Rép: ROADMAP (well, not yet really...
Bruno Marchal
I am no more sure you read the post, nor am I sure you really search
understanding.
>> Le 18-août-06, à 17:38, 1Z a écrit :
>>
>>> That is an explanation of mind-independence, not of existence.
>>> The anti-Platonist (e.g. the formalist) can claim that
>>> the truth of mathematical statments is mind-independent,
>>> but their existence isn't.
>>
>>
>> "Their" existence ? Mathematical statements needs "chatty" machines.
>
> Mathematics proceded for centuries without any machines at all.
Here you don't answer the question. In "their existence" you conflate
many things making your statement ambiguous. Also I was in the comp
context, and I was just saying that the mathematical statements need
the" human machine".
> If AR makes no existential commitments, it cannot lead
> to the existential conclusion that there is no such thing
> as matter.
No scientific theories can prove the non existence of *anything*. I
have made clear comp just shows that primary matter cannot have
explanatory purpose. Have you read the Universal Dovetailer Argument?
>> Of course! But that is what I am currently explaining. If you have
>> follow the UDA, then, even if you could not yet be completely
>> convinced
>> by each steps, you should at least be able to figure out in which
>> sense
>> "you", here and now, in the "shape" of an OM, to borrow the list
>> vocabulary, exist as a relative number.
>
>
> I cna't be persuaded of that without first being
> persuaded that numbers exist.
In which sense? We have already discussed this. I am not using the
expression "such number exists" in a sense stronger than any
mathematical user. You are the one adding unnecessary magic here. I am
such you believe numbers exist. Of course you don't believe in
"physical numbers", neither I do, giving that "physical" will already
be a "property" defined by infinities of relations between numbers,
etc.
You are the one assuming some "primary matter" without much precision.
You told me it has no property of its own, but you never did answer the
question of how could it could give rise to any property at all. Where
does that "primary matter" comes from? Why and how would that suddenly
explain qualia, and quanta, and more precisely how do you associate
consciousness to it without introducing actual third person infinities
(by UDA you can't, unless you throw up comp, that is, unless you do
introduce actual infinities in the third person description of minds).
(With comp the infinities appears or interfere with the 1-person views
only, through local probabilities).
If you really want to keep both "standard comp" *and* aristotelian
materialism/naturalism, you should better find some weakness in the UD
reasoning. There are subtler points where your criticism could be more
constructive it seems to me.
Bruno
Bruno Marchal
Plotinus's terms:
Primary Hypostases:
1) the ONE
2) the Divine Intellect
3) the all-soul
Secondary hypostases:
4) Intelligible Matter
5) Sensible Matter
With the UDA, you can already try
Primary Hypostases:
1) truth
2) third person communicable truth
3) first person truth
Secondary hypostases:
4) probability on computationnal consistent states/histories
5) probability on computational consistent true states/histories
With the lobian interview the self-referential correct intellect is
given by the modal logic G, and the self-referential truth (including
the non provable one) is given by G*. This gives the following
interpretation of a weaker version of UDA in arithmetic (comp is not
yet needed); the hypostases are with B for Godel's purely arithmetical
provability predicate (Beweisbar):
Primary Hypostases:
1) arithmetical truth (p)
2) provability (Bp)
3) provability-and-truth (Bp & p)
Secondary hypostases:
4) provability-and-consistency (Bp & ~B~p)
5) provability-and-consistency-and-truth (Bp & ~B~p & p)
But, thanks to incompleteness, and the fact that machine as rich as PA,
can reflect that incompleteness, some hypostases' discourses are
divided in two parts: the true, and the communicable (third person
provable) one. We get 8 hypostases:
Primary Hypostases:
1) arithmetical truth (p)
2) provability (G) -------- 2') the same, but described by G*
3) provability-and-truth (S4Grz, curiously enough it does not divide)
Secondary hypostases:
4) provability-and-consistency (Z)-------- 4') same, but described by
G* (= Z*)
5) provability-and-consistency-and-truth (X)-------- 5') same, but
described by G* (X*)
Until now, we have not yet introduced comp in the interview.
