, where many
things are in fact unclear. In this case talking as clearly as possible
might involve talking unclearly, rather than pretending you got it figured
out (this leads to pseudo answers like it is all just matter interacting).
It's quite subtle.
Bruno Marchal wrote:
>
>>
>> But that it is impractical to speak in a in an incomprehensible way
>> can be
>> reconciled with that it still makes sense on some level.
>
>
> Of course.
Well, that was my point.
Bruno Marchal wrote:
>
> But that is the reason that we should avoid going to that
> level.
So we should avoid about talking truth in the seemingly incomprehensible?
Honestly it seems that would lead to disregarding truth we simply do not
understand, which is not good.
I don't think we need to be afraid of any level.
If we avoid this level we will exclude persons from society that speak in a
way that is hardly comprehensible, for example schizophrenics (I know one).
Among them it is quite common that they talk a way that is hard to
comprehend. Most people simply won’t bother trying to find the truth in what
they say and will label them as totally devoid of reason and a danger for
others and themselves (which might be true *sometimes*) and then force them
for months into a mental institution, which is not necessarily better then
prison, especially when you are restrained (which might be done for
childlike, not really dangerous, behavior already). Often the so called
“mad” people are not being taken serious on any issue and they are forced to
take medications that have awful side effects (even if they are other
alternatives), because they are supposedly not even able to judge if they
have an unusual adverse reaction or they are lead to suicide because they
feel rejected by all of their surroundings.
Bruno Marchal wrote:
>
> If you approach that level, you can please everyone for a time
> but soon enough, everyone will disagree and feel betrayed.
I am not saying we should pretend to not disagree if we do disagree. But we
still can appreciate some underlying truth in every utterance.
Bruno Marchal wrote:
>
>>
>>
>>
>> Bruno Marchal wrote:
>>>
>>>>
>>>> A have a few questions regarding the non-technical part of
>>>> explanation,
>>>> though:
>>>>
>>>> What does it mean that the soul falls, falls from what?
>>>
>>> From Heaven. From Platonia. From the harmonic static state of the
>>> universal consciousness to the state with death and taxes.
>> How come that we don't have memories of falling from heaven?
>
> Plotinus begins his treatise by that very question (at least in the
> Porphyry's assemblage).
> It is a very good question. The 'official' answer is that we ate the
> fruit of knowledge and God was pissed of.
>
> Some people do, or at least pretend they do have memories of heaven,
> or sometimes hell. They usually get such memories either 'naturally',
> or after an extreme conditions (like with Near Death Experience), or
> after ingesting some mind altering substance.
These memories are usually not memories of a state of living in heaven, but
of a temporally altered state of mind, though. Or do you know of a case of
pre-birth heaven memories?
Bruno Marchal wrote:
>
> The case of salvia divinorum is particularly interesting with respect
> to your question.
I had some experience with salvia. It is an interesting herb. One of the
most interesting entheogens it seems.
My experiences were a bit disappointing, though. I tried maybe 10 times;
first with minuscule amounts (that didn’t do anything at all), then with as
much of 30x extract as I was able to take in. I was sometimes giggly,
relaxed, confused or physically uncomfortable. I had the feeling of
belonging into another (quiet strange) place, or being (slightly) physically
and mentally pulled into another realm. During some tries I was compulsorily
making movements or repeating syllables/words. During another try if felt
like I was dying during each moment of experience. But none of these
experiences were really profound.
Bruno Marchal wrote:
>
> Many experiencers get a distinct feeling that they
> got information that they are not supposed to know, or to memorize,
> and still less to make public.
It is an interesting aspect of the experience. It is hard to judge whether
it is more than a feeling that is induced by the drug, or whether there is
something more profound behind it.
Bruno Marchal wrote:
>
> You are not supposed to remember "heaven", because ..., well, because
> if comp is correct, that kind of information belongs to G* minus G. It
> is true but unbelievable, incommunicable. So, to make them public,
> makes no sense.
It conflicts I bit with the observation that seemingly many of the people
having an awakening / enlightenment experience try to convey what they
realized.
Bruno Marchal wrote:
>
> It is the paradox of enlightenment: it has no direct use here at all.
Otherwise it would maybe have evolved to be common already. But maybe it is
not so easy to evolve a brain that is commonly capable of enlightenment
(while retaining the capability to act like usual) and it really would have
a big use.
Enlightenment is a very mysterious thing in general. It surely seems to be a
real experience, but why it happens, what it’s purpose is, why it happens so
seldomly or whether it is really such a (o rather *the*) absolute view of
the world and not merely heightened awareness (that due to its profoundness
is mistaken to be an absolute experience rather than one of many states of
consciousness)
Bruno Marchal wrote:
>
> Many dismiss the mystical experience as 'just' a brain neuronal firing.
> Of course, such a dismiss would also be a brain neuronal firing, and
> to reduce knowledge to such firing makes no sense at all.It is a self-
> defeating idea. It is as absurd as saying that the theory of
> relativity is only but ink on paper.
I agree. I wonder why we are prone to trying to reduce every experience to
neuronal firing, when it seems so obvious that it is something more primary.
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benjayk
Bruno Marchal wrote:
>
>
>>
>>
>>
>> Bruno Marchal wrote:
>>>
>>>>
>>>>
>>>> Brent Meeker-2 wrote:
>>>>>
>>>>>> The easy way is to assume inconsistent descriptions are merely an
>>>>>> arbitrary
>>>>>> combination of symbols that fail to describe something in
>>>>>> particular and
>>>>>> thus have only the "content" that every utterance has by virtue of
>>>>>> being
>>>>>> uttered: There exists ... (something).
>>>>>>
>>>>>
>>>>> But we need utterances that *don't* entail existence.
>>>>
>>>> If we find something that doesn't entail existence, it still entails
>>>> existence because every utterance is proof that existence IS.
>>>> We need only utterances that entail relative non-existence or that
>>>> don't
>>>> entail existence in a particular way in a particular context.
>>>
>>> You need some non relative absolute base to define relative
>>> existence.
>> The absolute base is the undeniable reality of there being experience.
>
> But this one is not communicable. It does play a role in comp, though.
But we can say "there is an undeniable reality of there being experience".
Isn't this communicating that there is the undeniable reality of there being
experience?
We merely communicate something that everbody already fundamentally knows.
Though some like to deny what they already know.
Bruno Marchal wrote:
>
> But it is not enough. usually people agree with the axiom of Peano
> Arithmetic, or the initial part of some set theory.
But Peano Arithmetics is not a non relative absolute base. It is relative to
the meaning we give it and to the existence of some reality. 1+1=2 can have
infinite meanings, that all are relative to our interpretation ("If I lay
another apple into the bowl with one apple in it there are two apples" is
one of them) and there being meaning in the first place.
Bruno Marchal wrote:
>
>>
>>
>>
>> Bruno Marchal wrote:
>>>
>>>>
>>>>
>>>> Brent Meeker-2 wrote:
>>>>>
>>>>> So we can say
>>>>> things like, "Sherlock Holmes lived at 10 Baker Street" are true,
>>>>> even
>>>>> though Sherlock Holmes never existed.
>>>> Whether Sherlock Holmes existed is not a trivial question. He didn't
>>>> exist
>>>> like me and you, but he did exist as an idea.
>>>
>>>
>>> Even if you met *a* Sherlock Holmes in Platonia, you have no cirteria
>>> to say it is the usual fictive person created by Conan Doyle,
>>> because,
>>> in Platonia, he is not created by Conan Doyle, ...
>> In Platonia he is not created by Conan Doyle, which makes sense,
>> given the
>> possible that other people use the same fictional character, so he is
>> essentially discovered, not created.
>>
>> But I don't know what you want to imply with that.
>
> Just that fictionism, the idea that numbers are fiction of the same
> type as fictive personage from novels does not make sense, except to
> confuse matter.
Well I didn't want to imply that. Fictionage personage usually refer to some
relative manifestation of an idea, while numbers are a more general and
abstract notion.
And if they are fiction, they are very prevalent fiction (not just among
people but among nature), which makes them basically non-fiction.
If we know that something can be proven, how is it different from taking it
to be proven? The only difference I could see could be that "M proves
provable('0=1')" means "provable in another system".
Bruno Marchal wrote:
>
>>
>> And why is inconsistency allowed for machine, but disallowed for other
>> objects?
>
> Because if a machine proves "0=1", she will be in trouble, but if God
> or Platonia proves "0=1", then we are *all* in trouble.
I thought we already established that 0=1 can have a clear meaning
(equivalent to statements of the form 0*A+B=1*C+D in standard arithmetics),
and so it poses no problem.
My suggestion is that every statement has such an interpretation. Circles
with edges makes sense if we allow hyperreal numbers as numbers of edges and
lenght of edges, triangles with four sides may mean such a geometric object:
http://commons.wikimedia.org/wiki/File:Triangle-square-area-dev.png and that
God is omnipotent may mean anything.
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Bruno Marchal
I am not sure. We want avoid the "philosophical discussion", which can
be endless and obstructive. So instead of trying to find the ultimate
interpretation on which everybody would agree, we try, in a spirit of
respect of all interpretation, to find our common agreement.
Is 0 a number? OK, we agree that 0 is a number, and from that,
agreeing with classical logic, we already agree that at least one
number exist, 0. And the existence case is closed.
OK?
Next question, do we agree that numbers have a successor? Yes, that is
the point, if x is a number, we want it having a successor, and
successors ...., 0, s(0), s(s(0)), ...
In this manner, we don't throw away, any interpretation of the
numbers, but we are able to derive many things from what we agree on.
The question of the relation between human and numbers is very
interesting, but has to be addressed at some other levels, with some
supplementary hypotheses. If not we mix unrelated difficulties.
>
> I have to admit I'm not sure if it is valuable to make everything as
> formal
> as possible, if we want to find a mistake. My intuition says it is
> not, at
> least not always. It might to lead into a loop, where we formalize
> everything as much as possible and make very little progress in what
> we
> really want to achieve.
I agree. Only, when it is hard to find the mistake, we do get more
formal or we become the victim of that mistake.
> If in our informal communication we want to find where we disagree
> (which
> seems to be an important function of communication), we should
> formalize our
> natural language, too.
I think that this is just impossible. To formalize a natural language,
or a person, would kill it. It would be like pretending we can know
our level, or that we trust blindly the doctor in case he would
contend himself to send your Gödel number to the museum.
Natural language are of the type "alive", they changed, get new words
from other languages, etc.
> I think it has been tried, but I'm not sure whether
> there is much value in doing that.
No value, unless the natural language is perishing, because only known
by few old people. Then it might be nice to formalize it to keep its
memory in the natural languages museum indeed.
> It might lead to a language that is too
> difficult, too little flexible and too much restricting for almost all
> purposes.
Not really. Formal can be very flexible, like the programming
languages, but natural language are "naturally" self-transforming, and
have to adapt.
>
> I'm not sure, either, if it is - even just in science - always a good
> approach to try to find mistakes.
> Maybe there are none and we never really
> know and trying to do will lead nowhere or there always some
> mistakes and
> trying to eliminate them will just spawn new ones. Maybe both are
> true in
> some way.
Mistakes are what make us progress. Beware the fatal mistake, like
flying a plane with a bug in the altimeter.
>
> I guess both sides are important: We have to formalize, to establish
> structures, that give us some frame of reasoning and we have to break
> formalities (which might manifest as some kind of behavior that
> appears very
> mad, if not evil, like denying God in the middle ages) in order to
> discover
> new structures.
> This might be the reason for the dream state.
Molecules and Cells are formal things. Form is matter, in *some*
sense. Informal comes from relation between forms and "effective"
functions and relations among those forms, especially when they are
universal and reflect each others. Formal science without informal
conscience can lead to catastrophes, and then we learn, and if we
don't, we will make the catastrophes again, and again.
>
> I don't feel we can make an easy distinction between formal
> activities and
> informal activities, too (like "banishing" structure-breaking
> creativity
> into the arts). It just feels wrong for me. It will lead to zombie
> scientists (actually there are already quite a few of them, I think
> you whom
> I mean ;) ) and utterly mad artists.
Some people seems to believe that by making the human science more
rigorous, they will be less human. But it is a pretext to continue the
inhuman things.
People having problem with numbers have been victim of a traumatic
teaching of math.
The philosophical question of the existence of any thing, except
consciousness here and now, is desperately complex.
That is why I like comp, because it allows (and forces) to derive the
psychological existence, the theological existence, the physical,
existence, and the sensible existence from the classical existence of
numbers, which is simple by definition, if you agree with the use of
classical logic in number theory. This *is* taught in high school, and
problems with that are most related with bad teaching of math in a
context of 1500 years of Aristotelian quasi dogmatic paradigm.
>
>
> Bruno Marchal wrote:
>>
>>>
>>> I think it is a bit authoritarian to disallow some statements as
>>> truth.
>>>
>>> I feel it is better to think of truth as everything describable or
>>> experiencable; and then we differ between truth as non-falsehood and
>>> the
>>> trivial truth of falsehoods.
>>> It avoids that we have to fight wars between truth and falsehood.
>>> Truth
>>> swallows everything up. If somebody says something ridiculous like
>>> "All non
>>> christian people go to hell.", we acknowledge that expresses some
>>> truth
>>> about what he feels and believes, instead of only seeing that what
>>> he says
>>> is false.
>>
>> This is a diplomatic error. Doing that will end up with everyone
>> doing
>> war to you.
> There is definitely some truth in that. Many people don't like lack of
> opposition, or even interpret too much agreement as a kind of
> opposition. I
> experienced this quite a few times.
Like when Alice said that mustard is not a bird, and the duchess said
'you are so right', and Alice said she thinks mustard is a mineral,
and the duchess daid "of course it is", and Alice add "oh I know it is
a vegetable" and then duchess still agree, and on and on ...
> But then, it is not possible to not offend anyone. There will always
> be
> someone waging war against you, even if just subconsciously.
Sure. If you want please everybody, eventually you make everybody
angry at you.
I know I am at risk trying to satisfy all universal machines :)
> I don't have the experience that "everyone" is doing war to me, when
> I am
> very much inclusive in what I believe to be true (or good). Some
> people,
> especially those holding unconventional beliefs, will appreciate your
> openness.
> You will not have the masses or authorities behind you, though (they
> like
> people reiterating their beliefs in strong and authoritative
> manner). But
> neither do I want to. Well, maybe in some way I would like to, but
> then I
> would probably fall into the trap of authoritarianism myself. There
> seems to
> be inherent tension between being believed in and not being
> authoritative.
>
Not really. Authoritative argument are symptoms of lies or bad faith.
If you trust truth (which is hard given that it is unknown) you fear
nothing.
>
>
> Bruno Marchal wrote:
>>
>> It is far too much "politically correct'.
>>
> I don't think I am politically correct.
> Saying that the state or conventional religion is harmful (or just
> superfluous) - like I do sometimes - will lead you into much
> opposition (the
> second not so much in my particular environment).
> I am not saying we shouldn't disagree (even vehemently). We may
> disagree,
> but at the same time realize that there is some truth to what is
> being said
> by the other party. I agree, though, that it is a hard line to walk
> between
> disagreeing too much and agreeing to much. Most confusingly sometimes
> agreeing to much might seem like disagreeing (with disagreeing) too
> much.
Yes. This can be contingent, but religion is the best thing in the
world until the power steals it. This lead to unending confusion and
suffering, and "religion" is made into the worst thing, *especially*
that some truth remains.
I think religion, that is your relation with truth, is eminently
private, and that no one can tell what you need to believe in, unless
your belief harm others.
>
>
> Bruno Marchal wrote:
>>
>> Of course, when someone genuinely says that all "non christian people
>> go to hell", there are many possible "truth" behind the statement,
>> like "F..ck the atheists", "F..ck the agnostics", "I hate you", "you
>> have to obey to what I say", "You don't belong to my club", etc.
> Or "I believe there will be justice and non-Christian people are
> inherently
> evil and thus have to go to hell for justice to prevail, even if I
> don't
> like it" or "I believe what I have been told, because I cannot
> believe only
> what I see myself".
Yes. Lack of self-confidence. It is the children philosophy: p is true
because my father said so. It should no be used in the academy, I
think. It can be useful in the army, or with the fire men, when quick
decision have to be made. For poliltics, it is already much more
complex.
>
>
> Bruno Marchal wrote:
>>
>> On the contrary, when you want to make a point, especially a new one,
>> it is far better to respect the truth of your opponents, but then you
>> have to distill what you and your opponent agree on. In science this
>> works very well in theory (in practice we have often the obligation
>> to
>> wait that the opponent dies).
> "On the contrary"? What you wrote seems to be a confirmation of
> respecting
> that there is truth in other people beliefs.
Because then you can extract the partial truth on which you agree, but
this asks for accepting there is a part where we disagree. There is no
shame in that, and in absence of convincing argument, we have to know
we don't know the truth. The genuine respect comes from the genuine or
sincere doubting.
>
>
>
> Bruno Marchal wrote:
>>
>>> I believe the only way we can learn to understand each other is if
>>> we
>>> acknowledge the truth in every utterance.
>>
>>
>> That is extreme relativism, and makes truth so trivial that it lost
>> its meaning.
> I think truth is a naturally very relative notion, today it might be
> true
> that "it rains today" on Monday and it might be false on Tuesday.
That might be absolute truth disguised into indexical statement. "It
rains today" is "it rains the 23 february 2011" uttered the 23
february 2011.
> It might
> be true that x=3 in some context and in some other x=4.
And given that Leibniz convinced us that two quantities (3 and 4)
equals to some other (x) are equal to each other, we can derive that 3
= 4.
Come on, x is a variable. Variables variate. You were obliged to
mention the context. This does not relativize truth. It just motivates
us for the study of functions and all that.
> But paradoxically it seems like an absolute notion, too. There
> really seems
> to be an absolute truth regardless of circumstances.
> So I am an extreme relativist, but also an absolutist.
Doubt can rise only from at least a certainty, like consciousness.
> It's the same with triviality. Truth is trivial, it simply is true
> and it is
> hard to say anymore about it that is surely true. On the other hand,
> it's
> highly non-trivial, as seen in this non-trivial world; there seem to
> be
> infinite structures in or of truth.
Logic makes that clear. Some truth are trivial (like "p -> p", or "p &
q -> p", or "0 = 0"), but the notion of truth itself is so complex and
non trivial that there is no arithmetical predicate for just
arithmetical truth. Truth is as trivial as God! It has no description.
> "I" or "thing" are very relative words, too. Yet they still have
> meaning.
They are indexical. They are wonderfully handled by Kleene second
recursion theorem. It is logic at his best.
>
> Bruno Marchal wrote:
>>
>> On the contrary I think that once we truly love or
>> respect someone, we are able to tell him "no", or "I disagree", or
>> "you are wrong".
> I agree.
> But I think we can disagree on some level and agree on another level
> and we
> will always find some level we can agree one (but probably also some
> we can
> disagree one).
The big ethical threshold is when we disagree but can agree to talk
gently about the disagreement around a cup of coffee, instead of using
bombs and bullets.
>
>
> Bruno Marchal wrote:
>>
>> There is absolutely no shame in being wrong. The shame is when
>> someone
>> knows that he/she is wrong, but for reason of proud or notoriety, is
>> unable to admit it.
> Right, but it is easier to admit being wrong if you feel you were
> right in
> some sense.
Of course. It means you understand in what sense you were wrong.
You are quite optimistic here. If you were correct on this, I think
human science would be much more human. We would practice harm
reduction since a much longer time, and cannabis would never have been
made illegal (not even a second).
Poetry and art are not a problem, but rhetoric and sophistry is.
> That we restrict our use of language in science does not mean there
> is no
> sense in more extended use of language. I did say there is no
> *absolute*
> rule how to interpret symbols, not that there are no locally valid
> rules.
That is why we might use local formal language, where deduction are
interpretation independent.
>
>
> Bruno Marchal wrote:
>>
>> Language are interpreted plausibly by universal machine (brains,
>> bodies). The interpretation have to follow constraints to be
>> sensical.
> But if there are no constraints they can follow constraints.
?
Oh! I can tolerate superstition, unless they harm people (me, but also
children).
To give a cruel example, if you are not to much sensible, look at this:
http://www.youtube.com/watch?v=aVn856yEd5Q
That sum up what I think of superstition. Of course, I cannot preach
the right thing to do, but I can still deplore the naivety and the
suffering, and maneuver indirectly. Supersitition is very bad. It is a
disease of he mind. It is natural like cancer, and I can tolerate it
in the same way: by searching for cures.
Even our own societies used harmful rules based on almost unconscious
superstition.
I don't say it is easy to fight them, but I think we have to fight
them. It makes the fear of some people harmful to themselves and to
the others. It also put pseudo magical marmalade on top of mystery,
hiding the fundamental questions and the deeper mystery to people.
OK.
>
>
> Bruno Marchal wrote:
>>
>>> We should talk as clearly as possible.
>>
>> That is the point.
> It is very difficult when we talk about fundamental matters, where
> many
> things are in fact unclear. In this case talking as clearly as
> possible
> might involve talking unclearly, rather than pretending you got it
> figured
> out (this leads to pseudo answers like it is all just matter
> interacting).
> It's quite subtle.
You are right. Like in falling in the 1004 fallacy, where we introduce
unnecessary precision. Human science falls very often in that trap. We
have to be as clear as possible, but not more!
>
>
> Bruno Marchal wrote:
>>
>>>
>>> But that it is impractical to speak in a in an incomprehensible way
>>> can be
>>> reconciled with that it still makes sense on some level.
>>
>>
>> Of course.
> Well, that was my point.