With B = Beweisbar; comp can be translated by p -> Bp. This formula
characterized the Sigma1 formula (Visser Theorem), that is the RE sets,
the Wi, the accessible states by a Universal Machine (with CT).
Let V = G + (p -> Bp)
We get
Primary Hypostases:
1) Sigma1 arithmetical truth (p)
2) provability (V) -------- 2') the same, but described by G* (V*)
3) provability-and-truth (S4Grz1, curiously enough it does not divide)
Secondary hypostases:
4) provability-and-consistency (Z1)-------- 4') same, but described by
G* (= Z1*)
5) provability-and-consistency-and-truth (X1)-------- 5') same, but
described by G* (X1*)
The logical of the physical proposition should emerge at least in Z1*.
But actually the whole of S4Grz1, Z1*, and X1* define, at least
formally, a notion of arithmetical quantization.
Bruno
1Z
Bruno Marchal wrote:
> Hi Peter,
>
> I am no more sure you read the post, nor am I sure you really search
> understanding.
>
>
> >> Le 18-août-06, à 17:38, 1Z a écrit :
> >>
> >>> That is an explanation of mind-independence, not of existence.
> >>> The anti-Platonist (e.g. the formalist) can claim that
> >>> the truth of mathematical statments is mind-independent,
> >>> but their existence isn't.
> >>
> >>
> >> "Their" existence ? Mathematical statements needs "chatty" machines.
> >
> > Mathematics proceded for centuries without any machines at all.
>
>
> Here you don't answer the question. In "their existence" you conflate
> many things making your statement ambiguous.
No, "their" refers to mathematical statements.
"The anti-Platonist (e.g. the formalist) can claim that
the truth of mathematical statments is mind-independent,
but also that the existence of mathematical statments is not
mind-independent"
. Also I was in the comp
> context, and I was just saying that the mathematical statements need
> the" human machine".
>
>
> > If AR makes no existential commitments, it cannot lead
> > to the existential conclusion that there is no such thing
> > as matter.
>
> No scientific theories can prove the non existence of *anything*.
Of course they can, within the scientific standard
of proof. Perpetual motion machines, for instance.
> I
> have made clear comp just shows that primary matter cannot have
> explanatory purpose.
If minds are made of Platonically existing comptutations
or numbers, they don't need to be made of matter as
well. In that sense matter would we without purpose.
But that depends on the assumption that there is such
a thing as Platonic existence in the first place,
which needs ot be justified or at least clearly stated.
> Have you read the Universal Dovetailer Argument?
How important is the stuiff about Plotinus ?
> >> Of course! But that is what I am currently explaining. If you have
> >> follow the UDA, then, even if you could not yet be completely
> >> convinced
> >> by each steps, you should at least be able to figure out in which
> >> sense
> >> "you", here and now, in the "shape" of an OM, to borrow the list
> >> vocabulary, exist as a relative number.
> >
> >
> > I cna't be persuaded of that without first being
> > persuaded that numbers exist.
>
>
> In which sense? We have already discussed this. I am not using the
> expression "such number exists" in a sense stronger than any
> mathematical user.
Then you have no agument against matter.
> You are the one adding unnecessary magic here. I am
> such you believe numbers exist. Of course you don't believe in
> "physical numbers", neither I do, giving that "physical" will already
> be a "property" defined by infinities of relations between numbers,
If numbers don't exist in the sense that I exist,
then I cannot be a number.
> etc.
> You are the one assuming some "primary matter" without much precision.
The empirical approach does not need as much precision as
the rationalist approach.
> You told me it has no property of its own, but you never did answer the
> question of how could it could give rise to any property at all.
Some properties are instantiated and others are not. What matter
lends is the instantiation itself.
Matter is a bare substrate with no properties of its own. The question
may well be asked at this point: what roles does it perform ? Why not
dispense with matter and just have bundles of properties -- what does
matter add to a merely abstract set of properties? The answer is that
not all bundles of posible properties are instantiated, that they
exist.