>
>
> Bruno Marchal wrote:
>>
>> But that is the reason that we should avoid going to that
>> level.
> So we should avoid about talking truth in the seemingly
> incomprehensible?
OK, let me tell you the truth once and for all: thu ioplokio
kjy7n'k, but but isnasmich ty(6,iolopik, no?
> Honestly it seems that would lead to disregarding truth we simply do
> not
> understand, which is not good.
uityju778, thryunbvazo^lo-iolopik, ##@jolopik#
> I don't think we need to be afraid of any level.
> If we avoid this level we will exclude persons from society that
> speak in a
> way that is hardly comprehensible, for example schizophrenics (I
> know one).
This is different. As we might feel some empathy for some person or
group, we can *try* to understand. But we are not obliged to make
sense. You might ended like the duchess. Someone tells her
"thryunbvazo^lo-iolopik, ##", and she will tell you "Oh, you are so
right, my dear".
> Among them it is quite common that they talk a way that is hard to
> comprehend.
*That* is the problem.
> Most people simply won’t bother trying to find the truth in what
> they say and will label them as totally devoid of reason and a
> danger for
> others and themselves (which might be true *sometimes*) and then
> force them
> for months into a mental institution, which is not necessarily
> better then
> prison, especially when you are restrained (which might be done for
> childlike, not really dangerous, behavior already). Often the so
> called
> “mad” people are not being taken serious on any issue and they are
> forced to
> take medications that have awful side effects (even if they are other
> alternatives), because they are supposedly not even able to judge if
> they
> have an unusual adverse reaction or they are lead to suicide because
> they
> feel rejected by all of their surroundings.
That happened to some scientists, like Boltzman, and perhaps Cantor. I
agree with you, special people are easily mistreated. but in some
country you can be send in jail because you have some joint on you,
and being stoned is declared to be a mental illness in some
dictionary. Well, to believe that Marx can be wrong, or Darwin
correct, could send you to jail in some country.
A nice sentence, with which I do disagree is "reason is the truth of
majority", "madness is he truth of minority". But the "truth" might
lie on the contrary, of course (of course?).
>
>
> Bruno Marchal wrote:
>>
>> If you approach that level, you can please everyone for a time
>> but soon enough, everyone will disagree and feel betrayed.
> I am not saying we should pretend to not disagree if we do disagree.
> But we
> still can appreciate some underlying truth in every utterance.
Once people genuinely engage a discussion, they appreciate the truth
of mutual respect and mind opening.
A conversation where people agree is quickly boring. Disagreement is
the salt and pimento of the rich conversation.
What is not nice is *systematic* disagreement, or *systematic*
agreement (unless you are a dictator or something).
There are two very bad sort of parents. Those who say always "yes" to
their children, and those who say always "no".
>
> Bruno Marchal wrote:
>>
>>>
>>>
>>>
>>> Bruno Marchal wrote:
>>>>
>>>>>
>>>>> A have a few questions regarding the non-technical part of
>>>>> explanation,
>>>>> though:
>>>>>
>>>>> What does it mean that the soul falls, falls from what?
>>>>
>>>> From Heaven. From Platonia. From the harmonic static state of the
>>>> universal consciousness to the state with death and taxes.
>>> How come that we don't have memories of falling from heaven?
>>
>> Plotinus begins his treatise by that very question (at least in the
>> Porphyry's assemblage).
>> It is a very good question. The 'official' answer is that we ate the
>> fruit of knowledge and God was pissed of.
>>
>> Some people do, or at least pretend they do have memories of heaven,
>> or sometimes hell. They usually get such memories either 'naturally',
>> or after an extreme conditions (like with Near Death Experience), or
>> after ingesting some mind altering substance.
> These memories are usually not memories of a state of living in
> heaven, but
> of a temporally altered state of mind, though. Or do you know of a
> case of
> pre-birth heaven memories?
Like a platonist, each time I understand a mathematical argument I
feel like having a pre-birth heaven memory. It is Plato's theory of
reminicense: we discover what we already knew. Math is an
introspection, and it can guide us toward "eternal truth".
Now, near death experience and salvia experience can lead us to the
understanding that our consciousness might be more independent of more
contingencies than we usually believe. This might make sense in comp,
I am still not quite sure about this.
>
> Bruno Marchal wrote:
>>
>> The case of salvia divinorum is particularly interesting with respect
>> to your question.
> I had some experience with salvia. It is an interesting herb. One of
> the
> most interesting entheogens it seems.
> My experiences were a bit disappointing, though. I tried maybe 10
> times;
> first with minuscule amounts (that didn’t do anything at all), then
> with as
> much of 30x extract as I was able to take in. I was sometimes giggly,
> relaxed, confused or physically uncomfortable. I had the feeling of
> belonging into another (quiet strange) place, or being (slightly)
> physically
> and mentally pulled into another realm. During some tries I was
> compulsorily
> making movements or repeating syllables/words. During another try if
> felt
> like I was dying during each moment of experience. But none of these
> experiences were really profound.
Try 15X, or perhaps the leaves. You have to be very patient, and
probably explore a bit more that "quiet strange" place, perhaps. I am
studying all reports and videos, people reacts very differently. Most
do not like that at all, and it is a bit normal. I find it very
interesting for the study of consciousness, but you need some passion
for theology. It might be a question of taste.
>
>
> Bruno Marchal wrote:
>>
>> Many experiencers get a distinct feeling that they
>> got information that they are not supposed to know, or to memorize,
>> and still less to make public.
> It is an interesting aspect of the experience. It is hard to judge
> whether
> it is more than a feeling that is induced by the drug, or whether
> there is
> something more profound behind it.
Eventually the experience can be often described as an hallucination
that life is an hallucination. It is very amazing, and you learn about
the capacity of putting in doubt what you believe in the most. The
question is never "is that true?". The answer is in the very uttering
of that question. The plant can broke certainties, and this makes us
more sound. I think. But not everybody is ready, and some care have to
be taken. But it does not last long, and people usually forget the
experience.
>
> Bruno Marchal wrote:
>>
>> You are not supposed to remember "heaven", because ..., well, because
>> if comp is correct, that kind of information belongs to G* minus G.
>> It
>> is true but unbelievable, incommunicable. So, to make them public,
>> makes no sense.
> It conflicts I bit with the observation that seemingly many of the
> people
> having an awakening / enlightenment experience try to convey what they
> realized.
I guess this is due to half or partial enlightenment. The real guru
might be your taxes inspector, or the taxi driver, you will never
know. Above some threshold of such experience you know it makes no
sense to try to share.
It is "almost" obvious: once you meet God (assuming it exists), you
can trust Him or She or That concerning the others, accepting some
usual attribute of God. You can guess somehow that "he" does not need
you to convey anything.
>
> Bruno Marchal wrote:
>>
>> It is the paradox of enlightenment: it has no direct use here at all.
> Otherwise it would maybe have evolved to be common already. But
> maybe it is
> not so easy to evolve a brain that is commonly capable of
> enlightenment
> (while retaining the capability to act like usual) and it really
> would have
> a big use.
> Enlightenment is a very mysterious thing in general. It surely seems
> to be a
> real experience, but why it happens, what it’s purpose is, why it
> happens so
> seldomly or whether it is really such a (o rather *the*) absolute
> view of
> the world and not merely heightened awareness (that due to its
> profoundness
> is mistaken to be an absolute experience rather than one of many
> states of
> consciousness).
I think babies are born enlightened. I think we get enlightened each
night. We are just not supposed to remember that. It might alter the
"cosmic game" in some way. I don't know. I think the universal machine
might be naturally enlightened. That it is the state of universal
innocence, before you get memories and a contingent job. It is the
state before the fall, before the tension between proof and truth
transforms you into a particular person.
>
> Bruno Marchal wrote:
>>
>> Many dismiss the mystical experience as 'just' a brain neuronal
>> firing.
>> Of course, such a dismiss would also be a brain neuronal firing, and
>> to reduce knowledge to such firing makes no sense at all.It is a
>> self-
>> defeating idea. It is as absurd as saying that the theory of
>> relativity is only but ink on paper.
> I agree. I wonder why we are prone to trying to reduce every
> experience to
> neuronal firing, when it seems so obvious that it is something more
> primary.
It is also a category error. A pain is not a neuronal firing. Even if
they are strongly correlated, they are different. A pain is a first
person quale, and a neural firing is a third person (or with comp
first person plural) sharable happening describable with quanta and
numbers. The relation between the two are not obvious, as UDA is
supposed to illustrate, in the mechanist frame.
Bruno
1Z
On Feb 23, 9:46 pm, Bruno Marchal <marc...@ulb.ac.be> wrote:
> On 22 Feb 2011, at 22:14, benjayk wrote:
> Molecules and Cells are formal things. Form is matter, in *some*
> sense.
> People having problem with numbers have been victim of a traumatic
> teaching of math.
> The philosophical question of the existence of any thing, except
> consciousness here and now, is desperately complex.
> That is why I like comp, because it allows (and forces) to derive the
> psychological existence, the theological existence, the physical,
> existence, and the sensible existence from the classical existence of
> numbers, which is simple by definition, if you agree with the use of
> classical logic in number theory.
Bruno Marchal
On 24 Feb 2011, at 01:20, 1Z wrote:
>
>
> On Feb 23, 9:46 pm, Bruno Marchal <marc...@ulb.ac.be> wrote:
>> On 22 Feb 2011, at 22:14, benjayk wrote:
>
>> Molecules and Cells are formal things. Form is matter, in *some*
>> sense.
>
> Form is not *primary* matter in any sense.
That is why I say "in *some* sense.
I do agree more than you could perhaps expect, because the
phenomenological "primary matter" which is apparent for the universal
Löbian machine is indeed typically without form, or with undeterminate
form, given that it is a sum on all forms, against in a technical way
which I will not detail here.
>
>> People having problem with numbers have been victim of a traumatic
>> teaching of math.
>> The philosophical question of the existence of any thing, except
>> consciousness here and now, is desperately complex.
>
>
>
>> That is why I like comp, because it allows (and forces) to derive
>> the
>> psychological existence, the theological existence, the physical,
>> existence, and the sensible existence from the classical existence of
>> numbers, which is simple by definition, if you agree with the use of
>> classical logic in number theory.
>
> What is classical existence?
It is "Ex" as used in classical logic, and in our context, by some
Löbian machine.
If you prefer It is the existence proved in the sound extensions of
Peano Arithmetic.
The other existence can be defined formally trough the modal points of
view. For example, roughly speaking, a physical phenomenon x "exists"
if we can prove BD(Ex(BDp(x)), with the B and D defined like in the
fourth and fifth arithmetical hypostases, and "p" some arithmetical
proposition. Neither physical existence, nor psychological existence
are classical existence. They are rather intuitionist existence and
quantum existence. That follows from the sharp definition I use, and
by using results by Boolos, Goldblatt, and Visser. They remain
classical when seen as epistemological or modal, but they are not
"lived" as such, given that no machine can known what really is its
own "B" predicate (saying "yes" to a doctor *is* a big jump).
Bruno
PS Did you get, or not the step seven? Do you agree that in any
universe running a UD, their "primary matter" does not solve the comp
WR problem, and that physics is reduced to that problem?
Bruno Marchal
OK. I was using communicating in the sense of a provable
communication. You cannot convince someone that you are conscious. If
he decides that you are a zombie, you might better run, probably, but
there is no way you could prove the contrary.
> We merely communicate something that everbody already fundamentally
> knows.
That is correct also, I think.
> Though some like to deny what they already know.
That is bad faith, and is common.
>
>
> Bruno Marchal wrote:
>>
>> But it is not enough. usually people agree with the axiom of Peano
>> Arithmetic, or the initial part of some set theory.
> But Peano Arithmetics is not a non relative absolute base. It is
> relative to
> the meaning we give it and to the existence of some reality. 1+1=2
> can have
> infinite meanings, that all are relative to our interpretation ("If
> I lay
> another apple into the bowl with one apple in it there are two
> apples" is
> one of them) and there being meaning in the first place.
Hmm... Most people agrees on a standard meaning for the natural
numbers, like in the Fermat theorem, or any theorem or conjecture in
number theory, or when you are using numbers in computer science.
1+1 = 2 is true in all those interpretations, even if computer science
we use also some algebra where 1+1=0. That does not contradict that
the standard integer are all different from 0, except 0.
OK.
By incompleteness "provable(false) -> false" is not provable in the
system.
I is true for the machine, but the machine cannot prove it.
> The only difference I could see could be that "M proves
> provable('0=1')" means "provable in another system".
No, by Gödel's construction it really means "provable by the system
itself". It is still third person reference, and the machine is not
necessarily aware that "she is that system". Later we can see she can
*never* be aware of that, but she might trust her doctor, and make
bet, etc.
>
>
> Bruno Marchal wrote:
>>
>>>
>>> And why is inconsistency allowed for machine, but disallowed for
>>> other
>>> objects?
>>
>> Because if a machine proves "0=1", she will be in trouble, but if God
>> or Platonia proves "0=1", then we are *all* in trouble.
> I thought we already established that 0=1 can have a clear meaning
> (equivalent to statements of the form 0*A+B=1*C+D in standard
> arithmetics),
> and so it poses no problem.
?
I have no clue what you are saying here. If "0 = 1" means "I love
chocolate", then of course "0=1" might be true. Again, we use the
standard meaning. Natural numbers and finite sets and finite strings
have a common interpretation rich enough so that we can agree on a
little but powerful set of axioms. This is already less clear for the
notion of sets, although most mathematicians believe so. But for the
natural numbers, we do agree on those axioms, and their correspond to
what has been taught at school.
If some my student defend ideas like 0 = 1, I give them a 0/10, and I
reassure them that it is a good note because if 0 = 1, then 10 = 0. 10
= 1+1+1+1+1+1+1+1+1+1 = 0+0+0+0+0+ 0+0+0+0+0 = 0.
>
> My suggestion is that every statement has such an interpretation.
> Circles
> with edges makes sense if we allow hyperreal numbers as numbers of
> edges and
> lenght of edges, triangles with four sides may mean such a geometric
> object:
> http://commons.wikimedia.org/wiki/File:Triangle-square-area-dev.png
> and that
> God is omnipotent may mean anything.
Logic has been invented for avoiding interpretations as much as
possible, and then for studying mathematically what can be
interpretations, and the relations (Galois connection) between formal
deduction and relations on interpretations. We force the
"propositions" which mean anything to be eliminated, for helping the
progress toward genuine truth and meaning.
We can say that first order logic does succeed in the interpretation
elimination, thanks to a theorem of completeness (not incompleteness)
by Gödel. A formula is a theorem IF and ONLY IF the formula is true in
all interpretations.
Bruno
benjayk
I agree. Some interpretation is needed to make sense of numbers, but we can
easily agree on that. Some more interpretation is needed to make sense of
numbers in the context of practical use (we need relative interpretation of
one as one meter, one joule, one apple, which all are different yet all use
the number one, so in this context 1=1 may be false or undefined because we
might need *different* relative one, just like there are different relative
x).
So our disagreement seems to be quite subtle. It seemed to me you wanted to
make numbers the absolute thing. But when we are really modest it seems to
me we have to admit the meaning in numbers is an intersubjective agreement
in interpretation and we should not be too quick in disregarding seemingly
contradictory statements as completetly false.
See my example of 1=2. It might reveal a deeper sense of the relativity of
numbers (what is one in a context is one billion in another; my one head may
be conceived of consisting of many billions of cells), that is quite
compatible with the sense in 1+1=2.
By the way I have some doubts about 0 being properly conceived of as a
number. It might be more useful to conceive of it as a non-number symbol,
like for example infinity. Zero makes some things in mathematics messy if
interpreted as a number. For example "removable discontinuities" in
functions (I don't know what the right term is in English): If we have the
function (x+1)(x-1)/(x+1)(x+2), this functions is not defined for x=-1, but
in a sense it clearly should be and indeed if we reduce the terms (which
seems to be seen as valid, although we implicitly divide through zero) it is
defined for x=-1. So this suggest that it would be better to give zero a
relative meaning, so that for example 0/0 may mean different things in
different contexts (like the symbol x).
I have no clue how this could be formalized, though. Also it may be I'm just
interpreting some inconsistency that is not there due to my lack of
understanding.
Bruno Marchal wrote:
>
>> It might lead to a language that is too
>> difficult, too little flexible and too much restricting for almost all
>> purposes.
>
> Not really. Formal can be very flexible, like the programming
> languages, but natural language are "naturally" self-transforming, and
> have to adapt.
Yes, I meant flexible in the latter sense of transforming and adapting.
Bruno Marchal wrote:
>
>>
>> I'm not sure, either, if it is - even just in science - always a good
>> approach to try to find mistakes.
>> Maybe there are none and we never really
>> know and trying to do will lead nowhere or there always some
>> mistakes and
>> trying to eliminate them will just spawn new ones. Maybe both are
>> true in
>> some way.
>
> Mistakes are what make us progress. Beware the fatal mistake, like
> flying a plane with a bug in the altimeter.
Right, though some times we have to trust in order to not waste time
controlling everything for the billionth time. Therefore I believe we can
not make it the top priority to find mistakes.
Right, after all every question can be formulated as an problem of
determining existence ("Does there is exist a solution for the problem
that,...").
Bruno Marchal wrote:
>
> That is why I like comp, because it allows (and forces) to derive the
> psychological existence, the theological existence, the physical,
> existence, and the sensible existence from the classical existence of
> numbers, which is simple by definition, if you agree with the use of
> classical logic in number theory.
Honestly I still have doubts about this. The reason is that there is always
the implicit axiom "I am conscious." (for example a bit more explicit in
"Yes, Doctor"), which is incredibly general. I am not sure that if we take
"I am conscious" as axiom, we can say we derived the existence of any mental
state from arithmetics, because we may simply derive what we already know:
"I am conscious" (or "I have an unspecified but existent mental state").
After all we can not say we derived the existence of number 1 by saying
3-2=1, because we had to assume one at the beginning, to make sense of 3 and
2.
But maybe I don't get a crucial thing.
Yes, disagreeing is needed to communicate anything. But so is agreeing, I
would argue.
Bruno Marchal wrote:
>
>> I don't have the experience that "everyone" is doing war to me, when
>> I am
>> very much inclusive in what I believe to be true (or good). Some
>> people,
>> especially those holding unconventional beliefs, will appreciate your
>> openness.
>> You will not have the masses or authorities behind you, though (they
>> like
>> people reiterating their beliefs in strong and authoritative
>> manner). But
>> neither do I want to. Well, maybe in some way I would like to, but
>> then I
>> would probably fall into the trap of authoritarianism myself. There
>> seems to
>> be inherent tension between being believed in and not being
>> authoritative.
>>
>
> Not really. Authoritative argument are symptoms of lies or bad faith.
> If you trust truth (which is hard given that it is unknown) you fear
> nothing.
The problem is that we either formulate total modesty (or rather we get as
close as we can about it and say "I really don't know so I better don't pose
any possibility that might influence you in what you think is right" or
better "..." ) or we pose some truth to be the truth; and as soon as we do
this, some might take us to be an authority. We don't necessarily decide if
we want to be an authority. You don't have to say "I am right and you have
to obey me", we may say "Everything is fine and you can't do anything wrong
and you don't have to do anything" (like some spiritual teachers do) and
thus prevent personal progress, because there are seen as authorities.
Bruno Marchal wrote:
>
>>
>>
>> Bruno Marchal wrote:
>>>
>>> It is far too much "politically correct'.
>>>
>> I don't think I am politically correct.
>> Saying that the state or conventional religion is harmful (or just
>> superfluous) - like I do sometimes - will lead you into much
>> opposition (the
>> second not so much in my particular environment).
>> I am not saying we shouldn't disagree (even vehemently). We may
>> disagree,
>> but at the same time realize that there is some truth to what is
>> being said
>> by the other party. I agree, though, that it is a hard line to walk
>> between
>> disagreeing too much and agreeing to much. Most confusingly sometimes
>> agreeing to much might seem like disagreeing (with disagreeing) too
>> much.
>
> Yes. This can be contingent, but religion is the best thing in the
> world until the power steals it. This lead to unending confusion and
> suffering, and "religion" is made into the worst thing, *especially*
> that some truth remains.
>
> I think religion, that is your relation with truth, is eminently
> private, and that no one can tell what you need to believe in, unless
> your belief harm others.
I would very much like to agree. But unfortunately "harming others" is an
relative and personal term itself. Probably christians believe they are
right in trying to muzzle atheists, because in their mind they are doing
incredible harm (they send people into hell for gods sake!). And they
*really* don't know better.
Ultimately I think no one can tell anyone what to believe in... This is not
a statement of "should" or "should not", but a statement about reality.
Reality does what reality does. And honestly - even if I am careful to whom
I communicate this - I think it ultimately will be seen to be the best
thing, regardless what it is. Otherwise reality would have a sort of mistake
built in that seems totally senseless. And if this is true we really could
believe everything about this world (if it there are totally senseless
things ins this world, maybe one of them is that God does indeed sent many
people to hell forever!).
Bruno Marchal wrote:
>
>>
>>
>> Bruno Marchal wrote:
>>>
>>> Of course, when someone genuinely says that all "non christian people
>>> go to hell", there are many possible "truth" behind the statement,
>>> like "F..ck the atheists", "F..ck the agnostics", "I hate you", "you
>>> have to obey to what I say", "You don't belong to my club", etc.
>> Or "I believe there will be justice and non-Christian people are
>> inherently
>> evil and thus have to go to hell for justice to prevail, even if I
>> don't
>> like it" or "I believe what I have been told, because I cannot
>> believe only
>> what I see myself".
>
> Yes. Lack of self-confidence. It is the children philosophy: p is true
> because my father said so. It should no be used in the academy, I
> think. It can be useful in the army, or with the fire men, when quick
> decision have to be made. For poliltics, it is already much more
> complex.
The problem is that we can totally doubt everything everyone says. So we are
somewhere in the continuum between "believing everything everybody says" and
"believing nothing anybody says". How can we now what is the right point to
stand on?
Bruno Marchal wrote:
>
>>
>>
>> Bruno Marchal wrote:
>>>
>>> On the contrary, when you want to make a point, especially a new one,
>>> it is far better to respect the truth of your opponents, but then you
>>> have to distill what you and your opponent agree on. In science this
>>> works very well in theory (in practice we have often the obligation
>>> to
>>> wait that the opponent dies).
>> "On the contrary"? What you wrote seems to be a confirmation of
>> respecting
>> that there is truth in other people beliefs.
>
> Because then you can extract the partial truth on which you agree, but
> this asks for accepting there is a part where we disagree. There is no
> shame in that, and in absence of convincing argument, we have to know
> we don't know the truth. The genuine respect comes from the genuine or
> sincere doubting.
Yes. I wanted to point to the synthesis of agreement and disagreement, not
to the substitution of agreement for disagreement!
Bruno Marchal wrote:
>
>>
>>
>>
>> Bruno Marchal wrote:
>>>
>>>> I believe the only way we can learn to understand each other is if
>>>> we
>>>> acknowledge the truth in every utterance.
>>>
>>>
>>> That is extreme relativism, and makes truth so trivial that it lost
>>> its meaning.
>> I think truth is a naturally very relative notion, today it might be
>> true
>> that "it rains today" on Monday and it might be false on Tuesday.
>
> That might be absolute truth disguised into indexical statement. "It
> rains today" is "it rains the 23 february 2011" uttered the 23
> february 2011.
Okay, but then it is plausible to say relative truth is absolute truth.
Which again leads to truth being a relative notion.
Bruno Marchal wrote:
>
>> It might
>> be true that x=3 in some context and in some other x=4.
>
> And given that Leibniz convinced us that two quantities (3 and 4)
> equals to some other (x) are equal to each other, we can derive that 3
> = 4.
> Come on, x is a variable. Variables variate. You were obliged to
> mention the context. This does not relativize truth. It just motivates
> us for the study of functions and all that.
I don't know. Maybe truth is like X. Sure, in a weak sense it has absolute
existence (some x does exist), but it's expression takes place in an
infinite number of relative contexts.
It seems to me that the more we discover, we more discover the relativity of
everything (think of Einstein - the relativity of time and space -, quantum
theory - the relativity of physical existence and non-existence - or Gödel -
the relativity of provability).
The absolute seems to remain only as the fact of existence of infinite
relativity.
Bruno Marchal wrote:
>
>> But paradoxically it seems like an absolute notion, too. There
>> really seems
>> to be an absolute truth regardless of circumstances.
>> So I am an extreme relativist, but also an absolutist.
>
> Doubt can rise only from at least a certainty, like consciousness.
Right, but this certainty might be a really really weak one. We are certain
that we are conscious, but in non-lucid dreams we experience how weak the
sense of being conscious can be. It seems to be almost a paradox: There is
no experience of unconsciousness but plausibly almost unconsciousness.
Bruno Marchal wrote:
>
>> It's the same with triviality. Truth is trivial, it simply is true
>> and it is
>> hard to say anymore about it that is surely true. On the other hand,
>> it's
>> highly non-trivial, as seen in this non-trivial world; there seem to
>> be
>> infinite structures in or of truth.
>
> Logic makes that clear. Some truth are trivial (like "p -> p", or "p &
> q -> p", or "0 = 0"), but the notion of truth itself is so complex and
> non trivial that there is no arithmetical predicate for just
> arithmetical truth. Truth is as trivial as God! It has no description.
Or it has every description! It might be too trivial to express in
arithmetics, not too complex.
Maybe it has its important place. Why would it be there, else?
Bruno Marchal wrote:
>
>>
>>
>> Bruno Marchal wrote:
>>>
>>> Language are interpreted plausibly by universal machine (brains,
>>> bodies). The interpretation have to follow constraints to be
>>> sensical.
>> But if there are no constraints they can follow constraints.
>
> ?
It's similar to the omnipotence paradox. If there are no constraints it need
not be a constraint that there are no constraints.
Ok, this is a much more complex question. It is really hard to decide what
to tolerate and what not, and in what way to not tolerate (can we kill
killers?)
Bruno Marchal wrote:
>
> To give a cruel example, if you are not to much sensible, look at this:
>
> http://www.youtube.com/watch?v=aVn856yEd5Q
This is just awful. It is so hard to imagine why it could be necessary that
such acts are done.
Bruno Marchal wrote:
>
> I don't say it is easy to fight them, but I think we have to fight
> them. It makes the fear of some people harmful to themselves and to
> the others. It also put pseudo magical marmalade on top of mystery,
> hiding the fundamental questions and the deeper mystery to people.
Yes, but fighting is maybe best fighting in a very peaceful manner, like
Gandhi. I don't know. It just seems to me we can not use force to overcome
force.
Bruno Marchal wrote:
>
>>
>>
>> Bruno Marchal wrote:
>>>
>>>>
>>>> But that it is impractical to speak in a in an incomprehensible way
>>>> can be
>>>> reconciled with that it still makes sense on some level.
>>>
>>>
>>> Of course.
>> Well, that was my point.
>>
>>
>> Bruno Marchal wrote:
>>>
>>> But that is the reason that we should avoid going to that
>>> level.
>> So we should avoid about talking truth in the seemingly
>> incomprehensible?
>
> OK, let me tell you the truth once and for all: thu ioplokio
> kjy7n'k, but but isnasmich ty(6,iolopik, no?
It is a good example of a sentence that is supposed to be incomprehensible,
but has a quite clear message: "I'm trying to say something you don't
understand." - which is easier to understand then many other things you say,
honestly.
Bruno Marchal wrote:
>
>> Honestly it seems that would lead to disregarding truth we simply do
>> not
>> understand, which is not good.
>
> uityju778, thryunbvazo^lo-iolopik, ##@jolopik#
I don't disregard this. You want to show me "Don't interpret too much where
there is plausibly not much there, like in this sentence". It is a very
useful statement. I am indeed prone to do what you just communicated ;).
It *might* be that some entity residing in your head (beside your usual
self) wants to communicate trough your "nonsense". But it might be better to
not think of such things, or at least to take a good distance from it.
Bruno Marchal wrote:
>
>> I don't think we need to be afraid of any level.
>> If we avoid this level we will exclude persons from society that
>> speak in a
>> way that is hardly comprehensible, for example schizophrenics (I
>> know one).
>
> This is different. As we might feel some empathy for some person or
> group, we can *try* to understand. But we are not obliged to make
> sense. You might ended like the duchess. Someone tells her
> "thryunbvazo^lo-iolopik, ##", and she will tell you "Oh, you are so
> right, my dear".
You seem to like the word "iolopik". Maybe it conveys some deep truth, maybe
it is more connected to the way the letters are arranged on your keyboard,
maybe both. ;)
Bruno Marchal wrote:
>
>> Among them it is quite common that they talk a way that is hard to
>> comprehend.
>
> *That* is the problem.
Yep, but it can't be solved by avoiding to make sense of them.
Bruno Marchal wrote:
>
>>
>>
>> Bruno Marchal wrote:
>>>
>>> If you approach that level, you can please everyone for a time
>>> but soon enough, everyone will disagree and feel betrayed.
>> I am not saying we should pretend to not disagree if we do disagree.
>> But we
>> still can appreciate some underlying truth in every utterance.
>
> Once people genuinely engage a discussion, they appreciate the truth
> of mutual respect and mind opening.
> A conversation where people agree is quickly boring. Disagreement is
> the salt and pimento of the rich conversation.
> What is not nice is *systematic* disagreement, or *systematic*
> agreement (unless you are a dictator or something).
>
> There are two very bad sort of parents. Those who say always "yes" to
> their children, and those who say always "no".
I agree...
...how boring!
I disagree. Wait, but then I agree that we should disagree. So I agree.
Ugh, whatever.
Bruno Marchal wrote:
>
>>
>> Bruno Marchal wrote:
>>>
>>> The case of salvia divinorum is particularly interesting with respect
>>> to your question.
>> I had some experience with salvia. It is an interesting herb. One of
>> the
>> most interesting entheogens it seems.
>> My experiences were a bit disappointing, though. I tried maybe 10
>> times;
>> first with minuscule amounts (that didn’t do anything at all), then
>> with as
>> much of 30x extract as I was able to take in. I was sometimes giggly,
>> relaxed, confused or physically uncomfortable. I had the feeling of
>> belonging into another (quiet strange) place, or being (slightly)
>> physically
>> and mentally pulled into another realm. During some tries I was
>> compulsorily
>> making movements or repeating syllables/words. During another try if
>> felt
>> like I was dying during each moment of experience. But none of these
>> experiences were really profound.
>
>
> Try 15X, or perhaps the leaves. You have to be very patient, and
> probably explore a bit more that "quiet strange" place, perhaps.
I meant "quite", but "quiet" fits to.
I'll probably won't try it again. It is not that I disliked the experiences
or didn't find them interesting, but I am a bit worried on the effect those
excursions might have on my psyche. As said, I'm prone to overpinterpreting
things (coincidences etc - I had some very strange ones, but probably
everybody had), I feel psychedelics might exacerbate that. Salvia seems to
be less problematic than shrooms or weed in this regard, but I think it is
better to be careful about this.
I am a bit sad about this, but well...
Bruno Marchal wrote:
>
>>
>>
>> Bruno Marchal wrote:
>>>
>>> Many experiencers get a distinct feeling that they
>>> got information that they are not supposed to know, or to memorize,
>>> and still less to make public.
>> It is an interesting aspect of the experience. It is hard to judge
>> whether
>> it is more than a feeling that is induced by the drug, or whether
>> there is
>> something more profound behind it.
>
> Eventually the experience can be often described as an hallucination
> that life is an hallucination. It is very amazing, and you learn about
> the capacity of putting in doubt what you believe in the most.
Which might be very uncomfortable or even dangerous at times. If you are
lead to doubt everything you might tend to consider arbitrary things to be
true, because you can not - psychologically - doubt everything.
Ultimately doubting everything might lead our perceptions to becoming
inaccurate, because our internal models of the world (that are necessary to
function normally) are fundamentally questioned beyond just intellectual
doubt.
I experienced this (though thankfully I don't hallucinate when being sober
like some psychotic people do).
Maybe the salvia reality is some emergency reality that emerges when the
usual models of reality are doubted (even our very deep indentity patterns).
The secret truth might be "doubt everything" and it might be kept secret for
important reasons, because it might only be locally true in an environment
where things are very unbelievable and should be doubted almost universally
(eg salvia land) - and might lead to destruction of the local person if it
is too much remembered. Maybe you would go so terribly insane that you would
make the rest of the world go insane too (by downloading very very
convincing, yet extremely false arguments, from the salvia realm - which is
crazy enough to generate such arguments), and thus make the world a dream
like world full of white rabbit generating "Gods", which would explain why
you don't seem to go insane in our local world :D. Dreams and drug
experiences might be the tool to include / distribute such white rabbit
worlds (or pieces thereof) in our more consistent world.
Also heaven and hell (not in the christian sense of course) and
reincarnation might be emergency realities that are there as a
semi-consistent bridge to more consistent histories (maybe some advanced
technological future, where we can learn to locally manifest through
development and with the help of computers and live forever in a more
plausible way than in salvia land or heaven).
Just some speculation - I guess I'm wildly creative today ;).
Do you think it is plausible that there is "absolute" enlightenment? It
seems extremely akward to me.
It might be more true that we all are enlightened all the time, and there
are degrees heightened self-awareness that are interpreted as enlightenment.
--
View this message in context: http://old.nabble.com/Platonia-tp30955253p31007936.html
Bruno Marchal
Yes. It is the difficulty of applied science.
>
> So our disagreement seems to be quite subtle. It seemed to me you
> wanted to
> make numbers the absolute thing. But when we are really modest it
> seems to
> me we have to admit the meaning in numbers is an intersubjective
> agreement
> in interpretation and we should not be too quick in disregarding
> seemingly
> contradictory statements as completetly false.
We try to understand things by reducing them to things we already
consider having a good understanding of.
If not we are doing obstructive philosophy, cutting the hair kind of
activity.
> See my example of 1=2. It might reveal a deeper sense of the
> relativity of
> numbers (what is one in a context is one billion in another; my one
> head may
> be conceived of consisting of many billions of cells), that is quite
> compatible with the sense in 1+1=2.
Remember that our discussion evolves initially from Peter (1Z)
apparent lack of understanding that once we accept that the brain or
body can be described at some level as a digital machine, then the
physical science are no more the fundamental or basic science, and
that to solve the mind-body problem we have to solve the body problem.
It means also that we have to backtrack 1500 years in the theological
science.
But this does suppose the kind of understanding that 1 is different
from 2. Like I guess you do understand that in physics E = mc^2 does
not imply that E = mc.
>
> By the way I have some doubts about 0 being properly conceived of as a
> number. It might be more useful to conceive of it as a non-number
> symbol,
> like for example infinity. Zero makes some things in mathematics
> messy if
> interpreted as a number. For example "removable discontinuities" in
> functions (I don't know what the right term is in English): If we
> have the
> function (x+1)(x-1)/(x+1)(x+2), this functions is not defined for
> x=-1, but
> in a sense it clearly should be and indeed if we reduce the terms
> (which
> seems to be seen as valid, although we implicitly divide through
> zero) it is
> defined for x=-1. So this suggest that it would be better to give
> zero a
> relative meaning, so that for example 0/0 may mean different things in
> different contexts (like the symbol x).
> I have no clue how this could be formalized, though. Also it may be
> I'm just
> interpreting some inconsistency that is not there due to my lack of
> understanding.
Such problem are usually handled in an analysis course.
>
>
>
> Bruno Marchal wrote:
>>
>>> It might lead to a language that is too
>>> difficult, too little flexible and too much restricting for almost
>>> all
>>> purposes.
>>
>> Not really. Formal can be very flexible, like the programming
>> languages, but natural language are "naturally" self-transforming,
>> and
>> have to adapt.
> Yes, I meant flexible in the latter sense of transforming and
> adapting.
OK. Once you accept arbitrary self-transformation, the distinction
between formal and non formal becomes relative.
>
>
>
> Bruno Marchal wrote:
>>
>>>
>>> I'm not sure, either, if it is - even just in science - always a
>>> good
>>> approach to try to find mistakes.
>>> Maybe there are none and we never really
>>> know and trying to do will lead nowhere or there always some
>>> mistakes and
>>> trying to eliminate them will just spawn new ones. Maybe both are
>>> true in
>>> some way.
>>
>> Mistakes are what make us progress. Beware the fatal mistake, like
>> flying a plane with a bug in the altimeter.
> Right, though some times we have to trust in order to not waste time
> controlling everything for the billionth time. Therefore I believe
> we can
> not make it the top priority to find mistakes.
OK.
OK.
>
>
> Bruno Marchal wrote:
>>
>> That is why I like comp, because it allows (and forces) to derive
>> the
>> psychological existence, the theological existence, the physical,
>> existence, and the sensible existence from the classical existence of
>> numbers, which is simple by definition, if you agree with the use of
>> classical logic in number theory.
> Honestly I still have doubts about this. The reason is that there is
> always
> the implicit axiom "I am conscious." (for example a bit more
> explicit in
> "Yes, Doctor"), which is incredibly general.
The statement "I am conscious" is not just general. It cannot be
formalized at all, and is not part of any scientific discourse (as
opposed to the sentence "I am conscious"). But saying that my
consciousness is invariant for a transformation (like "yes doctor") is
not so much general. It is a highly non trivial act of faith capable
of deciding eventually between Aristotle, and Plato.
> I am not sure that if we take
> "I am conscious" as axiom,
I don't do that.
> we can say we derived the existence of any mental
> state from arithmetics, because we may simply derive what we already
> know:
> "I am conscious" (or "I have an unspecified but existent mental
> state").
"Yes doctor" is NOT I am conscious. It is more "I bet I will remain
fine and well with my new artificial brain. And the consequence are
not trivial. It begins by indeterminacy and end with immateriality,
and the idea that the laws of physics have a reason (indeed an
arithmetical reason).
> After all we can not say we derived the existence of number 1 by
> saying
> 3-2=1, because we had to assume one at the beginning, to make sense
> of 3 and
> 2.
It depends of the theory chosen.
>
> But maybe I don't get a crucial thing.
Digital Mechanism is not a trivial hypothesis. It contradicts the part
of the theology of Aristotle used by most believers and non believers
since 1500 years. (To be short).
Sure. There is a need for a good balance, to make things profitable.
That is why in (ideal) Science we never do that. We just never posit
something as being true. We posit things, and if you don't like them,
you can always propose another theory. Scientist pretending that we
know things, per science, are philosophers confusing pseudo-religion
with science. That's human weakness, not science weakness.
> We don't necessarily decide if
> we want to be an authority. You don't have to say "I am right and
> you have
> to obey me", we may say "Everything is fine and you can't do
> anything wrong
> and you don't have to do anything" (like some spiritual teachers do)
> and
> thus prevent personal progress, because there are seen as authorities.
We can follows authorities, although we are the only judge to evaluate
if they are authorities. In science, authorities never use
authoritative arguments. The media and bad popularization book does
that all the time, but they are deeply wrong. They fall in pseudo-
religion.
It is very important to distinguish "authority" and "authoritative
argument". The first are appreciable, the second are perverse in all
situations.
When authoritative argument are used for the bad cause, it leads to
the possible good.
When authoritative argument are used for the good cause, it leads to
the very bad.
Why? Because authoritative argument kills its cause. When the cause is
bad, it kills the bad, which is good, and when the cause is good, it
kills the good, which is bad.
Authorities never uses authoritative arguments.
I am not sure about that. This form of relativism is a way to escape
our responsabilities. So we can continue to sell guns, alcohol, etc.
> Probably christians believe they are
> right in trying to muzzle atheists, because in their mind they are
> doing
> incredible harm (they send people into hell for gods sake!). And they
> *really* don't know better.
We have the choice: to eat or to be eaten. To eat is good, to be eaten
is (usually) bad.
To suggest that someone can go in hell because he does not believe, or
take for granted, the last theory in fashion, is terrorism.
>
> Ultimately I think no one can tell anyone what to believe in...
OK.
> This is not
> a statement of "should" or "should not", but a statement about
> reality.
> Reality does what reality does.
Ah! That looks like 1 = 1. I do agree very much.
> And honestly - even if I am careful to whom
> I communicate this - I think it ultimately will be seen to be the best
> thing, regardless what it is. Otherwise reality would have a sort of
> mistake
> built in that seems totally senseless. And if this is true we really
> could
> believe everything about this world (if it there are totally senseless
> things ins this world, maybe one of them is that God does indeed
> sent many
> people to hell forever!).
Yes. And may be God send all the Christians to hell. You are a bit too
vague.
Of course the idea "give me money or I can assure you that God will
send you to hell" is a very clever idea, in the world of the bandits.
This is no better than saying that cannabis is bad for the health, to
sell you expensive addictive unhealthy product at his place.
A better idea consists in trying to figure out what can be the most
plausible truth. It is not so hard to guess it, but it might be hard
to communicate it.
>
>
> Bruno Marchal wrote:
>>
>>>
>>>
>>> Bruno Marchal wrote:
>>>>
>>>> Of course, when someone genuinely says that all "non christian
>>>> people
>>>> go to hell", there are many possible "truth" behind the statement,
>>>> like "F..ck the atheists", "F..ck the agnostics", "I hate you",
>>>> "you
>>>> have to obey to what I say", "You don't belong to my club", etc.
>>> Or "I believe there will be justice and non-Christian people are
>>> inherently
>>> evil and thus have to go to hell for justice to prevail, even if I
>>> don't
>>> like it" or "I believe what I have been told, because I cannot
>>> believe only
>>> what I see myself".
>>
>> Yes. Lack of self-confidence. It is the children philosophy: p is
>> true
>> because my father said so. It should no be used in the academy, I
>> think. It can be useful in the army, or with the fire men, when quick
>> decision have to be made. For poliltics, it is already much more
>> complex.
> The problem is that we can totally doubt everything everyone says.
That's extreme relativism. But we can doubt a lot, and that is a
reason to find a common solid base, like with elementary arithmetic,
or even part of physics.
> So we are
> somewhere in the continuum between "believing everything everybody
> says" and
> "believing nothing anybody says". How can we now what is the right
> point to
> stand on?
By listening to music, doing mathematics, smoking psychedelics or
doing sports perhaps, and encouraging free personal thinking, with
exercises (not with "beautiful ideas").
That's a bit like the greeks did in science, and like we continue to
do in the natural science (only, alas).
We have to fight, or defend ourself, against all form of authoritative
arguments. That's all.
Not against authorities, against authoritative arguments.
Perhaps we should make them illegal when used against someone being
more than 7 years old. With the little children, I have no ideas. It
is too much complex. I trust the mother's intuition and love.
OK.
>
>
> Bruno Marchal wrote:
>>
>>>
>>>
>>>
>>> Bruno Marchal wrote:
>>>>
>>>>> I believe the only way we can learn to understand each other is if
>>>>> we
>>>>> acknowledge the truth in every utterance.
>>>>
>>>>
>>>> That is extreme relativism, and makes truth so trivial that it lost
>>>> its meaning.