What does it mean to say something exists ? "..exists" is a meaningful
predicate of concepts rather than things. The thing must exist in some
sense to be talked about. But if it existed full, a statement like
"Nessie doesn't exist" would be a contradiction ...it would amout to
"the existing thign Nessie doesnt exist". However, if we take that the
"some sense" in which the subject of an "...exists" predicate exists is
only initially as a concept, we can then say whether or not the concept
has something to refer to. Thus "Bigfoot exists" would mean "the
concept 'Bigfoot' has a referent".
What matter adds to a bundle of properties is existence. A non-existent
bundle of properties is a mere concept, a mere possibility. Thus the
concept of matter is very much tied to the idea of contingency or
"somethingism" -- the idea that only certain possible things exist.
The other issue matter is able to explain as a result of having no
properties of its own is the issue of change and time. For change to be
distinguishable from mere succession, it must be change in something.
It could be a contingent natural law that certain properties never
change. However, with a propertiless substrate, it becomes a logical
necessity that the substrate endures through change; since all changes
are changes in properties, a propertiless substrate cannot itself
change and must endure through change. In more detail here
> Where
> does that "primary matter" comes from?
The empricial evidence indicates that there was never a time when it
didn't.
exist.
> Why and how would that suddenly
> explain qualia,
The Hard Problems boils down to the problem of reducing qualia
to mathematical strutures. If mathematical structures is not all there
is,
the problem can be evaded. If qualia are fundamental properties
of matter, alongside structural-mathemaitcal ones, they do
not need to be reduced.
> and quanta,
Quanta are an observed, empirical fact. Empricists (Somethingists)
accept that there are facts which cannot be explained by
apriori reasoning. There is no particular reason
why matter should not behave quantum-ly or why
it should behave classically.
> and more precisely how do you associate
> consciousness to it without introducing actual third person infinities
Why would you think I am assuming infinities ? If you make
the assumption that everything is mathematical, and someone
claims that some things are not Turing-emulable, I suppose
that would force you to the conclusion that they
exceed they are unemulable becasue they
exceed the capacity of TMs quantitively.
But if it is a brute fact that some things are fundamentally
mathematical, that is all you need to explain
why they ar nto emulabe. A mathemtical reason
is not needed, and would in fact be paradoxical.
> (by UDA you can't, unless you throw up comp, that is, unless you do
> introduce actual infinities in the third person description of minds).
> (With comp the infinities appears or interfere with the 1-person views
> only, through local probabilities).
>
> If you really want to keep both "standard comp" *and* aristotelian
> materialism/naturalism, you should better find some weakness in the UD
> reasoning.
No I don't. The UDA cannot show we are products of a UD
unless it can show that the UD has the same kind of
existene we have. Computationalism could be true
in a material universe. It could be a brute fact that matter
exists and Platonia doesn't. Or vice versa. Either way,
it would be a brute fact and not an entailment of
standard computationalism.
> There are subtler points where your criticism could be more
> constructive it seems to me.
Arguments cannot lead to conclusions that are nto already implicit in
their
premisses. That is as subtle as I need to be.
> Bruno
Bruno Marchal
Le 20-août-06, à 21:09, 1Z a écrit :
> If minds are made of Platonically existing comptutations
> or numbers, they don't need to be made of matter as
> well. In that sense matter would we without purpose.
>
> But that depends on the assumption that there is such
> a thing as Platonic existence in the first place,
> which needs ot be justified or at least clearly stated.
I already told you that I interpret
There exists a prime number "in plato heaven",
by
"There exist a prime number" is true independently of me, you, the
universe ...
comp does not need a magical platonic realm in your sense. I don't
introduce it for the notion of matter and it would be a fatal damage
for comp if we were needing such a magic stuff for numbers.
Comp needs just arithmetical realism AR. It is just the idea that the
truth value of arithmetical proposition, including existential
propositions, does not depend on me or of any cognition apparatus
(indeed "cognition apparatus" are defined, with comp, by relation
between numbers, like in Artificial Intelligence, or in comp cognitive
science.