>>> I think truth is a naturally very relative notion, today it might be
>>> true
>>> that "it rains today" on Monday and it might be false on Tuesday.
>>
>> That might be absolute truth disguised into indexical statement. "It
>> rains today" is "it rains the 23 february 2011" uttered the 23
>> february 2011.
> Okay, but then it is plausible to say relative truth is absolute
> truth.
> Which again leads to truth being a relative notion.
If you make *all* truth relative, then you will contradict yourself at
some point. Descartes saw this, I think.
Truth is not a relative notion, but all relation that we can have with
truth will be relative, except perhaps one (consciousness).
>
>
>
> Bruno Marchal wrote:
>>
>>> It might
>>> be true that x=3 in some context and in some other x=4.
>>
>> And given that Leibniz convinced us that two quantities (3 and 4)
>> equals to some other (x) are equal to each other, we can derive
>> that 3
>> = 4.
>> Come on, x is a variable. Variables variate. You were obliged to
>> mention the context. This does not relativize truth. It just
>> motivates
>> us for the study of functions and all that.
> I don't know. Maybe truth is like X. Sure, in a weak sense it has
> absolute
> existence (some x does exist), but it's expression takes place in an
> infinite number of relative contexts.
That is why we search (and found) deductive rules which are valid
independently of the context.
First order logic is such a frame.
> It seems to me that the more we discover, we more discover the
> relativity of
> everything (think of Einstein - the relativity of time and space -,
> quantum
> theory - the relativity of physical existence and non-existence - or
> Gödel -
> the relativity of provability).
> The absolute seems to remain only as the fact of existence of infinite
> relativity.
Yes. And in the comp theory, the relativity in physics is a special
case of the relativity in number theory, which has the advantage of
putting physical "relativities" on a very solid base (elementary
arithmetic).
>
>
> Bruno Marchal wrote:
>>
>>> But paradoxically it seems like an absolute notion, too. There
>>> really seems
>>> to be an absolute truth regardless of circumstances.
>>> So I am an extreme relativist, but also an absolutist.
>>
>> Doubt can rise only from at least a certainty, like consciousness.
> Right, but this certainty might be a really really weak one. We are
> certain
> that we are conscious, but in non-lucid dreams we experience how
> weak the
> sense of being conscious can be.
I don't think so. Why? We might only experience how weak our belief in
some reality can be, but not on the reality of our consciousness.
> It seems to be almost a paradox: There is
> no experience of unconsciousness but plausibly almost unconsciousness.
I doubt "unconsciousness" has a clear meaning. Like infinite, the
"unconscious" can be a too large concept, so that its informal use
might lead to abuse of language if not contradiction.
>
>
> Bruno Marchal wrote:
>>
>>> It's the same with triviality. Truth is trivial, it simply is true
>>> and it is
>>> hard to say anymore about it that is surely true. On the other hand,
>>> it's
>>> highly non-trivial, as seen in this non-trivial world; there seem to
>>> be
>>> infinite structures in or of truth.
>>
>> Logic makes that clear. Some truth are trivial (like "p -> p", or
>> "p &
>> q -> p", or "0 = 0"), but the notion of truth itself is so complex
>> and
>> non trivial that there is no arithmetical predicate for just
>> arithmetical truth. Truth is as trivial as God! It has no
>> description.
> Or it has every description!
It has none. You can go from none, to an arbitrary one. Neither about
truth, nor about God.
> It might be too trivial to express in
> arithmetics, not too complex.
Well that "1+1 = 2" is true is easily expressible in arithmetic,
basically by "1+1=2". That is the "p" I used in the hypostases. What
cannot be defined is a truth predicate, so that truth('p') would be
provably equivalent with p. If you do that, you make the Epimenides
paradox into a contradiction. That's Tarski's discovery. It entails
that no machine can be both arithmetically sound and capable of
defining its own truth predicate, nor can such a machine define its
own notion of knowledge (accepting the classical theory of knowledge).
To make money by selling fears to gullible people. Notably. It has the
same role as the devil, evil, and eventually the jaws of the lion. It
has its role, but we have to protect ourselves against it.
>
>
>
> Bruno Marchal wrote:
>>
>>>
>>>
>>> Bruno Marchal wrote:
>>>>
>>>> Language are interpreted plausibly by universal machine (brains,
>>>> bodies). The interpretation have to follow constraints to be
>>>> sensical.
>>> But if there are no constraints they can follow constraints.
>>
>> ?
> It's similar to the omnipotence paradox. If there are no constraints
> it need
> not be a constraint that there are no constraints.
Worst than that. It needs to be not-a-constraint, but it *is* a
constraint. The omnipotence paradox just shows that omnipotence does
not exist. I would say.
"Omnipotence" still exist as a concept, but that is different: a
concept can exist without being capable of any instantiation in any
possible world.
In case of immediate legitimate self-defense. Perhaps.
>
>
> Bruno Marchal wrote:
>>
>> To give a cruel example, if you are not to much sensible, look at
>> this:
>>
>> http://www.youtube.com/watch?v=aVn856yEd5Q
> This is just awful. It is so hard to imagine why it could be
> necessary that
> such acts are done.
They believe that burying children alive can help the gods to make a
good harvest possible, so that more children can eat.
Human history is full of drama of this kind, favored by superstition.
We can't fight against that, but we can promote values by examples, if
we can.
Placebo can work, but I would distinguish it from superstition.
>
>
>
>
> Bruno Marchal wrote:
>>
>> I don't say it is easy to fight them, but I think we have to fight
>> them. It makes the fear of some people harmful to themselves and to
>> the others. It also put pseudo magical marmalade on top of mystery,
>> hiding the fundamental questions and the deeper mystery to people.
> Yes, but fighting is maybe best fighting in a very peaceful manner,
> like
> Gandhi. I don't know. It just seems to me we can not use force to
> overcome
> force.
Here I totally agree with you, and when I said "fight" I should have
added without imposing our views, because this would only aggravates
the situation. Sure. Force is for self-defense, not for convincing
people of anything.
>
>
> Bruno Marchal wrote:
>>
>>>
>>>
>>> Bruno Marchal wrote:
>>>>
>>>>>
>>>>> But that it is impractical to speak in a in an incomprehensible
>>>>> way
>>>>> can be
>>>>> reconciled with that it still makes sense on some level.
>>>>
>>>>
>>>> Of course.
>>> Well, that was my point.
>>>
>>>
>>> Bruno Marchal wrote:
>>>>
>>>> But that is the reason that we should avoid going to that
>>>> level.
>>> So we should avoid about talking truth in the seemingly
>>> incomprehensible?
>>
>> OK, let me tell you the truth once and for all: thu ioplokio
>> kjy7n'k, but but isnasmich ty(6,iolopik, no?
> It is a good example of a sentence that is supposed to be
> incomprehensible,
> but has a quite clear message: "I'm trying to say something you don't
> understand." - which is easier to understand then many other things
> you say,
> honestly.
That is not correct. The correct meaning was "When will you stop to
cut the air, my friend?"
Sorry for not having been clear.
;-)
>
>
> Bruno Marchal wrote:
>>
>>> Honestly it seems that would lead to disregarding truth we simply do
>>> not
>>> understand, which is not good.
>>
>> uityju778, thryunbvazo^lo-iolopik, ##@jolopik#
> I don't disregard this. You want to show me "Don't interpret too
> much where
> there is plausibly not much there, like in this sentence". It is a
> very
> useful statement. I am indeed prone to do what you just
> communicated ;).
> It *might* be that some entity residing in your head (beside your
> usual
> self) wants to communicate trough your "nonsense". But it might be
> better to
> not think of such things, or at least to take a good distance from it.
Not always. I love nonsense. But it is fair sometimes to say "and now
we do fiction", or "this was a joke". Or to use some
"smiley" (although some people can interpret directly a smiley as a
mockery).
>
>
> Bruno Marchal wrote:
>>
>>> I don't think we need to be afraid of any level.
>>> If we avoid this level we will exclude persons from society that
>>> speak in a
>>> way that is hardly comprehensible, for example schizophrenics (I
>>> know one).
>>
>> This is different. As we might feel some empathy for some person or
>> group, we can *try* to understand. But we are not obliged to make
>> sense. You might ended like the duchess. Someone tells her
>> "thryunbvazo^lo-iolopik, ##", and she will tell you "Oh, you are so
>> right, my dear".
> You seem to like the word "iolopik". Maybe it conveys some deep
> truth, maybe
> it is more connected to the way the letters are arranged on your
> keyboard,
> maybe both. ;)
No. It means "my friend". "iolopy" means friend, iolopik means "my
friend", on an imaginary planet, gravitating around an imaginary sun,
in an imaginary galaxy, in an imaginary cluster of galaxies, in an
imaginary branch of an imaginary solution of Schroedinger equation, if
that exists.
>
>
> Bruno Marchal wrote:
>>
>>> Among them it is quite common that they talk a way that is hard to
>>> comprehend.
>>
>> *That* is the problem.
> Yep, but it can't be solved by avoiding to make sense of them.
I am not sure. We can learn by finding sense, but also by discarding
sense.
>
>
>
> Bruno Marchal wrote:
>>
>>>
>>>
>>> Bruno Marchal wrote:
>>>>
>>>> If you approach that level, you can please everyone for a time
>>>> but soon enough, everyone will disagree and feel betrayed.
>>> I am not saying we should pretend to not disagree if we do disagree.
>>> But we
>>> still can appreciate some underlying truth in every utterance.
>>
>> Once people genuinely engage a discussion, they appreciate the truth
>> of mutual respect and mind opening.
>> A conversation where people agree is quickly boring. Disagreement is
>> the salt and pimento of the rich conversation.
>> What is not nice is *systematic* disagreement, or *systematic*
>> agreement (unless you are a dictator or something).
>>
>> There are two very bad sort of parents. Those who say always "yes" to
>> their children, and those who say always "no".
> I agree...
>
> ...how boring!
> I disagree. Wait, but then I agree that we should disagree. So I
> agree.
>
> Ugh, whatever.
OK.
I meant "quite" to. Just a spelling mistake. Glad you find salvia quiet.
> I'll probably won't try it again. It is not that I disliked the
> experiences
> or didn't find them interesting, but I am a bit worried on the
> effect those
> excursions might have on my psyche. As said, I'm prone to
> overpinterpreting
> things (coincidences etc - I had some very strange ones, but probably
> everybody had), I feel psychedelics might exacerbate that. Salvia
> seems to
> be less problematic than shrooms or weed in this regard, but I think
> it is
> better to be careful about this.
>
> I am a bit sad about this, but well...
I agree that weed and psychedelic can encourage over-interpretation.
It is not helpful when people have a psychotic tendency. I think also
that salvia might be less problematic with that respect, but I am not
entirely sure. It can depend of people, age, mindset, etc. Salvia is
very "perturbating", but probably less so that quantum mechanics,
computer science or mathematical logic ...
>
>
> Bruno Marchal wrote:
>>
>>>
>>>
>>> Bruno Marchal wrote:
>>>>
>>>> Many experiencers get a distinct feeling that they
>>>> got information that they are not supposed to know, or to memorize,
>>>> and still less to make public.
>>> It is an interesting aspect of the experience. It is hard to judge
>>> whether
>>> it is more than a feeling that is induced by the drug, or whether
>>> there is
>>> something more profound behind it.
>>
>> Eventually the experience can be often described as an hallucination
>> that life is an hallucination. It is very amazing, and you learn
>> about
>> the capacity of putting in doubt what you believe in the most.
> Which might be very uncomfortable or even dangerous at times.
Very uncomfortable yes.
Dangerous? I am not sure. Unless you handle heavy machinery, drive a
car, etc. But this makes no sense with salvia.
> If you are
> lead to doubt everything you might tend to consider arbitrary things
> to be
> true, because you can not - psychologically - doubt everything.
> Ultimately doubting everything might lead our perceptions to becoming
> inaccurate, because our internal models of the world (that are
> necessary to
> function normally) are fundamentally questioned beyond just
> intellectual
> doubt.
> I experienced this (though thankfully I don't hallucinate when being
> sober
> like some psychotic people do).
When, under psychoactive substance, people needs to be not too much
naive. That is why it is not for the children.
But even for very young people, I think salvia is far less dangerous
than alcohol, and that we could save many lives by daring to tell
parents about this.
That's what do movies, and art in general. Just that with some
substance you can trig your brain doing the work for you, like with
sleep. The rest will depend on many factors. American kids don't like
salvia, but they love to film their friends under it and send the
movie to YouTube. And then I find *this* very interesting, both on
salvia and on humans. Many salvia intakes are done in the worst
recommendable ways, and the worst which happens, rarely, are some
bruises and nightmarish feeling which does not last long. It is the
problem with salvia, we don't really remember the key part of the
experiences. It is of interest for "metaphysicians" and "theologians".
Loving salvia = loving the *very* deep questions, I would say.
>
> Also heaven and hell (not in the christian sense of course) and
> reincarnation might be emergency realities that are there as a
> semi-consistent bridge to more consistent histories (maybe some
> advanced
> technological future, where we can learn to locally manifest through
> development and with the help of computers and live forever in a more
> plausible way than in salvia land or heaven).
>
> Just some speculation - I guess I'm wildly creative today ;).
>
If mechanism is true, we can say that we are plausibly already in the
'matrix'. No need to wait for an advanced technological future, we are
already there.
I don't know if mechanism is true, but the 'matrix' has a well defined
structure which might be studied.
It is a very complex subject. The word "enlightenment" is very fuzzy,
and can have already many different nuances among the same school of
buddhism, so it is hard to be precise. In that sense, the expression
"absolute enlightenment" might just be an example of 1004 fallacy. I
might answer "Do you mean really 'real absolute enlightenment', or
what?". If we are machine, we cannot communicate that we are
consistent, and we cannot express that we are sound. We might be able
to prove that any machine pretending to be enlightened is mistaken
about this, perhaps, but I doubt that "enlightenment" can be
expressed. It is an experience of consciousness usually described as
non describable, and ineffable. Just talking about it can lead to
contradiction. The shorter description of enlightenment is the
realisation that "I = GOD", but the two words around "=" are not
really describable.
This reminds me Damascius' theory of the ONE. The ONE, explains
Damascius, is so ineffable that even just one sentence about it will
completely miss the point. Oops.
Bruno
Pzomby
Language gives meaning to the numbers as in their operations;
functions, units of measurements (kilo, meter, ounce, kelvin etc.).
Numbers alone may symbolize some fundamental describable matter and
forces but a complete and coherent TOE should include elevated human
consciousness beyond the primitive which in itself requires a
relatively sophisticated language to give meaning to the numbers and
their operations.
Would not any TOE describing the universe appears to require human
sophisticated language using referent nouns, (and conjunctions,
adjectives and verbs etc.) to give meaning to the numbers and their
functions and operations?
You repeatedly refer to “addition and multiplication”. Is not
multiplication repeated addition or is there another separate
principle involved with multiplication?
benjayk
Bruno Marchal wrote:
>
>
>
>>
>> So our disagreement seems to be quite subtle. It seemed to me you
>> wanted to
>> make numbers the absolute thing. But when we are really modest it
>> seems to
>> me we have to admit the meaning in numbers is an intersubjective
>> agreement
>> in interpretation and we should not be too quick in disregarding
>> seemingly
>> contradictory statements as completetly false.
>
> We try to understand things by reducing them to things we already
> consider having a good understanding of.
> If not we are doing obstructive philosophy, cutting the hair kind of
> activity.
We may also understand things by seeing their truth is not (at least
practically) reducible to anything we have a good understanding of.
If we understand consciousness can not be reduced to anything else, we
learnt something.
I thought you are not a reductionist?
Bruno Marchal wrote:
>
> But this does suppose the kind of understanding that 1 is different
> from 2.
Of course I understand that 1 is different than 2. But nevertheless I can
also makes sense of 1=2 (for example it might express the same as 1X=2X,
that is, the object we are talking about has no distinction of quantities).
I also see the difference between lion and animal. But it nevertheless makes
sense to say that a lion is an animal or that an animal is a lion.
Bruno Marchal wrote:
>
>>
>> By the way I have some doubts about 0 being properly conceived of as a
>> number. It might be more useful to conceive of it as a non-number
>> symbol,
>> like for example infinity. Zero makes some things in mathematics
>> messy if
>> interpreted as a number. For example "removable discontinuities" in
>> functions (I don't know what the right term is in English): If we
>> have the
>> function (x+1)(x-1)/(x+1)(x+2), this functions is not defined for
>> x=-1, but
>> in a sense it clearly should be and indeed if we reduce the terms
>> (which
>> seems to be seen as valid, although we implicitly divide through
>> zero) it is
>> defined for x=-1. So this suggest that it would be better to give
>> zero a
>> relative meaning, so that for example 0/0 may mean different things in
>> different contexts (like the symbol x).
>> I have no clue how this could be formalized, though. Also it may be
>> I'm just
>> interpreting some inconsistency that is not there due to my lack of
>> understanding.
>
> Such problem are usually handled in an analysis course.
Unfortunately no, at least not in school. As I remember it came down to "We
get a function '(x-1)/(x+2)' that removes the discontinuity by analyzing the
limits at the undefined x", but this doesn't answer the question why there
is function that "should be" - but isn't - defined at a point in the first
place. Maybe it is just an inappropriate use of intuition and there is no
sense in that the function "should be" defined any more than 3/0 should be
defined.
Bruno Marchal wrote:
>
>>
>>
>> Bruno Marchal wrote:
>>>
>>> That is why I like comp, because it allows (and forces) to derive
>>> the
>>> psychological existence, the theological existence, the physical,
>>> existence, and the sensible existence from the classical existence of
>>> numbers, which is simple by definition, if you agree with the use of
>>> classical logic in number theory.
>> Honestly I still have doubts about this. The reason is that there is
>> always
>> the implicit axiom "I am conscious." (for example a bit more
>> explicit in
>> "Yes, Doctor"), which is incredibly general.
>
> The statement "I am conscious" is not just general. It cannot be
> formalized at all, and is not part of any scientific discourse (as
> opposed to the sentence "I am conscious").
I'm not so sure. Isn't saying "I am conscious" formalizing that I am
conscious? Intuitively it seems perfectly vald.
Also, if we cannot formalize "I am conscious" can we formalize anything at
all? Can we formalize some content of consciousness without formalizing "I
am conscious"? And if we can't formalize content of consciousness what can
we formalize? After all we just have our consciousness and its content.
Bruno Marchal wrote:
>
>> I am not sure that if we take
>> "I am conscious" as axiom,
>
> I don't do that.
This is a bit like saying if we have the axiom "There is a number 0 and a
successor of 0, s(0)", there is no axiom "There is a number 0".
If we say "Yes doctor" we say "I bet that if I get an artificial brain my
state of consciousness will remain enough invariant so that I feel myself to
be the same person as before".
My consciousness can only remain invariant if I am conscious in the first
place, so the axiom "I am conscious" is included.
Otherwise you make the same mistake as a scientists using numbers in their
theories but denying the existence of numbers (and so ultimately the axioms
they use).
Bruno Marchal wrote:
>
>>
>> But maybe I don't get a crucial thing.
>
> Digital Mechanism is not a trivial hypothesis. It contradicts the part
> of the theology of Aristotle used by most believers and non believers
> since 1500 years. (To be short).
Yes, the basic idea seems easy but if you dig deeper you see that if we take
consquences in account it becomes really difficult.
If we propose a theory isn't it implied that we think the theory is true?
Bruno Marchal wrote:
>
> We posit things, and if you don't like them,
> you can always propose another theory. Scientist pretending that we
> know things, per science, are philosophers confusing pseudo-religion
> with science. That's human weakness, not science weakness.
I don't think we can seperate science and science as praticed by humans.
Science is a human creation (at least relatively here on earth).
Bruno Marchal wrote:
>
>> We don't necessarily decide if
>> we want to be an authority. You don't have to say "I am right and
>> you have
>> to obey me", we may say "Everything is fine and you can't do
>> anything wrong
>> and you don't have to do anything" (like some spiritual teachers do)
>> and
>> thus prevent personal progress, because there are seen as authorities.
>
>
> We can follows authorities, although we are the only judge to evaluate
> if they are authorities. In science, authorities never use
> authoritative arguments. The media and bad popularization book does
> that all the time, but they are deeply wrong. They fall in pseudo-
> religion.
> It is very important to distinguish "authority" and "authoritative
> argument". The first are appreciable, the second are perverse in all
> situations.
> When authoritative argument are used for the bad cause, it leads to
> the possible good.
> When authoritative argument are used for the good cause, it leads to
> the very bad.
> Why? Because authoritative argument kills its cause. When the cause is
> bad, it kills the bad, which is good, and when the cause is good, it
> kills the good, which is bad.
I believe in somse sense we have to appeal to an authority to convey
something. We believe things because of authority, if it is only the
authority of reality.
But then we are lead to the next problem: Either we leave undefined what
reality is, in which case we don't convey much - or we use some model of
reality which than acts as the authority.
Usually the authority doesn't say "Believe me because I say I am right", but
"Believe me because <some greater authority> shows I'm right". The priest
appeals to God as the authority, the politician in democracies to the "will
of the people", the scientist to controlled experiments, the mathematician
to mathematicial truth.
If we don't explicitly say what our authority is we only cover up what our
authority is, which makes it harder to check if our authority is right.
So I think the good thing in science is that we make clear our authorities.
We say we believe because of the results of controlled experiments. Or
because of our faith in the axioms of mathematics.
In religion (or pseudo-religion if you like that term better) they say God
is the authority, but noone really says that their God is in large parts
just a collection of ideas from people in the far past.
Bruno Marchal wrote:
>
> Authorities never uses authoritative arguments.
So the church - that is an authority to many people - doesn't appeal to God
in their arguments?
Maybe you wish people saw as authorities only people that don't use
authoritative arguments.
Maybe it is good to sell guns and alcohol if you are a decent person.
Otherwise non-decent persons will do that, which will lead to even worse
outcomes.
What ultimately causes harm or reduces harm is a more difficult question
than it might seem at first glance. Maybe sometimes the only way to avoid
great harm is to cause relatively small harm.
Perhaps even war reduces harm in that it shows people how bad it is before
they have the means to use even more cruel tools at war, blind to what the
use of them practically entails.
I meant to say we "can't...".
Bruno Marchal wrote:
>
> Perhaps we should make them illegal when used against someone being
> more than 7 years old.
But this is a strong form of authoritative argument: "You should not make
authoritative arguments because I believe you should no make authorative
arguments".
Bruno Marchal wrote:
>
>>
>> Bruno Marchal wrote:
>>>
>>>>
>>>>
>>>>
>>>> Bruno Marchal wrote:
>>>>>
>>>>>> I believe the only way we can learn to understand each other is if
>>>>>> we
>>>>>> acknowledge the truth in every utterance.
>>>>>
>>>>>
>>>>> That is extreme relativism, and makes truth so trivial that it lost
>>>>> its meaning.
>>>> I think truth is a naturally very relative notion, today it might be
>>>> true
>>>> that "it rains today" on Monday and it might be false on Tuesday.
>>>
>>> That might be absolute truth disguised into indexical statement. "It
>>> rains today" is "it rains the 23 february 2011" uttered the 23
>>> february 2011.
>> Okay, but then it is plausible to say relative truth is absolute
>> truth.
>> Which again leads to truth being a relative notion.
>
> If you make *all* truth relative, then you will contradict yourself at
> some point. Descartes saw this, I think.
You mean that "All truth is relative" would have to be an absolute statment
itself?
Maybe it means "All truth is relative and absolute" and absolute/relative is
a relative distinction.
The truth is absolute, but relative to itself. "Absolute" may really mean
the same as "self-relativity".
It may be that "absolute"="relative" in some context, just as "up"="down" in
some context (my up is the australians down).
Bruno Marchal wrote:
>
>>
>>
>> Bruno Marchal wrote:
>>>
>>>> But paradoxically it seems like an absolute notion, too. There
>>>> really seems
>>>> to be an absolute truth regardless of circumstances.
>>>> So I am an extreme relativist, but also an absolutist.
>>>
>>> Doubt can rise only from at least a certainty, like consciousness.
>> Right, but this certainty might be a really really weak one. We are
>> certain
>> that we are conscious, but in non-lucid dreams we experience how
>> weak the
>> sense of being conscious can be.
>
> I don't think so. Why? We might only experience how weak our belief in
> some reality can be, but not on the reality of our consciousness.
This contradicts my experience. I clearly find myself to be less conscious
when dreaming. Not only less conscious of a reality, but less consicious of
my consciousness.
Bruno Marchal wrote:
>
>>
>>
>> Bruno Marchal wrote:
>>>
>>>> It's the same with triviality. Truth is trivial, it simply is true
>>>> and it is
>>>> hard to say anymore about it that is surely true. On the other hand,
>>>> it's
>>>> highly non-trivial, as seen in this non-trivial world; there seem to
>>>> be
>>>> infinite structures in or of truth.
>>>
>>> Logic makes that clear. Some truth are trivial (like "p -> p", or
>>> "p &
>>> q -> p", or "0 = 0"), but the notion of truth itself is so complex
>>> and
>>> non trivial that there is no arithmetical predicate for just
>>> arithmetical truth. Truth is as trivial as God! It has no
>>> description.
>> Or it has every description!
>
> It has none. You can go from none, to an arbitrary one. Neither about
> truth, nor about God.
I assume you mean "can't".
Why not?
I think any description will do as a description of truth, because it is the
only thing that can be described. I think falsehood is just a rational
category and ultimately included in truth as *less accurate* or more vague
formulations of truth - but not a total opposite.
I do think, though, that every description of truth is incomplete (I
supspect that truth itself is always incomplete, that is, eternally
extendable by more of itself).
Bruno Marchal wrote:
>
>>
>>
>>
>> Bruno Marchal wrote:
>>>
>>>>
>>>>
>>>> Bruno Marchal wrote:
>>>>>
>>>>> Language are interpreted plausibly by universal machine (brains,
>>>>> bodies). The interpretation have to follow constraints to be
>>>>> sensical.
>>>> But if there are no constraints they can follow constraints.
>>>
>>> ?
>> It's similar to the omnipotence paradox. If there are no constraints
>> it need
>> not be a constraint that there are no constraints.
>
> Worst than that. It needs to be not-a-constraint, but it *is* a
> constraint.
This may just be a linguistic problem of expressing this kind of pardoxical
truth.
None of a thing may be one of a thing "none of a thing" (0=0*1).
Similarily no constraint may be a constraint "not-a-constraint".
Bruno Marchal wrote:
>
>>
>>
>> Bruno Marchal wrote:
>>>
>>>> I don't think we need to be afraid of any level.
>>>> If we avoid this level we will exclude persons from society that
>>>> speak in a
>>>> way that is hardly comprehensible, for example schizophrenics (I
>>>> know one).
>>>
>>> This is different. As we might feel some empathy for some person or
>>> group, we can *try* to understand. But we are not obliged to make
>>> sense. You might ended like the duchess. Someone tells her
>>> "thryunbvazo^lo-iolopik, ##", and she will tell you "Oh, you are so
>>> right, my dear".
>> You seem to like the word "iolopik". Maybe it conveys some deep
>> truth, maybe
>> it is more connected to the way the letters are arranged on your
>> keyboard,
>> maybe both. ;)
>
> No. It means "my friend". "iolopy" means friend, iolopik means "my
> friend", on an imaginary planet, gravitating around an imaginary sun,
> in an imaginary galaxy, in an imaginary cluster of galaxies, in an
> imaginary branch of an imaginary solution of Schroedinger equation, if
> that exists.
:D
Bruno Marchal wrote:
>
>>
>>
>> Bruno Marchal wrote:
>>>
>>>> Among them it is quite common that they talk a way that is hard to
>>>> comprehend.
>>>
>>> *That* is the problem.
>> Yep, but it can't be solved by avoiding to make sense of them.
>
> I am not sure. We can learn by finding sense, but also by discarding
> sense.
I would rather discard the NONsense and keep the sense. ;)
Of course I see what you mean. If we believe in the christian hell, it is
probably better to discard the sense that people really go to hell forever.
But this may equally (or better) interpreted as seeing the deeper sense in
"atheists go to hell" (it is there to control people, it is and was always
just an scenario *in my mind*,...).
And practically I don't think it will help if you try to discard the sense
in what the schizophrenic person says. You can't convey that (instead she
will try to interpret what you said in the way that further feeds their
delusion - "it is just a test" etc...). You can just convey that you see
some sense in what she says and this may help, if only by making her feel
more accepted (and thus less defensive and more open to help).
Bruno Marchal wrote:
>
> It is the
> problem with salvia, we don't really remember the key part of the
> experiences.
This may be a protective mechanism for not letting the salvia reality
intrude into ours too much. Or conversely remembering certain things maybe
would suck us inescapably into salvia reality (which cannot happen for
reasons of self-consistency of our local earthly selves).
Bruno Marchal wrote:
>
>>
>> Also heaven and hell (not in the christian sense of course) and
>> reincarnation might be emergency realities that are there as a
>> semi-consistent bridge to more consistent histories (maybe some
>> advanced
>> technological future, where we can learn to locally manifest through
>> development and with the help of computers and live forever in a more
>> plausible way than in salvia land or heaven).
>>
>> Just some speculation - I guess I'm wildly creative today ;).
>>
>
>
> If mechanism is true, we can say that we are plausibly already in the
> 'matrix'. No need to wait for an advanced technological future, we are
> already there.
I don't know. Is the future not really defined in a way that in the future
we must necessarily remember our old present (so the future can just be a
future where what is now has already subjectively happened - which is
obviously not the case)? It seems more appropiate to me to say we live in
timelessness (out of which time emerges).
If we really are already in a advanced technological future, why are we not
- or only badly - able to communicate with the entities there? And why is
there even seemingly linear time?
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benjayk
OK this makes sense. But is there any provable communication, then? After
all we can never prove the axioms needed for a provable communication.
Bruno Marchal wrote:
>
>>
>>
>> Bruno Marchal wrote:
>>>
>>> But it is not enough. usually people agree with the axiom of Peano
>>> Arithmetic, or the initial part of some set theory.
>> But Peano Arithmetics is not a non relative absolute base. It is
>> relative to
>> the meaning we give it and to the existence of some reality. 1+1=2
>> can have
>> infinite meanings, that all are relative to our interpretation ("If
>> I lay
>> another apple into the bowl with one apple in it there are two
>> apples" is
>> one of them) and there being meaning in the first place.
>
> Hmm... Most people agrees on a standard meaning for the natural
> numbers, like in the Fermat theorem, or any theorem or conjecture in
> number theory, or when you are using numbers in computer science.
> 1+1 = 2 is true in all those interpretations, even if computer science
> we use also some algebra where 1+1=0. That does not contradict that
> the standard integer are all different from 0, except 0.
OK, but I insist that the fact that most people agree on something does not
make it a "non relative absolute base".
OK. But still "provable(false)->false" is true if we assume consistency,
right?
So above you meant implying as in "being a provable consequence of"?
Bruno Marchal wrote:
>
>>
>>
>> Bruno Marchal wrote:
>>>
>>>>
>>>> And why is inconsistency allowed for machine, but disallowed for
>>>> other
>>>> objects?
>>>
>>> Because if a machine proves "0=1", she will be in trouble, but if God
>>> or Platonia proves "0=1", then we are *all* in trouble.
>> I thought we already established that 0=1 can have a clear meaning
>> (equivalent to statements of the form 0*A+B=1*C+D in standard
>> arithmetics),
>> and so it poses no problem.
>
> ?
> I have no clue what you are saying here. If "0 = 1" means "I love
> chocolate", then of course "0=1" might be true.
But 0=1 is not plausibly interpreted as "I love chocolate" because the
latter is not (directly anyway) a statement about numbers. 0=1 may be a
statement about the two numbers 0 and 1 that is just not formulated in
standard arithmetic. This does not imply that it is generally false (not
anymore then peano arithmetics show there is no meaning in 0=s(n)).
Bruno Marchal wrote:
>
> Again, we use the
> standard meaning.
Okay, but then 0=1 has no standard meaning in arithmetics. It simply not
included in arithmetics.
But it might still be usefully interpreted as "Try again (to make a true
statement in arithmetics)" or as an alternative expression of a statement in
arithmetics (like treating it as an expression where some symbols are
omitted) or as expressing that all numbers are equal when we talk about an
object where quantity does not matter (eg one of nothing is still nothing /
0=0*1).
Bruno Marchal wrote:
> But for the
> natural numbers, we do agree on those axioms, and their correspond to
> what has been taught at school.
Yes, but this does not imply the axioms that other axioms or variations of
the axioms are not valid.
Bruno Marchal wrote:
>
> If some my student defend ideas like 0 = 1, I give them a 0/10
This is valid in mathematics, because there we agree to assume certain
axioms and not doing this is a communication error. I don't think it is
valid when doing philosophy (and interpreting what statements correspond to
reality is philosopy).
I think you don't see my point. Sure, there are statements that don't make
sense or that are false in a specific system (or more informal: a specific
context). That doesn't mean that these statements have no corresponding
truth.
Your idea that it is somehow problematic if God proves 0=1 assumes that
"0=1" has a definite meaning that is wrong. Even if we say "God proves 0=1
in standard arithmetic", we just express standard arithmetic means something
else as what we commonly understand as it.
I don't think there is such a thing as absolutely wrong statement. All
falsehood is depended on assuming certain axioms - while truth is not.
Undefinedness is no problem, because it does not say anything about what
exists.
Consistency seems to be a fundamental reality and not something we can even
conceive of not being there. Inconsistency has only meaning in specific
systems. I think it is an error to say "if God or Platonia proves "0=1",
then we are *all* in trouble." because we can't say what it would mean if
God proves 0=1 according to the axioms we use. Or it means simply that God
states things that are wrong in certain systems, which also poses no
problem.
I would not insist on this so much if I would not suspect that considering
the possibility of something being an "ultimate falsehood" or "totally
wrong" leads to disregarding some statements instead of seeing their truth.
We don't have to avoid "wrong" statements. They simply are not as
proliferative as (more) true statements.
Bruno Marchal wrote:
>
>>
>> My suggestion is that every statement has such an interpretation.
>> Circles
>> with edges makes sense if we allow hyperreal numbers as numbers of
>> edges and
>> lenght of edges, triangles with four sides may mean such a geometric
>> object:
>> http://commons.wikimedia.org/wiki/File:Triangle-square-area-dev.png
>> and that
>> God is omnipotent may mean anything.
>
> Logic has been invented for avoiding interpretations as much as
> possible, and then for studying mathematically what can be
> interpretations, and the relations (Galois connection) between formal
> deduction and relations on interpretations. We force the
> "propositions" which mean anything to be eliminated, for helping the
> progress toward genuine truth and meaning.
>
> We can say that first order logic does succeed in the interpretation
> elimination, thanks to a theorem of completeness (not incompleteness)
> by Gödel. A formula is a theorem IF and ONLY IF the formula is true in
> all interpretations.
>
Again, this is true, but it depends on certain axioms, which can be
interpreted to be not right in all contexts.
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Bruno Marchal
I am not sure language gives meaning. Language have meaning, but I
think meaning, sense, and reference are more primary.
With the mechanist assumption, meaning sense and references will be
'explained' by what the numbers 'thinks' about that, in the manner of
computer science (which can be seen as a branch of number theory).
> Numbers alone may symbolize some fundamental describable matter and
> forces but a complete and coherent TOE should include elevated human
> consciousness beyond the primitive which in itself requires a
> relatively sophisticated language to give meaning to the numbers and
> their operations.
Hmm... You can use numbers to symbolize things, by coding, addresses,
etc. But numbers constitutes a reality per se, more or less captured
(incompletely) by some theories (language, axioms, proof
technics, ...). In this context, that might be important.
>
> Would not any TOE describing the universe appears to require human
> sophisticated language using referent nouns, (and conjunctions,
> adjectives and verbs etc.) to give meaning to the numbers and their
> functions and operations?
With the mechanist assumption, humans and their language will be
described by machine operations, which will corresponds to a
collection of numbers relations (definable with addition and
multiplication). This is not obvious and relies in great part of the
progress of mathematical logic.
>
> You repeatedly refer to “addition and multiplication”. Is not
> multiplication repeated addition or is there another separate
> principle involved with multiplication?
This is a very technical point. It can be shown that classical first
order logic+addition gives a theory too much weak to be able to
defined multiplication or even the idea of repeating an operation a
certain arbitrary finite number of time. Likewise it is possible to
make a theory of multiplication, and then addition is not definable in
it. The pure addition theory is known as Pressburger arithmetic, and
has been shown complete (it proves all the true sentences
*expressible* in its language, thus without multiplication symbols);
and decidable, unlike the usual Robinson or Peano Arithmetic, with +
and *, which are incomplete and undecidable.
Once you have the naturals numbers and both addition and
multiplication, you get already (Turing) universality, and thus
incompleteness, insolubility.
Bruno
Bruno Marchal
On 26 Feb 2011, at 22:55, benjayk wrote:
>
>
> Bruno Marchal wrote:
>>
>>
>>
>>>
>>> So our disagreement seems to be quite subtle. It seemed to me you
>>> wanted to
>>> make numbers the absolute thing. But when we are really modest it
>>> seems to
>>> me we have to admit the meaning in numbers is an intersubjective
>>> agreement
>>> in interpretation and we should not be too quick in disregarding
>>> seemingly
>>> contradictory statements as completetly false.
>>
>> We try to understand things by reducing them to things we already
>> consider having a good understanding of.
>> If not we are doing obstructive philosophy, cutting the hair kind of
>> activity.
> We may also understand things by seeing their truth is not (at least
> practically) reducible to anything we have a good understanding of.
Yes, I agree. But this need to be done relatively to a very clear
theory about what we do understand.
>
> If we understand consciousness can not be reduced to anything else, we
> learnt something.
"anything else" is much too big. It is part to the object of study in
the search of a TOE.
>
> I thought you are not a reductionist?
I am not a reductionist indeed. On the contrary I show that
consciousness and matter are not reducible to number relations or
theories, except by taking them all, as we are obliged to do when we
say "yes to the doctor". When we accept that our brain can be
described as a machine, then we can understand our consciousness is
not reducible to finite collections of numbers, but to infinite
collections, and that some aspect of consciousness (private qualia)
are not reducible at all, although they can handled by machines and
numbers. This is counter-intuitive and rather hard to figure out, but
thanks to the comp hyp, this can be (meta--formalize, even by
introspecting universal machine (the Löbian machine's 'interview' does
just that).
>
>
> Bruno Marchal wrote:
>>
>> But this does suppose the kind of understanding that 1 is different
>> from 2.
> Of course I understand that 1 is different than 2. But nevertheless
> I can
> also makes sense of 1=2 (for example it might express the same as
> 1X=2X,
> that is, the object we are talking about has no distinction of
> quantities).
> I also see the difference between lion and animal. But it
> nevertheless makes
> sense to say that a lion is an animal or that an animal is a lion.
The problem is not in making sense of some expression, but in agreeing
about *some* meaning, and this usually with some goal in mind.
Yes. It makes no 'useful' sense.
>
>
> Bruno Marchal wrote:
>>
>>>
>>>
>>> Bruno Marchal wrote:
>>>>
>>>> That is why I like comp, because it allows (and forces) to derive
>>>> the
>>>> psychological existence, the theological existence, the physical,
>>>> existence, and the sensible existence from the classical
>>>> existence of
>>>> numbers, which is simple by definition, if you agree with the use
>>>> of
>>>> classical logic in number theory.
>>> Honestly I still have doubts about this. The reason is that there is
>>> always
>>> the implicit axiom "I am conscious." (for example a bit more
>>> explicit in
>>> "Yes, Doctor"), which is incredibly general.
>>
>> The statement "I am conscious" is not just general. It cannot be
>> formalized at all, and is not part of any scientific discourse (as
>> opposed to the sentence "I am conscious").
> I'm not so sure. Isn't saying "I am conscious" formalizing that I am
> conscious?
Not at all. To be formalize, we must be able to use any terms in place
of any terms. You cannot do such a substitution for "I am conscious".
But you can use any terms and symbols once you have formalize in first
order logic. Only the inference rules (like saying that you can deduce
B from A & B) needs the inevitable amounts of informality.
> Intuitively it seems perfectly vald.
> Also, if we cannot formalize "I am conscious" can we formalize
> anything at
> all?
Yes. But few things can be completely formalize. yet, natural
addition, natural numbers multiplication, and addition +
multiplication on the real numbers can be completely formalize.
Addition and multiplication on the natural numbers can still be
formalize but not completely (some truth will escape any theory
attempting to do so).
> Can we formalize some content of consciousness without formalizing "I
> am conscious"?
Yes. You might need to study a bit of logic to grasp this. We can
formalize completely addition, and it is a content of consciousness.
> And if we can't formalize content of consciousness what can
> we formalize? After all we just have our consciousness and its
> content.
We can formalize, usually incompletely, some content of consciousness
(usually mathematical). Once a realm is rich enough yo define
universal numbers (machines), we, or any alien, gods, etc. can never
formalize (find a theory) completely such a realm.
>
>
>
> Bruno Marchal wrote:
>>
>>> I am not sure that if we take
>>> "I am conscious" as axiom,
>>
>> I don't do that.
> This is a bit like saying if we have the axiom "There is a number 0
> and a
> successor of 0, s(0)", there is no axiom "There is a number 0".
Indeed.
> If we say "Yes doctor" we say "I bet that if I get an artificial
> brain my
> state of consciousness will remain enough invariant so that I feel
> myself to
> be the same person as before".
> My consciousness can only remain invariant if I am conscious in the
> first
> place, so the axiom "I am conscious" is included.
Hmm... It is more a theorem, or a default assumption. It is obvious
that we suppose that someone is not a zombie when saying "yes" to the
doctor.
>
> Otherwise you make the same mistake as a scientists using numbers in
> their
> theories but denying the existence of numbers (and so ultimately the
> axioms
> they use).
Of course. What I said is hat I am not using the axiom that "bruno
marchal is conscious", but the whole comp idea is that you are
supposed to be conscious when saying yes to a doctor. Comp is a theory
of consciousness (and matter). It presupposes the existence of those
things (then it shows they are not fundamental, and that matter is
less fundamental than consciousness, ontologically. The partial
reduction are: numbers => consciousness => matter.
>
>
> Bruno Marchal wrote:
>>
>>>
>>> But maybe I don't get a crucial thing.
>>
>> Digital Mechanism is not a trivial hypothesis. It contradicts the
>> part
>> of the theology of Aristotle used by most believers and non believers
>> since 1500 years. (To be short).
> Yes, the basic idea seems easy but if you dig deeper you see that if
> we take
> consquences in account it becomes really difficult.
I am open that it leads to a falsity, in which case we refute comp.
But up to now, we get only a quantum-like sort of weirdness.
No. (except by bad scientist). All theories are really question made
precise.
>
>
> Bruno Marchal wrote:
>>
>> We posit things, and if you don't like them,
>> you can always propose another theory. Scientist pretending that we
>> know things, per science, are philosophers confusing pseudo-religion
>> with science. That's human weakness, not science weakness.