Bruno
1Z
> Content-Type: text/enriched; charset=ISO-8859-1
> Content-Transfer-Encoding: quoted-printable
> X-Google-AttachSize: 1201
>
>
>
> Le 20-août-06, à 21:09, 1Z a écrit :
>
>
>
> or numbers, they don't need to be made of matter as
>
> well. In that sense matter would we without purpose.
>
>
> But that depends on the assumption that there is such
>
> a thing as Platonic existence in the first place,
>
> which needs ot be justified or at least clearly stated.
>
>
>
> I already told you that I interpret
>
>
> There exists a prime number "in plato heaven",
>
>
> by
>
>
>
> "There exist a prime number" is true independently of me, you, the
> universe ...
>
>
> comp does not need a magical platonic realm in your sense. I don't
> introduce it for the notion of matter and it would be a fatal damage
> for comp if we were needing such a magic stuff for numbers.
>
> Comp needs just arithmetical realism AR. It is just the idea that the
> existential propositions</underline></bold>, does not depend on me or
> of any cognition apparatus (indeed "cognition apparatus" are defined,
> with comp, by relation between numbers, like in Artificial
> Intelligence, or in comp cognitive science.
If Plato's heaven doesn't exist, I can't be in it.
If numbers do not explain my existence -- explaining
how a strucuture like a physial world would emerge from
a UD if a UD existed does not explain my *existence* --
then something else does, such as matter.
> Bruno
>
>
>
> http://iridia.ulb.ac.be/~marchal/
>
>
> --Apple-Mail-7--391547409--
Bruno Marchal
Le 21-août-06, à 13:34, 1Z a écrit :
> If Plato's heaven doesn't exist, I can't be in it.
I can hardly not agree with that.
>
> If numbers do not explain my existence -- explaining
> how a strucuture like a physial world would emerge from
> a UD if a UD existed does not explain my *existence* --
> then something else does, such as matter.
1) I don't think think so at all. Even if numbers cannot explain your
existence, it does not follows that matter can explain it, nor God, nor
anything else a priori. Actually, assuming the comp hyp., the UDA shows
precisely why a notion of primitive matter cannot explain the mind.
2) Numbers, and the UD, by existing just in the usual sense of realist
mathematicians (like in statements similar to "it exists a perfect
number") explains completely your (correct, non illusory) *feeling*
of existence, including both the sharable part of it (quanta) and the
unsharable part of it (the qualia).
3) ... and all this in a testable way, given that comp makes precise
predictions.
Let me simplify to be clearer. The TOE has made progress:
1) Copenhagen TOE:
-Numbers
-Wave equation
-Unintelligible mind theory (collapse)
2) Everett TOE:
-Wave equation
-Comp
3) your servitor:
-Comp
All what I say is that if comp is true, then
1) by UDA, we have to derive the wave equation (UDA explains why we
have to)
2) by the arithmetical UDA, we know at least one way how to retrieve
it (by the interview of a UTM)
Bruno
1Z
Bruno Marchal wrote:
> Le 21-août-06, à 13:34, 1Z a écrit :
>
>
> > If Plato's heaven doesn't exist, I can't be in it.
>
>
> I can hardly not agree with that.
>
>
> >
> > If numbers do not explain my existence -- explaining
> > how a strucuture like a physial world would emerge from
> > a UD if a UD existed does not explain my *existence* --
> > then something else does, such as matter.
>
>
> 1) I don't think think so at all. Even if numbers cannot explain your
> existence, it does not follows that matter can explain it, nor God, nor
> anything else a priori.
Matter has been a succesful explanation for many centuries -- an
aposteriori explanation. Who said that only apriori explanations are
acceptable ?
Is that the premiss underlying your other premisses ?
> Actually, assuming the comp hyp., the UDA shows
> precisely why a notion of primitive matter cannot explain the mind.
Matter can explain anything computationalism or
mathematics can explain, since any computaiotnal
or mathematical structurecan be implmented in matter.
It can also provide support for time and qulia, and
explain away HP universes.