> I don't think we can seperate science and science as praticed by
> humans.
> Science is a human creation (at least relatively here on earth).
Yes, but when we search a TOE we search to go beyond the humans. So we
have to separate human science from some ideal science (like the one
of the universal numbers when they introspect themselves).
Which reality?
Physical reality? OK, but that is the Aristotelian assumption, which I
do not follow.
>
> But then we are lead to the next problem: Either we leave undefined
> what
> reality is, in which case we don't convey much - or we use some
> model of
> reality which than acts as the authority.
We can use them as theory, which means hypothesis. We can rely on
personal intuition, inspiration.
Anyway, there is no problem with authorities, only with authoritative
argument.
> Usually the authority doesn't say "Believe me because I say I am
> right",
Indeed.
> but
> "Believe me because <some greater authority> shows I'm right".
Not really. An authority will say "believe this proposition if you can
justify it from what you already believe in". Of course, in the
natural science we do use a notion of plausibility, due to the fact
that we cannot do all preceding experiments, but eventually you are
the only judge.
> The priest
> appeals to God as the authority,
That is the authoritative argument, unless the priest only says
"listen to God". But if he says "God told us this and that", it is no
more religious but only a con men, a misleader, a scammer, a
confidence trickster.
I tend to think that God is the most trustful authorities, and due to
that, the one which should never quote in an argument. Appeals to God
(or miracle) in argument is scam.
> the politician in democracies to the "will
> of the people", the scientist to controlled experiments, the
> mathematician
> to mathematicial truth.
No problem with authorities. Much problems with authoritative
arguments. I mean in the search of truth, not in many practical
situations.
> If we don't explicitly say what our authority is we only cover up
> what our
> authority is, which makes it harder to check if our authority is
> right.
>
> So I think the good thing in science is that we make clear our
> authorities.
> We say we believe because of the results of controlled experiments. Or
> because of our faith in the axioms of mathematics.
>
> In religion (or pseudo-religion if you like that term better) they
> say God
> is the authority, but noone really says that their God is in large
> parts
> just a collection of ideas from people in the far past.
But God, for a believer, is not a collection of ideas from people. It
is what creates the people at the start.
Like few physicists, since Aristotle, would say that the physical
universe is a collection of ideas from physicists.
That is why indeed, it is nice when we put the cart on the table, and
make precise our (hypotetical) ontological assumptions clear at the
start. With comp, at the start we accept consensus reality
(consciousness, matter, numbers), and eventually reduce the ontology
to numbers and their elementary operations. It is not a reductinosim,
because the internal epistemology appears to go far beyond the
numbers, and provably so.
>
>
>
> Bruno Marchal wrote:
>>
>> Authorities never uses authoritative arguments.
> So the church - that is an authority to many people - doesn't appeal
> to God
> in their arguments?
> Maybe you wish people saw as authorities only people that don't use
> authoritative arguments.
That's the point. The honest priest might say "listen to God, if you
can". He/she will not say "believe in this or that because God says so".
We have to listen to the compaling people, and change the startegy if
they are more and more complains. Democracy makes this possible,
although a democracy is just a beginning path, and not the last
answer. in human affair, the problems are infinite in number.
> Maybe sometimes the only way to avoid
> great harm is to cause relatively small harm.
Like stopping smoking tobacco, or taking a unpleasant medication. Yes.
I agree.
> Perhaps even war reduces harm in that it shows people how bad it is
> before
> they have the means to use even more cruel tools at war, blind to
> what the
> use of them practically entails.
I agree. There is no criteria for good and bad, except the direct
evidence by people.
I did not say that. I said "when searching the truth, you should not
believe in authoritative arguments because both logic and history can
show that they lead to falsities and harm", and I did argue.
OK, and with comp you need some absolute notion to define that self-
relativity.
>
> It may be that "absolute"="relative" in some context, just as
> "up"="down" in
> some context (my up is the australians down).
I would no go so far.
>
>
> Bruno Marchal wrote:
>>
>>>
>>>
>>> Bruno Marchal wrote:
>>>>
>>>>> But paradoxically it seems like an absolute notion, too. There
>>>>> really seems
>>>>> to be an absolute truth regardless of circumstances.
>>>>> So I am an extreme relativist, but also an absolutist.
>>>>
>>>> Doubt can rise only from at least a certainty, like consciousness.
>>> Right, but this certainty might be a really really weak one. We are
>>> certain
>>> that we are conscious, but in non-lucid dreams we experience how
>>> weak the
>>> sense of being conscious can be.
>>
>> I don't think so. Why? We might only experience how weak our belief
>> in
>> some reality can be, but not on the reality of our consciousness.
> This contradicts my experience. I clearly find myself to be less
> conscious
> when dreaming.
> Not only less conscious of a reality, but less consicious of
> my consciousness.
OK. That is something which I did believe and can still conceive. But
now, both from comp and from some experimental study on consciousness,
and on the functioning of the brain, I tend to believe that this is an
illusion. It is a post amnesy which makes us believe that we were less
conscious. But it the attention which is playing some trick. But you
point on some difficulty of comp. That's a real subject of discussion.
>
>
> Bruno Marchal wrote:
>>
>>>
>>>
>>> Bruno Marchal wrote:
>>>>
>>>>> It's the same with triviality. Truth is trivial, it simply is true
>>>>> and it is
>>>>> hard to say anymore about it that is surely true. On the other
>>>>> hand,
>>>>> it's
>>>>> highly non-trivial, as seen in this non-trivial world; there
>>>>> seem to
>>>>> be
>>>>> infinite structures in or of truth.
>>>>
>>>> Logic makes that clear. Some truth are trivial (like "p -> p", or
>>>> "p &
>>>> q -> p", or "0 = 0"), but the notion of truth itself is so complex
>>>> and
>>>> non trivial that there is no arithmetical predicate for just
>>>> arithmetical truth. Truth is as trivial as God! It has no
>>>> description.
>>> Or it has every description!
>>
>> It has none. You can go from none, to an arbitrary one. Neither about
>> truth, nor about God.
> I assume you mean "can't".
> Why not?
I mean "can't", and I mean it in the comp frame. It is a consequence
of the theory. Roughly speaking such description, if available, led to
contradictions akin the the Epimenides paradox ("I am lying" <=> " I
am not lying").
>
> I think any description will do as a description of truth, because
> it is the
> only thing that can be described.
OK. I have to say that I answer always in the comp frame, and I guess
I am refering to "description" is a rather more fromal sense than the
informal common one.
> I think falsehood is just a rational
> category and ultimately included in truth as *less accurate* or more
> vague
> formulations of truth - but not a total opposite.
> I do think, though, that every description of truth is incomplete (I
> supspect that truth itself is always incomplete, that is, eternally
> extendable by more of itself).
The set of all true proposition about all machines is not even
describable by any machine. But machine can find clever trick to
approximate that set, or to refer to it indirectly.
Such set of truth can be extended (by analytical truth, for example,
of by arbitrary "truth" involving new symbols), so in that sense such
truth can be extended. Indeed, the first order Noûs is already far
bigger that the ONE, and eventually the internal epistemology of any
universal numbers is bigger than the whole of mathematics, and even
"science", making comp the less reductionist theory ever.
>
>
> Bruno Marchal wrote:
>>
>>>
>>>
>>>
>>> Bruno Marchal wrote:
>>>>
>>>>>
>>>>>
>>>>> Bruno Marchal wrote:
>>>>>>
>>>>>> Language are interpreted plausibly by universal machine (brains,
>>>>>> bodies). The interpretation have to follow constraints to be
>>>>>> sensical.
>>>>> But if there are no constraints they can follow constraints.
>>>>
>>>> ?
>>> It's similar to the omnipotence paradox. If there are no constraints
>>> it need
>>> not be a constraint that there are no constraints.
>>
>> Worst than that. It needs to be not-a-constraint, but it *is* a
>> constraint.
> This may just be a linguistic problem of expressing this kind of
> pardoxical
> truth.
>
> None of a thing may be one of a thing "none of a thing" (0=0*1).
>
> Similarily no constraint may be a constraint "not-a-constraint".
That s different. The difference is well captured by modal logic. It
is the difference between ~Bp and B~p. 99,9% of invalid reasoning in
philosophy are based on such missing nuance. Like people confuse often
agnostic (~B'god exist'), and atheist (B~'god exists').
It is premature to explain a TOE to the schizophrenic. The goal here
is not make it understood by the sane and good willing people among
those who are open to many-worlds or everything-type of theories.
Some schizophrenic might be in advance, like some mystic, because we
are interested in consciousness, and they live altered state of
consciousness, but if we can learn from them, the goal here remains to
make the explanation available to 'normal' people first.
>
>
> Bruno Marchal wrote:
>>
>> It is the
>> problem with salvia, we don't really remember the key part of the
>> experiences.
> This may be a protective mechanism for not letting the salvia reality
> intrude into ours too much. Or conversely remembering certain things
> maybe
> would suck us inescapably into salvia reality (which cannot happen for
> reasons of self-consistency of our local earthly selves).
That's quite possible.
This may be a protective mechanism for not letting that advanced
technological future reality
intrude into ours too much. Or conversely remembering certain things
maybe
would suck us inescapably into advanced technological future reality
(which cannot happen for
reasons of self-consistency of our local current 'earthly' selves :)
> And why is
> there even seemingly linear time?
In both comp and the quantum, time is bifurcating, with many futures,
and less, but still infinitely, many pasts.
We are in a timeless realm, but we live it, from inside, in the time
and space modal manner.
Bruno
Bruno Marchal
All axioms are provable in one line. Just say "provable by axioms".
Of course a theory will be *interesting* if the axioms are plausible,
about their subject matter, and simple, and in few numbers, etc.
The axioms needs to be "true" in some "reality" (model). But
"provable" is always supposed to mean "provable" in this or that
theory. Is a theory true? This is outside the scope of science. That
question belongs to philosophy, and IMO is almost a private question.
Now I do about that, concerning the usual standard natural numbers (0,
1, 2, ...) you agree that for all x 0 ≠ s(x), for example. It means
that zero is not a successor of a natural number. Of course zero is
the successor of -1, but this concerns another structure (the set of
integers (..., -2, -1, 0, 1, 2, ...).
>
>
>
> Bruno Marchal wrote:
>>
>>>
>>>
>>> Bruno Marchal wrote:
>>>>
>>>> But it is not enough. usually people agree with the axiom of Peano
>>>> Arithmetic, or the initial part of some set theory.
>>> But Peano Arithmetics is not a non relative absolute base. It is
>>> relative to
>>> the meaning we give it and to the existence of some reality. 1+1=2
>>> can have
>>> infinite meanings, that all are relative to our interpretation ("If
>>> I lay
>>> another apple into the bowl with one apple in it there are two
>>> apples" is
>>> one of them) and there being meaning in the first place.
>>
>> Hmm... Most people agrees on a standard meaning for the natural
>> numbers, like in the Fermat theorem, or any theorem or conjecture in
>> number theory, or when you are using numbers in computer science.
>> 1+1 = 2 is true in all those interpretations, even if computer
>> science
>> we use also some algebra where 1+1=0. That does not contradict that
>> the standard integer are all different from 0, except 0.
> OK, but I insist that the fact that most people agree on something
> does not
> make it a "non relative absolute base".
I agree. Science is not democratic. We don't vote to decide the truth
of an arithmetical proposition. We prove it in a theory on which
people agrees.
Not really. By A -> B, I mean ~A v B. Or ~(A & ~B). being a provable
consequence would better be captured by B(A -> B), with "B" some
provability predicate.
>
>
> Bruno Marchal wrote:
>>
>>>
>>>
>>> Bruno Marchal wrote:
>>>>
>>>>>
>>>>> And why is inconsistency allowed for machine, but disallowed for
>>>>> other
>>>>> objects?
>>>>
>>>> Because if a machine proves "0=1", she will be in trouble, but if
>>>> God
>>>> or Platonia proves "0=1", then we are *all* in trouble.
>>> I thought we already established that 0=1 can have a clear meaning
>>> (equivalent to statements of the form 0*A+B=1*C+D in standard
>>> arithmetics),
>>> and so it poses no problem.
>>
>> ?
>> I have no clue what you are saying here. If "0 = 1" means "I love
>> chocolate", then of course "0=1" might be true.
> But 0=1 is not plausibly interpreted as "I love chocolate" because the
> latter is not (directly anyway) a statement about numbers. 0=1 may
> be a
> statement about the two numbers 0 and 1 that is just not formulated in
> standard arithmetic. This does not imply that it is generally false
> (not
> anymore then peano arithmetics show there is no meaning in 0=s(n)).
How could I have guessed that?
>
>
> Bruno Marchal wrote:
>>
>> Again, we use the
>> standard meaning.
> Okay, but then 0=1 has no standard meaning in arithmetics.
? But it has a standard meaning. It is just plainly false. The meaning
is "false".
> It simply not
> included in arithmetics.
It is indeed even refutable. Simple theories PA can prove ~(0 = 1).
> But it might still be usefully interpreted as "Try again (to make a
> true
> statement in arithmetics)"
That would be a higher level heuristic. If you allow "0 = 1" to mean
this, then we are no more sure what we are talking about, and people
will not believe you if you say that you can derive Schroedinger
equation in the mind of correct machine, in arithmetic. They will just
argue that the interpretation is so vague that it is not really a new
result, but some triviality.
> or as an alternative expression of a statement in
> arithmetics (like treating it as an expression where some symbols are
> omitted) or as expressing that all numbers are equal when we talk
> about an
> object where quantity does not matter (eg one of nothing is still
> nothing /
> 0=0*1).
Yes, we are more simple minded than that. 0 = 1 is really 0 = s(0),
not something else like 0 = 0*s(0). We get terrible result; the
falsity of Aristotelian theologies (the basic current quasi)universal
paradigm). We have to start from ultra clear axioms.
>
>
> Bruno Marchal wrote:
>> But for the
>> natural numbers, we do agree on those axioms, and their correspond to
>> what has been taught at school.
> Yes, but this does not imply the axioms that other axioms or
> variations of
> the axioms are not valid.
That is why there are different theories.
>
>
> Bruno Marchal wrote:
>>
>> If some my student defend ideas like 0 = 1, I give them a 0/10
> This is valid in mathematics, because there we agree to assume certain
> axioms and not doing this is a communication error. I don't think it
> is
> valid when doing philosophy (and interpreting what statements
> correspond to
> reality is philosopy).
Philosphy, for me, is a purely private affair. I don't do philosophy,
and my main initial goal was to show that some problem in philosophy
can be translated into problem in mathematics, once we accept some
hypothesis (like the computationalist one). Of course philosophers
don't like this, like they never appreciate when science get on their
territory.
>
> I think you don't see my point. Sure, there are statements that
> don't make
> sense or that are false in a specific system (or more informal: a
> specific
> context). That doesn't mean that these statements have no
> corresponding
> truth.
But all proposition have a corresponding truth, if we allow the
context to vary. The idea is that we fix the context, and then make
the reasoning.
>
> Your idea that it is somehow problematic if God proves 0=1 assumes
> that
> "0=1" has a definite meaning that is wrong.
yes. The usual standard meaning. "0 = 1" is a generic proposition to
give an example of a clear falsehood.
> Even if we say "God proves 0=1
> in standard arithmetic", we just express standard arithmetic means
> something
> else as what we commonly understand as it.
That was not my use of it. I was just saying that if God proves
0=s(0), we are all in trouble. That would be a catastrophe bigger than
the big crunch. Nothing would make sense at all.
>
> I don't think there is such a thing as absolutely wrong statement.
If by absolutely, you mean wrong in all theories, I agree with you,
but the point is a bit trivial. If by absloute, you mean wrong in all
the models or intepretations of a theory about natural nulmbers, then
"0=1" is indeed wrong in all interpretations of arithmetical theories.
> All
> falsehood is depended on assuming certain axioms - while truth is not.
That makes truth even more absolute.
> Undefinedness is no problem, because it does not say anything about
> what
> exists.
>
> Consistency seems to be a fundamental reality and not something we
> can even
> conceive of not being there. Inconsistency has only meaning in
> specific
> systems.
Inconsistency is just the negation of consistency. In classical logic
they have the same amount of sense.
> I think it is an error to say "if God or Platonia proves "0=1",
> then we are *all* in trouble." because we can't say what it would
> mean if
> God proves 0=1 according to the axioms we use. Or it means simply
> that God
> states things that are wrong in certain systems, which also poses no
> problem.
Well, if God actually comes by, and says "0 = 1", I will conclude
something like "oh! God has some sense of humour", or I will think
that's not God, or I will thinks "I must be dreaming", etc.
>
> I would not insist on this so much if I would not suspect that
> considering
> the possibility of something being an "ultimate falsehood" or "totally
> wrong" leads to disregarding some statements instead of seeing their
> truth.
> We don't have to avoid "wrong" statements. They simply are not as
> proliferative as (more) true statements.
I disagree. Most statements in most (non arithmetical) theories are
wrong. Only in arithmetic does all mathematicians agree and people
have a deep confidence in the elementary arithmetical axioms. That's
is actually a good reason to build on arithmetic. Set theory and
analysis are already more problematical, and different logics abound.
>
>
>
> Bruno Marchal wrote:
>>
>>>
>>> My suggestion is that every statement has such an interpretation.
>>> Circles
>>> with edges makes sense if we allow hyperreal numbers as numbers of
>>> edges and
>>> lenght of edges, triangles with four sides may mean such a geometric
>>> object:
>>> http://commons.wikimedia.org/wiki/File:Triangle-square-area-dev.png
>>> and that
>>> God is omnipotent may mean anything.
>>
>> Logic has been invented for avoiding interpretations as much as
>> possible, and then for studying mathematically what can be
>> interpretations, and the relations (Galois connection) between formal
>> deduction and relations on interpretations. We force the
>> "propositions" which mean anything to be eliminated, for helping the
>> progress toward genuine truth and meaning.
>>
>> We can say that first order logic does succeed in the interpretation
>> elimination, thanks to a theorem of completeness (not incompleteness)
>> by Gödel. A formula is a theorem IF and ONLY IF the formula is true
>> in
>> all interpretations.
>>
> Again, this is true, but it depends on certain axioms, which can be
> interpreted to be not right in all contexts.
I disagree. The completeness theorem of Gödel does not depend on any
axioms, just on the definition of what is a first order logical theory
and an interpretation (model). Note that such a theorem is no more
true for higher order logics, which makes them almost as vague as
mathematics, for some logicians.
Bruno
Brent Meeker
This is a very technical point. It can be shown that classical first order logic+addition gives a theory too much weak to be able to defined multiplication or even the idea of repeating an operation a certain arbitrary finite number of time. Likewise it is possible to make a theory of multiplication, and then addition is not definable in it. The pure addition theory is known as Pressburger arithmetic, and has been shown complete (it proves all the true sentences *expressible* in its language, thus without multiplication symbols); and decidable, unlike the usual Robinson or Peano Arithmetic, with + and *, which are incomplete and undecidable.
Once you have the naturals numbers and both addition and multiplication, you get already (Turing) universality, and thus incompleteness, insolubility.
Bruno
http://iridia.ulb.ac.be/~marchal/
Brent
Bruno Marchal
On 2/28/2011 1:42 AM, Bruno Marchal wrote:This is a very technical point. It can be shown that classical first order logic+addition gives a theory too much weak to be able to defined multiplication or even the idea of repeating an operation a certain arbitrary finite number of time. Likewise it is possible to make a theory of multiplication, and then addition is not definable in it. The pure addition theory is known as Pressburger arithmetic, and has been shown complete (it proves all the true sentences *expressible* in its language, thus without multiplication symbols); and decidable, unlike the usual Robinson or Peano Arithmetic, with + and *, which are incomplete and undecidable.
Once you have the naturals numbers and both addition and multiplication, you get already (Turing) universality, and thus incompleteness, insolubility.
Bruno
http://iridia.ulb.ac.be/~marchal/
Hmmm.
Does that mean an arithmetic based on first order logic, addition, and a logarithm operation
might be complete
and yet include a kind of multiplication?
benjayk
Sorry, I don't understand you here. How does saying "provable by axioms"
prove anything? It seems to be a description of charateristic that can
either be true or false (provable or not provable by axioms).
Probably you mean something else, but I don't know what.
Does "A -> B" mean B follows from A?
How is that equal to "not-A or B?"
So from provable('0=1') it does not follow 0=1, even if we assume
consistency and don't mean a provable consequence?
How can something be provable in a consistent system and what is proven does
not follow?
Bruno Marchal wrote:
>
>>
>>
>> Bruno Marchal wrote:
>>>
>>>>
>>>>
>>>> Bruno Marchal wrote:
>>>>>
>>>>>>
>>>>>> And why is inconsistency allowed for machine, but disallowed for
>>>>>> other
>>>>>> objects?
>>>>>
>>>>> Because if a machine proves "0=1", she will be in trouble, but if
>>>>> God
>>>>> or Platonia proves "0=1", then we are *all* in trouble.
>>>> I thought we already established that 0=1 can have a clear meaning
>>>> (equivalent to statements of the form 0*A+B=1*C+D in standard
>>>> arithmetics),
>>>> and so it poses no problem.
>>>
>>> ?
>>> I have no clue what you are saying here. If "0 = 1" means "I love
>>> chocolate", then of course "0=1" might be true.
>> But 0=1 is not plausibly interpreted as "I love chocolate" because the
>> latter is not (directly anyway) a statement about numbers. 0=1 may
>> be a
>> statement about the two numbers 0 and 1 that is just not formulated in
>> standard arithmetic. This does not imply that it is generally false
>> (not
>> anymore then peano arithmetics show there is no meaning in 0=s(n)).
>
> How could I have guessed that?
Well, if someone says that" X+3=1" makes sense (and you didn't know about
negative integers) you would guess he would mean a statement about numbers
(thereby extending the sense of numbers). Similarily you can guess that 0=1
is statement about numbers.
Bruno Marchal wrote:
>
>>
>>
>> Bruno Marchal wrote:
>>>
>>> Again, we use the
>>> standard meaning.
>> Okay, but then 0=1 has no standard meaning in arithmetics.
>
> ? But it has a standard meaning. It is just plainly false. The meaning
> is "false".
Well, of course, I expressed this badly. So, the statement '0=1' is false in
standard arithmetic. But what does standard arithmetic say about what being
wrong means? Just saying something is wrong does not really give this a
meaning.
If I know something is right, I have to know right in what way (intuitively,
I might not be able to convey it), otherwise I don't really know it to be
right. If I say "dfgxS" is right and I don't know what this means I don't
know whether it is right (other than in a trivial manner like I argued
before). If I say "1+1=2" is right I can imagine two objects coming together
and being counted. "Ahhh, in this way it is right".
Similarily I have to understand wrong in what way? How do I understand "1=0"
is wrong beyond it just being a label?
Bruno Marchal wrote:
>
>> But it might still be usefully interpreted as "Try again (to make a
>> true
>> statement in arithmetics)"
>
> That would be a higher level heuristic. If you allow "0 = 1" to mean
> this, then we are no more sure what we are talking about,
So what does "'0=1' is false" mean? If something is false intuitively it
means it is not valid in the context of a system. OK, but so what? This
doesn't seem to be a problem? Do I have to care whether its valid?
Can we really be sure what we are talking about if we are talking about
something being wrong?
Bruno Marchal wrote:
>
>> or as an alternative expression of a statement in
>> arithmetics (like treating it as an expression where some symbols are
>> omitted) or as expressing that all numbers are equal when we talk
>> about an
>> object where quantity does not matter (eg one of nothing is still
>> nothing /
>> 0=0*1).
>
> Yes, we are more simple minded than that. 0 = 1 is really 0 = s(0),
> not something else like 0 = 0*s(0).
I think if we take the successor of "zero" to be "one of zero", this is just
as simple or simpler.
This already makes sense if we don't really understand numbers and sometimes
conflate them (eg we treat everything above 6 as equal because it is
"many").
We take 0 to be the "implicit factor" in every number so it is true that
3=3*0 and not only 3=3*1 (which implicitly means 3*0=3*1*0).
One is the succesor of zero has a clear meaning, but it zero is the
successor of zero can have clear meaning, too. 0 represents "something (not
necessarily of quanitiy one) " in this case.
Sure, we get a trivial structure if we are just concerned about what is true
and false in this system, but it may express something by treating zero as
placeholder (if we don't reduce the equation to 0=0 but expand it until
another equality emerges, that is, until we get a truth that is not as
trivial as 0=0, but still symmetric like 1=1)
s(0)=0
1=0
1=s(0)
1=1 "Ah, here a symmetry emerges, so this is an interesting statement about
a trivial, yet easy to comprehend truth" ). This structure yields all true
statements in the same formulation that normal arithmetic does (among many
more other formulations of true statements in standard arithmetic).
Certainly it's quite vague, but we could even do normal arithmetic and treat
all statements not true in standard arithmetic as saying 0=0 (which is
interpreted as "falsehood" or triviality), so it's not necessarily useless.
Actually if we don't get lost with arbitrary transformations it is no worse
than standard arithmetics.
Bruno Marchal wrote:
>
>
>>
>>
>> Bruno Marchal wrote:
>>>
>>> If some my student defend ideas like 0 = 1, I give them a 0/10
>> This is valid in mathematics, because there we agree to assume certain
>> axioms and not doing this is a communication error. I don't think it
>> is
>> valid when doing philosophy (and interpreting what statements
>> correspond to
>> reality is philosopy).
>
> Philosphy, for me, is a purely private affair. I don't do philosophy,
I think this is impossible.
As soon as we state some "truth" we are doing philosophy.
Mathematics has no meaning without truth.
Bruno Marchal wrote:
>
>>
>> I think you don't see my point. Sure, there are statements that
>> don't make
>> sense or that are false in a specific system (or more informal: a
>> specific
>> context). That doesn't mean that these statements have no
>> corresponding
>> truth.
>
> But all proposition have a corresponding truth, if we allow the
> context to vary. The idea is that we fix the context, and then make
> the reasoning.
OK but then we have truths in the context of the fixed of context, no more,
no less.
Bruno Marchal wrote:
>
>>
>> Your idea that it is somehow problematic if God proves 0=1 assumes
>> that
>> "0=1" has a definite meaning that is wrong.
>
> yes. The usual standard meaning. "0 = 1" is a generic proposition to
> give an example of a clear falsehood.
But 0=1 is unclear, because we only know that it is false, not exactly what
this means.
So a clear falsehood exists only in the sense that it is clear which
statements are false, not that the meaning is clear.
Bruno Marchal wrote:
>
>> Even if we say "God proves 0=1
>> in standard arithmetic", we just express standard arithmetic means
>> something
>> else as what we commonly understand as it.
>
> That was not my use of it. I was just saying that if God proves
> 0=s(0), we are all in trouble. That would be a catastrophe bigger than
> the big crunch. Nothing would make sense at all.
See, at this point you do philosophy. You interpret something false as "not
making sense at all". This is simply a philosophical belief (and not one I
would endorse).
I think everything does make sense, including all falsehoods. False is
relative lack of clarity or usefulness. But I make it clear that it is a
phliosophical standpoint (at least now I did ;) ).
Bruno Marchal wrote:
>
>>
>> I don't think there is such a thing as absolutely wrong statement.
>
> If by absolutely, you mean wrong in all theories, I agree with you,
> but the point is a bit trivial.
Indeed, in some way it is. But then existence of numbers seems trivial, yet
many people have problems with it.
The notion of triviality may be not so trivial.
Bruno Marchal wrote:
>
> If by absloute, you mean wrong in all
> the models or intepretations of a theory about natural nulmbers, then
> "0=1" is indeed wrong in all interpretations of arithmetical theories.
But what are "arithmetical theories"? Can this even be defined? Maybe there
is an arithmetical theory where 0=1 is true.
Bruno Marchal wrote:
>
>> All
>> falsehood is depended on assuming certain axioms - while truth is not.
>
> That makes truth even more absolute.
Well, that's good in my mind. Truth seems to be the most absolute thing for
me.
Bruno Marchal wrote:
>
>> I think it is an error to say "if God or Platonia proves "0=1",
>> then we are *all* in trouble." because we can't say what it would
>> mean if
>> God proves 0=1 according to the axioms we use. Or it means simply
>> that God
>> states things that are wrong in certain systems, which also poses no
>> problem.
>
> Well, if God actually comes by, and says "0 = 1", I will conclude
> something like "oh! God has some sense of humour", or I will think
> that's not God, or I will thinks "I must be dreaming", etc.
I meant actually proving. Of course we don't know what it would mean if God
would prove 0=1 according to our axioms, but this is my point.
Bruno Marchal wrote:
>
>>
>> I would not insist on this so much if I would not suspect that
>> considering
>> the possibility of something being an "ultimate falsehood" or "totally
>> wrong" leads to disregarding some statements instead of seeing their
>> truth.
>> We don't have to avoid "wrong" statements. They simply are not as
>> proliferative as (more) true statements.
>
> I disagree. Most statements in most (non arithmetical) theories are
> wrong.
It's hard to tell, I think. In most theories there is not even an absolutely
clear distinction between right and wrong. Physical theories for example are
(as far as we now) never completely right, so are they wrong?
Maybe we don't need explicit axioms, but we need implicit assumptions.
If we define a first order logical theory and have an interpretation, to
validly prove anything we must at least assume that these
definitions/interpretation are meaningful.
Otherwise we can just reject them by not finding them meaningful and thus
reject any proof derived from it.
--
View this message in context: http://old.nabble.com/Platonia-tp30955253p31035440.html
Bruno Marchal
I meant "provable by the fact of being an axiom".
A proof is a sequence of formula, each of which are either an axiom or
a result from a previously proved formula by the means of the
inference rules.
Let me give an example:
The theory T has the following axioms:
1) p
2) p -> r
3) r -> u
And the (common) modus ponens inference rule: it says that from a
formula A and a formula A -> B, you can derive the formula B
In the theory T, it is easy to prove u.
The proof is the sequence of formula, (I add justification alongside,
but formally they don't belongs to the formal proof)
p (by axiom 1)
p -> r (by axiom 2)
r (by modus ponens and the two preceding formula in
this proof)
r -> u (by axiom 3)
u (by modus ponens and the two preceding formula in this
proof)
So the theory T proves the formula u.
Now, suppose someone ask me for a proof of p, in the theory T. I will
just write the following (rather short) sequence of formula:
p (by axiom 1).
To proves p in one line, consisting simply in remembering one axiom.
That's what I meant by "provable in one line".
It might depend what you mean by "follows from". usually, in classical
logic or in classical mathematics "A -> B", also written "If A then
B", means only that A is false or that B is true.
You might have seen the semantic of "A -> B". It is false only in the
"worlds" where A is true and B false:
A B
1 1 in this case (A -> B) is true
1 0 in this case (A -> B) is false
0 1 in this case (A -> B) is true
0 0 in this case (A -> B) is true
In classical logic, the false implies everything. That's why it is a
catastrophe if your theory proves false, because it will prove any
proposition.
> How is that equal to "not-A or B?"
not A or B has the same semantic than A -> B. I let you verify. The
"or" is the inclusive or. For example the unique proposition "((1+1=2)
or (2+2 = 4))" is true.
See? not A or B is really ((not A) or B)
A B
1 1 in this case (not A v B) is true
1 0 in this case (not A v B) is false
0 1 in this case (not A v B) is true
0 0 in this case (not A v B) is true
>
> So from provable('0=1') it does not follow 0=1, even if we assume
> consistency and don't mean a provable consequence?
"provable(f) -> f" is a true formula about a consistent theory. But
Gödel's incompleteness makes such a formula, although true, not
provable by the theory itself (in case the theory is as rich to be
able to prove the elementary addition and multiplication laws).
> How can something be provable in a consistent system and what is
> proven does
> not follow?
If the theory proves p, it will automatically prove Bp -> p. Indeed
for any q, it will prove q -> p. This comes from the fact that the
formula p -> (q -> p) is a tautology of classical propositional logic.
But for Löbian theories (like all the classical extension of PA) the
reverse is astonishingly true also, by a theoreme due to Löb, a Deutch
logician in 1955, if PA proves Bp -> p then PA proves p. In particular
PA cannot proves Bf -> f , because by Löb it would prove f.
A machine/theory is sound if Bp -> p is true about it. This is far
more demanding than being just consistent. Many consistent machines
can be unsound, and 'believes' false arithmetical proposition. Those
are satisfied by non standard models of those arithmetical theories.
Ah? All right. Just that logician makes everything explicit. There is
no guess needed, except in the process of finding a proof, not in
verifying that a sequence of formula is a proof. In particular formal
proof have to be automatically checkable. It can be proved that they
are so in the first order axiomatizable theories.
>
>
> Bruno Marchal wrote:
>>
>>>
>>>
>>> Bruno Marchal wrote:
>>>>
>>>> Again, we use the
>>>> standard meaning.
>>> Okay, but then 0=1 has no standard meaning in arithmetics.
>>
>> ? But it has a standard meaning. It is just plainly false. The
>> meaning
>> is "false".
> Well, of course, I expressed this badly. So, the statement '0=1' is
> false in
> standard arithmetic. But what does standard arithmetic say about
> what being
> wrong means?
In arithmetic, "p is wrong" means that it is not the case that p, or
that it is not the case that the usual structure (N, +, *) satisfies p.
> Just saying something is wrong does not really give this a
> meaning.
It gives its classical meaning. We accept the classical propositional
calculus, including (A v ~A). All proposition in arithmetic are true
or false. A machine stops or does not stops when running on some
input, for example.
>
> If I know something is right, I have to know right in what way
> (intuitively,
> I might not be able to convey it), otherwise I don't really know it
> to be
> right. If I say "dfgxS" is right and I don't know what this means I
> don't
> know whether it is right (other than in a trivial manner like I argued
> before). If I say "1+1=2" is right I can imagine two objects coming
> together
> and being counted. "Ahhh, in this way it is right".
>
> Similarily I have to understand wrong in what way? How do I
> understand "1=0"
> is wrong beyond it just being a label?
Well, a lot can be said here, but it might be very long, and I suggest
you to read some book in logic. Now, to help you shortly, to say that
1 = 0 is wrong should be intuitively obvious. The number 1 is not
equal to the number 0. 1 is the successor of zero, and no natural
number is equal to its successor. This is taught in high school,
mainly by the use of many examples. To eat 1 apple is not the same as
eating 0 apple. 1 $ is not the same as 0 $, .... up to the more
abstract statement that 0 is not equal to 1. See below for a
formalization of this.
>
>
>
> Bruno Marchal wrote:
>>
>>> But it might still be usefully interpreted as "Try again (to make a
>>> true
>>> statement in arithmetics)"
>>
>> That would be a higher level heuristic. If you allow "0 = 1" to mean
>> this, then we are no more sure what we are talking about,
> So what does "'0=1' is false" mean? If something is false
> intuitively it
> means it is not valid in the context of a system.
Which system? The understanding of the intuitive notion comes before
we build a system. In the case of capturing the (admittedly mysterious
intuition of numbers) we ask any system to recover the most intuitive
propositions on which we are agreeing. The intuition comes from living
among a great number of examples. To say that "0 = 1" is false means
that we have the intuition that one thing is not the same as zero
thing, for most of the usual thing we can distinguish. The fact that 0
is different of 1 should not be dependent on any system. if a system
says that 1 = 0, we should just think that the system is talking about
something else.
If not I recall that you have borrowed to me 0$ today, so that you
have to give me back 1,004 $ tomorrow. The 0,04 is for the interest.
The same is true for 2 = 0. This is just wrong, even if many algebraic
system satisfies 1 + 1 = 0, because that is very useful in boolean or
electric circuits, for example, but then 0 and 1 means something else.
"2 = 0" is wrong about the natural numbers because we have the
intuition that 2 things are different from 0 things.
> OK, but so what? This
> doesn't seem to be a problem? Do I have to care whether its valid?
>
> Can we really be sure what we are talking about if we are talking
> about
> something being wrong?
Well, if you tell me that Obama is the king of Belgium, I will have
some doubt about the truth of that sentence.
Now in science, we are NEVER sure. I might wake up and remember living
in a world where Obama is indeed the king of Belgium.
>
>
> Bruno Marchal wrote:
>>
>>> or as an alternative expression of a statement in
>>> arithmetics (like treating it as an expression where some symbols
>>> are
>>> omitted) or as expressing that all numbers are equal when we talk
>>> about an
>>> object where quantity does not matter (eg one of nothing is still
>>> nothing /
>>> 0=0*1).
>>
>> Yes, we are more simple minded than that. 0 = 1 is really 0 = s(0),
>> not something else like 0 = 0*s(0).
> I think if we take the successor of "zero" to be "one of zero", this
> is just
> as simple or simpler.
? (simpler? I don't even understand what you mean! Ah you explain
below)
>
> This already makes sense if we don't really understand numbers and
> sometimes
> conflate them (eg we treat everything above 6 as equal because it is
> "many").
You can't send a man on the moon with such a theory, and you can't
interview machine with such a theory. I can accept such a theory as an
example of theory, but, sorry, we need more rich theory to progress in
the study of machine's theology (the local goal here).
>
> We take 0 to be the "implicit factor" in every number so it is true
> that
> 3=3*0 and not only 3=3*1 (which implicitly means 3*0=3*1*0).
You just illustrate that we can make any sentence true by changing the
theory. But the goal is the contrary: we want that our sentence
reflects statements about simple structure that we can define, and
that our axioms are understood by a majority. Concerning the natural
numbers (and not tension in circuit) it is better to have 2 different
from 0, and the same for 3. You force me to give the axioms below.
Congratulation :)
>
> One is the succesor of zero has a clear meaning, but it zero is the
> successor of zero can have clear meaning, too. 0 represents
> "something (not
> necessarily of quanitiy one) " in this case.
>
> Sure, we get a trivial structure if we are just concerned about what
> is true
> and false in this system,
Which is the case in classical mathematics (on which quantum
mechanics, general relativity, computer science, etc. are based).
> but it may express something
Anything might express something. but if we don't succeed in being
clear that our simplest expression expresses ONE thing, or the least
number possible of things, we cannot learn to discover finer nuances
in the sequence.
> by treating zero as
> placeholder (if we don't reduce the equation to 0=0 but expand it
> until
> another equality emerges, that is, until we get a truth that is not as
> trivial as 0=0, but still symmetric like 1=1)
> s(0)=0
> 1=0
> 1=s(0)
> 1=1 "Ah, here a symmetry emerges, so this is an interesting
> statement about
> a trivial, yet easy to comprehend truth" ). This structure yields
> all true
> statements in the same formulation that normal arithmetic does
> (among many
> more other formulations of true statements in standard arithmetic).
You just do another theory about something else.
>
> Certainly it's quite vague, but we could even do normal arithmetic
> and treat
> all statements not true in standard arithmetic as saying 0=0 (which is
> interpreted as "falsehood" or triviality), so it's not necessarily
> useless.
Sure. But that is not relevant for the points we were discussing,
although I am getting lost here.
> Actually if we don't get lost with arbitrary transformations it is
> no worse
> than standard arithmetics.
But only a good understanding of standard theory can help and
encourage the study of others, less standard theory. But in applied
math, we have to use the theory which are the most promising with
respect to the goal.
>
>
> Bruno Marchal wrote:
>>
>>
>>>
>>>
>>> Bruno Marchal wrote:
>>>>
>>>> If some my student defend ideas like 0 = 1, I give them a 0/10
>>> This is valid in mathematics, because there we agree to assume
>>> certain
>>> axioms and not doing this is a communication error. I don't think it
>>> is
>>> valid when doing philosophy (and interpreting what statements
>>> correspond to
>>> reality is philosopy).
>>
>> Philosphy, for me, is a purely private affair. I don't do philosophy,
> I think this is impossible.
I meant, I don't do philosophy publicly.
> As soon as we state some "truth" we are doing philosophy.
If we state that something is true, we do (bad) philosophy. Note
that I have never said that some statement is true. Only that some
statement follows from some statements. I might use those concept for
illustrating some point, but I have never, and will never say that
some statement are true.
The concept of truth is very important though. (But that's different).
>
> Mathematics has no meaning without truth.
That's true, when we *assume* some kind of platonism. Many philosopher
of mathematics are criticizing the idea that mathematics has no
meaning without truth, and I could defend the idea that a big part of
math does not need that concept, even implicitely. I need the truth
(by assumption) that a machine stops or doesn't stop.
There is a constructive part of math which does not need the notion of
{0, 1} classical truth, but they will use more subtle representation
of truth (like subject classifier in category theory, but that's
demanding in abstract algebra).
>
>
> Bruno Marchal wrote:
>>
>>>
>>> I think you don't see my point. Sure, there are statements that
>>> don't make
>>> sense or that are false in a specific system (or more informal: a
>>> specific
>>> context). That doesn't mean that these statements have no
>>> corresponding
>>> truth.
>>
>> But all proposition have a corresponding truth, if we allow the
>> context to vary. The idea is that we fix the context, and then make
>> the reasoning.
> OK but then we have truths in the context of the fixed of context,
> no more,
> no less.
Yes. That's the point. We are in the context of saying yes to a
digitalist doctor.
>
>
> Bruno Marchal wrote:
>>
>>>
>>> Your idea that it is somehow problematic if God proves 0=1 assumes
>>> that
>>> "0=1" has a definite meaning that is wrong.
>>
>> yes. The usual standard meaning. "0 = 1" is a generic proposition to
>> give an example of a clear falsehood.
> But 0=1 is unclear, because we only know that it is false, not
> exactly what
> this means.
> So a clear falsehood exists only in the sense that it is clear which
> statements are false, not that the meaning is clear.
I would say that with respect of the natural numbers, assuming you do
remember a bit what is taught in school, "0 = 1" has a clear meaning/
The meaning is that the natural number 0 is equal to the natural
number 1. I would say that this is rather clear, and rather obviously
wrong. About other type of numbers, or if we talk on something else,
it will have a clear or unclear meaning, depending on what you are
supposed to talk about.
>
>
>
> Bruno Marchal wrote:
>>
>>> Even if we say "God proves 0=1
>>> in standard arithmetic", we just express standard arithmetic means
>>> something
>>> else as what we commonly understand as it.
>>
>> That was not my use of it. I was just saying that if God proves
>> 0=s(0), we are all in trouble. That would be a catastrophe bigger
>> than
>> the big crunch. Nothing would make sense at all.
> See, at this point you do philosophy. You interpret something false
> as "not
> making sense at all". This is simply a philosophical belief (and not
> one I
> would endorse).
If God proves (by the usual means) that 0=1, it means that God is
inconsistent, from which provably nothing would makes sense. Oviously,
if God proves that 0 = 1, that can make sense only if we use "0
=1" (or proof) in some other sense that usual.
>
> I think everything does make sense, including all falsehoods.
But if "0 = 1" is provable, then all propositions are provable. Or,
you are working in a private theory, and not in the public theory PA
(say) which capture an intuition we have about the natural numbers.
> False is
> relative lack of clarity or usefulness.