> 2) Numbers, and the UD, by existing just in the usual sense of realist
> mathematicians (like in statements similar to "it exists a perfect
> number") explains completely your (correct, non illusory) *feeling*
> of existence, including both the sharable part of it (quanta) and the
> unsharable part of it (the qualia).
Only if the "usual sense of realist mathematicians" is
a sense amouting to the kind of existence I actually
have (even if I mistakenly think that is material existence,
I still have ot exist in some sense in order to make the mistake!).
But that is what I have been saying all along. The argumentative
work is being done by the hidden assumption of Platonism,
not the explicit assumption of computationalism.
> 3) ... and all this in a testable way, given that comp makes precise
> predictions.
>
> Let me simplify to be clearer. The TOE has made progress:
>
>
> 1) Copenhagen TOE:
>
> -Numbers
> -Wave equation
> -Unintelligible mind theory (collapse)
>
>
>
> 2) Everett TOE:
>
> -Wave equation
Everett is compatible with standard computationalism.
It doesn't have to assume computationalism. Any non-magical
theory of mind will do.
> -Comp
>
> 3) your servitor:
>
> -Comp
Not just computationalism, because you need to
assume a UD exists
a) " just in the usual sense of realist mathematicians"
[ a "realist mathematician" being a Platonist .. ]
b) in some way real enough for me to be part of its output.
Computationalsim is a thesis about minds, not about maths...
jam...@prodigy.net
----- Original Message -----From: Bruno MarchalSent: Monday, August 21, 2006 6:39 AMSubject: Re: Rép: ROADMAP (well, not yet really...
skip
I already told you that I interpret
There exists a prime number "in plato heaven",
by
"There exist a prime number" is true independently of me, you, the universe ...
comp does not need a magical platonic realm in your sense. I don't introduce it for the notion of matter and it would be a fatal damage for comp if we were needing such a magic stuff for numbers.
Comp needs just arithmetical realism AR. It is just the idea that the truth value of arithmetical proposition, including existential propositions, does not depend on me or of any cognition apparatus (indeed "cognition apparatus" are defined, with comp, by relation between numbers, like in Artificial Intelligence, or in comp cognitive science.
Bruno
There exist infinite prime numbers in Plato's heaven and 1000 of them can dance on the point of a pin.I am sure you have something better thn that!
John
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Bruno Marchal
Le 22-août-06, à 05:32, <jam...@prodigy.net> a écrit :
Feynman discovered quantum computation by asking himself how many bits
can be handled for a period of time on the point of a pin.
Engineers would appreciate to know how many primes numbers we could
encode on a pin. This is not a silly question, although out of topic in
our fundamental quest, I guess.
Bruno
jam...@prodigy.net
Bruno Marchal
Le 21-août-06, à 16:23, 1Z a écrit :
>
>
> Bruno Marchal wrote:
>> Le 21-août-06, à 13:34, 1Z a écrit :
>>
>>
>>> If Plato's heaven doesn't exist, I can't be in it.
>>
>>
>> I can hardly not agree with that.
>>
>>
>>>
>>> If numbers do not explain my existence -- explaining
>>> how a strucuture like a physial world would emerge from
>>> a UD if a UD existed does not explain my *existence* --
>>> then something else does, such as matter.
>>
>>
>> 1) I don't think think so at all. Even if numbers cannot explain your
>> existence, it does not follows that matter can explain it, nor God,
>> nor
>> anything else a priori.
>
> Matter has been a succesful explanation for many centuries -- an
> aposteriori explanation. Who said that only apriori explanations are
> acceptable ?
> Is that the premiss underlying your other premisses ?
I talk about primitive or primary matter. Just show me one text where
that notion explain anything.
I have never find a physical theory using it, except that it is
implicitly assume in the background, but the notion are never referred
too.
>
>
>> Actually, assuming the comp hyp., the UDA shows
>> precisely why a notion of primitive matter cannot explain the mind.
>
> Matter can explain anything computationalism or
> mathematics can explain, since any computaiotnal
> or mathematical structurecan be implmented in matter.