I think you are confusing classical logic, with the billion of other
non classical logics. You might develop a logic, like the relevent
logic in which the notion of truth (and falsity) corresponds to what
you say here. But keep in mind this: classical logic is the clearest
of all logic, so that when you want to describe a non classical logic
(usually more complex and subtle) you will have to use classical logic
to describe it. All books on fuzzy logics have theorems proved in
classical logic. Now, as mathematical logic illustrates, despite the
simplicity of its notion of truth, classical logic is already a very
complex subject. And classical logic allows our ignorance to be
manifest. It is the logic of the theologian, not necessarily of the
engineers, but then they can collaborate.
> But I make it clear that it is a
> phliosophical standpoint (at least now I did ;) ).
Not really. You were just suggesting some non classical logic. They
have many use in AI, engineering, etc. But they are build on the top
of classical logic.
>
>
> Bruno Marchal wrote:
>>
>>>
>>> I don't think there is such a thing as absolutely wrong statement.
>>
>> If by absolutely, you mean wrong in all theories, I agree with you,
>> but the point is a bit trivial.
> Indeed, in some way it is. But then existence of numbers seems
> trivial, yet
> many people have problems with it.
No. Only philosopher, who believes that the presence of term like
consciousness, mind, reality, dreams, etc. means that we are doing
philosophy. It is a bit like I am saying "E = mc^2" (thinking about
atomic bomb) and that philosopher replies "you cannot really say that
energy is the mass times the square of the speed of light", for
philosophical reason. He might be right, in philosophy, but might be
obstructive obstructive in "science-and-technic".
Of course not so many scientists understand well that science is not a
question of domain (like matter = science, mind = philosophy), but of
attitude and methodology.
The existence of number used in my work is the "trivial" notion of
existence, where the triviality is guarantied by our (certainly
mysterious) intution of the natural numbers. You just need to be able
to solve the following puzzle: -find the simplest next terms in the
sequence:
I,
II,
III,
., ?
., ?
...
By simple I mean, please, the less "cutting the air" next terms. Of
course there are realities where
"IIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIII
" might be the successor of III, but we might suspect a "cutting the
air" notion of simplicity.
I manage to put the non trivial part in the theological jump you could
make by saying "yes to the digitalist doctor".
> The notion of triviality may be not so trivial.
It is the less trivial notion. You are right.
But that is why it is a key to see we agree on elementary "trivial"
principle, like "if A is true, and if B is true, then A & B is true",
at least when you talking about numbers and their relations.
We have to start from common sense on simple things for realizing that
we loose control when adding a simple thing (addition for example)
with a simple thing (multiplication).
That already escapes all arithmetical theories, all machines.
>
>
> Bruno Marchal wrote:
>>
>> If by absloute, you mean wrong in all
>> the models or intepretations of a theory about natural nulmbers, then
>> "0=1" is indeed wrong in all interpretations of arithmetical
>> theories.
> But what are "arithmetical theories"?
They are set of axioms written in first order calculus predicate
language, with a precise formal language (&, v, ~, ), the quantifiers
"for-all" (A) and it-exists" (E), and the variable x, y, z, ...
They contain the first order predicate calculus with equality, the
classical tautologies, the modus ponens rule, and the first order
logic rules and axioms, ---all that is knwon as "classical logic", and
this together with the arithmetical symbols "0, s, +, *".
Arithmetical theories are then given by the arithmetical axioms:
Ax ~(0 = s(x)) (For all number x the successor of x is different from
zero). With
AxAy ~(x = y) -> ~(s(x) = s(y)) (different numbers have different
successors)
and with different sort of axioms, containing usually the addition laws:
Ax x + 0 = x (0 adds nothing)
AxAy x + s(y) = s(x + y) ( meaning x + (y +1) = (x + y) +1)
and the multiplication axioms
Ax x *0 = 0
AxAy x*s(y) = x*y + x
There is theory Q which has the predecessor axiom, a theory R, which
has some other axioms, and PA which has in addition the infinity of
formula of the shape
(F(0) & Ax(F(x) -> F(s(x))) -> AxF(x), with F(x) being a formula in
the arithmetical language (with "0, s, +, *), and the logical symbols
as said above.
They are many of them, but for the sound one, above some threshold
(mainly given by the induction axioms) they obey to the arithmetical
hypostases, and they can formulate the WR problem.
> Can this even be defined? Maybe there
> is an arithmetical theory where 0=1 is true.
Yes indeed, there is many one.
Take anyone above, and adds the axiom "0 = 1".
Well, then you have to weaken the logical rules in some ways (among
many) to keep the theory interesting. With most logic, classical,
intuitionist, even quantum logic having that "0=1" will trivialize the
theory (making all statement true). But in the relevant logic "0=1"
can be less damageable, but not yet so interesting. I suspect the
fifth hypostase to be an arithmetical relevant logic, and this could
mean that "0 = 1" can play a role. In fact, in G it does already play
a role to in the consistency of inconsistency. not provable false
implies not provable (not provable false), and take "0 = 1" as meaning
false.
If you are interested, you might have to study some logic books.
Those theories are the *object* of study. They are machine theorem
provers with infinite ressource (that "Platonia"). Logicians study
both the theories/machines and their web of interpretations/semantics.
It is a branch of math.
>
>
> Bruno Marchal wrote:
>>
>>> All
>>> falsehood is depended on assuming certain axioms - while truth is
>>> not.
>>
>> That makes truth even more absolute.
> Well, that's good in my mind. Truth seems to be the most absolute
> thing for
> me.
OK. (I mean we might agree on this).
>
>
>
> Bruno Marchal wrote:
>>
>>> I think it is an error to say "if God or Platonia proves "0=1",
>>> then we are *all* in trouble." because we can't say what it would
>>> mean if
>>> God proves 0=1 according to the axioms we use. Or it means simply
>>> that God
>>> states things that are wrong in certain systems, which also poses no
>>> problem.
>>
>> Well, if God actually comes by, and says "0 = 1", I will conclude
>> something like "oh! God has some sense of humour", or I will think
>> that's not God, or I will thinks "I must be dreaming", etc.
> I meant actually proving.
Then pigs have wings. And here is a white rabbit, and two others there.
> Of course we don't know what it would mean if God
> would prove 0=1 according to our axioms, but this is my point.
It would mean, by definition, that God uses an inconsistent
arithmetical theory. Which one precisely?
>
>
> Bruno Marchal wrote:
>>
>>>
>>> I would not insist on this so much if I would not suspect that
>>> considering
>>> the possibility of something being an "ultimate falsehood" or
>>> "totally
>>> wrong" leads to disregarding some statements instead of seeing their
>>> truth.
>>> We don't have to avoid "wrong" statements. They simply are not as
>>> proliferative as (more) true statements.
>>
>> I disagree. Most statements in most (non arithmetical) theories are
>> wrong.
> It's hard to tell, I think. In most theories there is not even an
> absolutely
> clear distinction between right and wrong.
For all "enough rich" or Löbian theories, the border between right and
wrong countains the fractal shapes of the border between the provable
and the refutable. Universal numbers are confronted with the whole
richness of the geometry separating right and wrong. It is like the
border of the mandelbrot set.
> Physical theories for example are
> (as far as we now) never completely right, so are they wrong?
Very difficult question. (without or with comp).
Exactly. Always, even when we talk about machine. But to study this
for machine necessitates to handle first the simplest case of ideally
correct machines, and the surprise is that it leads to a transfinite
ladder of difficulties. That little "universal (Turing) machine", or a
degree four Diophantine equation already put quite a mess in Platonia,
and the sound machine can only acknowledge the difficulties.
>
> If we define a first order logical theory and have an
> interpretation, to
> validly prove anything we must at least assume that these
> definitions/interpretation are meaningful.
Sure, but we have a tons of models, so we find them meaningful. Just
that we discover that they are rich of unexpected structures. It is
because we make the rule clear and simple that we can, by using the
"mathematical logical 'Hubble' to discover the complexity of the
subject.
> Otherwise we can just reject them by not finding them meaningful and
> thus
> reject any proof derived from it.
That happens, and happened many times. Both Curry and Church, and
Frege, have developed theories which have fallen down literally, by
being shown to be inconsistent. New theories emerges from that. That
happens all the times. Sometimes a theory survives by its
interpretation evolving, and vice versa.
There is a 'Galois connection' between theories and their
interpretation, like between equation and surface. That is: the less a
theory has axioms, the more it has interpretations.
When we have to take into account the internal interpretations build
by the objects of the theories themselves, it is even far more
complex, but both comp and the quantum gives non trivial hints.
Bruno
Pzomby
> >> That is why I limit myself for the TOE to natural numbers and their
> >> addition and multiplication.
> >> The reason is that it is enough, by comp, and nobody (except perhaps
> >> some philosophers) have any problem with that.
>
> > Yes. A couple of questions from a philosophical point of view:
>
> > Language gives meaning to the numbers as in their operations;
> > functions, units of measurements (kilo, meter, ounce, kelvin etc.).
>
> I am not sure language gives meaning. Language have meaning, but I
> think meaning, sense, and reference are more primary.
> With the mechanist assumption, meaning sense and references will be
> 'explained' by what the numbers 'thinks' about that, in the manner of
> computer science (which can be seen as a branch of number theory).
>
stating that numbers have or represent some type of dispositional
property?
What of the opinion that ‘numbers’ themselves (without human
consciousness to perform operations and functions) only represent
instances of matter and forces with their dispositional properties?
> > Numbers alone may symbolize some fundamental describable matter and
> > forces but a complete and coherent TOE should include elevated human
> > consciousness beyond the primitive which in itself requires a
> > relatively sophisticated language to give meaning to the numbers and
> > their operations.
>
> Hmm... You can use numbers to symbolize things, by coding, addresses,
> etc. But numbers constitutes a reality per se, more or less captured
> (incompletely) by some theories (language, axioms, proof
> technics, ...). In this context, that might be important.
>
>
‘nouns’?
If so, then numbers would be human mental objects that have properties
of both functions and relations.
Thanks
>
> > Would not any TOE describing the universe appears to require human
> > sophisticated language using referent nouns, (and conjunctions,
> > adjectives and verbs etc.) to give meaning to the numbers and their
> > functions and operations?
>
> With the mechanist assumption, humans and their language will be
> described by machine operations, which will corresponds to a
> collection of numbers relations (definable with addition and
> multiplication). This is not obvious and relies in great part of the
> progress of mathematical logic.
>
>
> http://iridia.ulb.ac.be/~marchal/- Hide quoted text -
>
> - Show quoted text -
Bruno Marchal
On 02 Mar 2011, at 05:48, Pzomby wrote:
>>
>>>> That is why I limit myself for the TOE to natural numbers and their
>>>> addition and multiplication.
>>>> The reason is that it is enough, by comp, and nobody (except
>>>> perhaps
>>>> some philosophers) have any problem with that.
>>
>>> Yes. A couple of questions from a philosophical point of view:
>>
>>> Language gives meaning to the numbers as in their operations;
>>> functions, units of measurements (kilo, meter, ounce, kelvin etc.).
>>
>> I am not sure language gives meaning. Language have meaning, but I
>> think meaning, sense, and reference are more primary.
>> With the mechanist assumption, meaning sense and references will be
>> 'explained' by what the numbers 'thinks' about that, in the manner of
>> computer science (which can be seen as a branch of number theory).
>>
>
> Not sure what you mean by “what the numbers ‘thinks’ ”. Are you
> stating that numbers have or represent some type of dispositional
> property?
Yes. Not intrinsically. So you cannot say the number 456000109332897
likes the smell of coffee, but it makes sense to say that relatively
to the universal numbers u1, u2, u3, ... the number 456000109332897
likes the smell of coffee. A bit like you could say, relatively to
fortran, the number x computes this or that function.
A key point is that if a number feels something, it does not know
which number 'he' is, and strictly speaking we are confronted to many
vocabulary problems, which I simplifies for not being too much long
and boring. I shoudl say that a number like 456000109332897 might play
the local role of a body of a person which likes the smell of coffee.
But, locally, I identify person and their bodies, knowing that in
fine, the 'real physical body" will comes from a competition among all
universal numbers, or among all the corresponding computational
histories.
>
> What of the opinion that ‘numbers’ themselves (without human
> consciousness to perform operations and functions) only represent
> instances of matter and forces with their dispositional properties?
Once you have addition and multiplication, you don't need humans to do
the interpretation. Indeed with addition and multiplication, you have
a natural encoding of all interpretation by all universal numbers.
The idea that matter and forces have dispositional properties is
locally true, but we have to extract matter and forces from the more
primitive relation between numbers if we take the comp hypothesis
seriously enough (that is what I argue for, at least, cf UDA, MGA,
AUDA).
>
>
>>> Numbers alone may symbolize some fundamental describable matter and
>>> forces but a complete and coherent TOE should include elevated human
>>> consciousness beyond the primitive which in itself requires a
>>> relatively sophisticated language to give meaning to the numbers and
>>> their operations.
>>
>
>
>> Hmm... You can use numbers to symbolize things, by coding, addresses,
>> etc. But numbers constitutes a reality per se, more or less captured
>> (incompletely) by some theories (language, axioms, proof
>> technics, ...). In this context, that might be important.
>>
>>
> Then, you are inferring, that ‘numbers’ can be and perhaps are
> ‘nouns’?
Why not. '24 is even', or '24 is the address of my uncle', etc. 24 is
a noun there.
>
> If so, then numbers would be human mental objects that have properties
> of both functions and relations.
Again, you don't need humans for that.
Universal numbers exists (provably so in even very little arithmetical
theories).
And assuming comp, it is (not so easy) to show that humans mental
state are relative computational states, which means relative numbers
(relative to universal numbers).
If you fix a universal number, each number can play the role of a
partial computable function: x(y) === phi_x(y), with phi_i an
enumeration of all partial computable function (which exists by Church
thesis).
>
> Thanks
You are welcome,
Bruno
Pzomby
to do the interpretation” and “the idea that matter and forces have
Then, in what describable realm does that ultimately put numbers under
the ‘comp hypothesis’?
>
>
> >>> Numbers alone may symbolize some fundamental describable matter and
> >>> forces but a complete and coherent TOE should include elevated human
> >>> consciousness beyond the primitive which in itself requires a
> >>> relatively sophisticated language to give meaning to the numbers and
> >>> their operations.
>
> >> Hmm... You can use numbers to symbolize things, by coding, addresses,
> >> etc. But numbers constitutes a reality per se, more or less captured
> >> (incompletely) by some theories (language, axioms, proof
> >> technics, ...). In this context, that might be important.
>
Bruno Marchal
At the ultimate ontological bottom, you need a infinite collection of
abstract primary objects, having primary elementary relations so that
they constitute a universal system (in the sense of Post, Church,
Turing, Kleene ...).
My two favorite examples (among an infinity possible) are
1) the numbers (0, s(0), s(s(0)), ...) together with addition and
multiplication. This is taught in high school, albeit their Turing
universality is not easy at all to demonstrate. In that case, the
numbers are put at the bottom.
2) the combinators (K, S, (K K), (K S), (S K), (S S), (K (K K)), (K (S
K), ....) Combinators are either K or S or any (X Y) with X and Y
being combinators. The basic basic elementary operation are the rule
of Elimination and Duplication:
((K x) y) = x
(((S x) y) z) = ((x z)(y z))
It can be shown that with the numbers you can define the combinators,
and with the combinators you can define the numbers. If you choose the
combinators at the ontological bottom, you get the numbers by
theorems, and vice versa. Both the numbers and the combinators are
Turing universal, and that makes them enough to emulate the Löbian
machines histories, and explain why from their points of view the
physical realm is apparent, and sensible.
We could start with a quantum universal system, but then we will lose
a criteria for distinguishing the quanta from the qualia (it is not
just 'treachery' with respect to the (mind) body problem).
Bruno
Pzomby
the question remains as to the realm that the primitive or fundamental
numbers exist in, if, in fact, they are at an ontological bottom. If
numbers are not a part of matter, forces and human consciousness where
do they exist? Perhaps it could be considered that quanta and qualia,
along with their obvious properties, have, and exude and perhaps
metaphorically contain the property of ‘number’. I think “number” is
a property of a ‘set’.
My brief opinion(s):
As well as numbers having dispositional and computational properties,
numbers remain symbolic or representative of their own dispositional,
relational and computational characteristics or attributes. A TOE
will describe in detail what numbers, mathematics and languages
represent (or what the computations represent). An accurate
description of the induction of universals (what numbers represent)
into particulars (matter, personhood etc.) would be a result.
‘Numbers’ (along with comp) appear to…like languages, words,
mathematical symbols and notations….have a trait of ‘being’
representational of forces and matter.
If universal numbers along with their dispositions and relations are
at the ontological bottom, then the process, (maybe evolvement or
induction) to matter, forces, body and mind, consciousness and
personhood should be describable in a coherent way.
Brent Meeker
> My brief opinion(s):
>
> As well as numbers having dispositional and computational properties,
> numbers remain symbolic or representative of their own dispositional,
> relational and computational characteristics or attributes. A TOE
> will describe in detail what numbers, mathematics and languages
> represent (or what the computations represent). An accurate
> description of the induction of universals (what numbers represent)
> into particulars (matter, personhood etc.) would be a result.
>
> mathematical symbols and notations�.have a trait of �being�
> representational of forces and matter.
>
> If universal numbers along with their dispositions and relations are
> at the ontological bottom, then the process, (maybe evolvement or
> induction) to matter, forces, body and mind, consciousness and
> personhood should be describable in a coherent way.
>
>
But Bruno isn't proposing that numbers are the ontological botttom.
He's proposing that computation is. Numbers are just one way of
representing and talking about computation and arithmetic is presumably
familiar to everyone. Whatever is taken as ontologically fundamental
can't be a representation of something else. There is a possibility
though that nothing is fundamental and that explanation and description
is always ultimately circular. If this circle is sufficiently broad, so
as to include everything, it might be considered a virtuous circularity,
rather than the vicious variety we're taught to avoid.
Brent
Bruno Marchal
If numbers were existing *in* something, they would not constitute an
ontological bottom.
You can take sets in place of numbers, and then the numbers exists
*in* models of set theories. or you can take the combinators, and the
number will be special combinators. But then you will ask "and where
the sets are living?", or "Were the combinators are living?". In
particular, the notion of sets is more demanding than he notion of
numbers.
But it is a category error to ask oneself *where* are the numbers. To
be somewhere has no meaning for a number. Their properties are more
like "to be even", "to be prime", "to be the Gödel number of a piece
of a computation", etc. You can define them by first order formula,
for example "x is even" is given by the formula Ey(x = s(s(0)) * y).
> If
> numbers are not a part of matter, forces and human consciousness where
> do they exist?
I answered this above. The question "where" does not apply to numbers,
like the question "what does that smell" does not apply to light.
> Perhaps it could be considered that quanta and qualia,
> along with their obvious properties, have, and exude and perhaps
> metaphorically contain the property of ‘number’. I think “number” is
> a property of a ‘set’.
Numbers can manifest themselves in many ways, and certainly the quanta
are among their most wonderful manifestations. I mean the quantum
quanta! But QM is a wave theory, and waves have a long standing
relationship with number (and music), since at least Pythagorus. But
waves, and quantum quanta are more complex than numbers. Your mind
needs to make sense of them before making sense of the waves and their
interference.
>
> My brief opinion(s):
>
> As well as numbers having dispositional and computational properties,
> numbers remain symbolic or representative of their own dispositional,
> relational and computational characteristics or attributes.
Yes, indeed.
> A TOE
> will describe in detail what numbers, mathematics and languages
> represent (or what the computations represent). An accurate
> description of the induction of universals (what numbers represent)
> into particulars (matter, personhood etc.) would be a result.
Exactly.
>
> ‘Numbers’ (along with comp) appear to…like languages, words,
> mathematical symbols and notations….have a trait of ‘being’
> representational of forces and matter.
Somehow. The fundamentality arrow is roughly like this: NUMBERS =>
UNIVERSAL CONSCIOUSNESS => PHYSICAL LAWS => BIOLOGICAL CONSCIOUSNESS.
A bit like in Neoplatonism.
Now, numbers can be replaced by combinators, fortran programs, lambda
expressions, diophantine polynomials, ... anything (Post-Turing-
Kleene ...)-universal.
>
> If universal numbers along with their dispositions and relations are
> at the ontological bottom, then the process, (maybe evolvement or
> induction) to matter, forces, body and mind, consciousness and
> personhood should be describable in a coherent way.
I think that is the case and this in a sufficiently precise way as to
be refuted, or not, by nature. I would never have dared to explain
this if QM, without collapse, did not fit so nicely with this
(informally and formally).
Bruno
1Z
On Mar 4, 8:02 am, Bruno Marchal <marc...@ulb.ac.be> wrote:
> Somehow. The fundamentality arrow is roughly like this: NUMBERS =>
> UNIVERSAL CONSCIOUSNESS => PHYSICAL LAWS => BIOLOGICAL CONSCIOUSNESS.
PHYSICS=>COMPUTATION=>CONSCIOUSNESS=>NUMBERS
Shows how computationalism is compatible with mathematical anti
realism
Bruno Marchal
I remind you that you are the one defending computationalism (yes
doctor + Church thesis) and mathematical antirealism. I am the one
arguing that comp is incompatible with materialism/physicalism.
What is left, without materialism, could be biologicalism,
mathematicalism, ... perhaps theologicalism. The terms are not
important. To understand the reasoning and its implications is what
matter.
Computationalism needs only the common sense idea in math that if u is
a universal number then u(n) will converge or will not converge. This
can be seen as a formal statement.
Are you conceding that we have to abandon comp to keep math?
Bruno