Read UDA. Primary matter is shown to be without any explanatory
purpose. You can still believe in it, like anyone can believe that car
are really pulled by invisible horses, and no thermodynamician will be
able to prove that wrong. They can only argue it is unnecessary. All
the same with UDA: it shows that primary matter has no purpose.
>
> It can also provide support for time and qulia, and
> explain away HP universes.
All serious people in the philosophy of mind agree that the mind-body
problem is not yet solved. Even Dennett agrees on this in the last
chapter of his "consciousness explained". Matter makes things worst
because, at least with comp, we have to justify it without positing it.
>
>> 2) Numbers, and the UD, by existing just in the usual sense of realist
>> mathematicians (like in statements similar to "it exists a perfect
>> number") explains completely your (correct, non illusory) *feeling*
>> of existence, including both the sharable part of it (quanta) and the
>> unsharable part of it (the qualia).
>
> Only if the "usual sense of realist mathematicians" is
> a sense amouting to the kind of existence I actually
> have (even if I mistakenly think that is material existence,
> I still have ot exist in some sense in order to make the mistake!).
>
> But that is what I have been saying all along. The argumentative
> work is being done by the hidden assumption of Platonism,
> not the explicit assumption of computationalism.
>
>> 3) ... and all this in a testable way, given that comp makes precise
>> predictions.
>>
>> Let me simplify to be clearer. The TOE has made progress:
>>
>>
>> 1) Copenhagen TOE:
>>
>> -Numbers
>> -Wave equation
>> -Unintelligible mind theory (collapse)
>>
>>
>>
>> 2) Everett TOE:
>>
>> -Wave equation
>
> Everett is compatible with standard computationalism.
> It doesn't have to assume computationalism. Any non-magical
> theory of mind will do.
Well, actually I do agree a bit with you here. But comp is assumed by
almost all many-worlder. This is because comp is the only known theory
of mind which does not posit actual infinities, and in general people
attracted to MW are motivated by searching a theory compatatible with
reasonable approach to the mind.
>
> Not just computationalism, because you need to
> assume a UD exists
No. The UD exists by AR, without which CT would not make sense.
I recall that by "the UD exists", I mean just that the truth of some
existential proposition in number theory is independent of me.
I'm afraid you are defending a (widespread) aristotelian misconception
of Platonia, like if it was some magical realm in which the numbers
exists, when I just mean the usual meaning of existence of numbers. Yes
the usual meaning is platonist. Mathematicians are almost all platonist
about natural numbers, even the week-end.
I think that if you study the UDA, it will be easier for you to
interpret the terms by the use I make of them.
Bruno
Bruno Marchal
Le 22-août-06, à 18:06, <jam...@prodigy.net> a écrit :
> So where is the "key" to translate number-monsters into
> "thought-monsters"?
In front of you. Computer or universal machine, or universal numbers.
More explanation in the posts.
Bruno
jam...@prodigy.net
----- Original Message -----
From: "Bruno Marchal" <mar...@ulb.ac.be>
To: <everyth...@googlegroups.com>
Sent: Wednesday, August 23, 2006 7:56 AM
Subject: Re: Rép: ROADMAP (well, not yet really...
Le 22-août-06, à 18:06, <jam...@prodigy.net> a écrit :
> So where is the "key" to translate number-monsters into
> "thought-monsters"?
In front of you. Computer or universal machine, or universal numbers.
More explanation in the posts.
Bruno
-------------------
Not as I see it. I tried to describe what I thought and ended up with the
question you emphasized above.
The posts (many of them) take the 'translational' key for granted, others
have similar doubts to mine.
No "understandable" bridging occurred for those who do not start from the
inside of the "number world". In any religion: you have to believe to
believe.
John
--
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1Z
Bruno Marchal wrote:
> Le 21-août-06, à 16:23, 1Z a écrit :
>
> >
> >
> > Bruno Marchal wrote:
> >> Le 21-août-06, à 13:34, 1Z a écrit :
> >>
> >>
> >>> If Plato's heaven doesn't exist, I can't be in it.
> >>
> >>
> >> I can hardly not agree with that.
> >>
> >>
> >>>
> >>> If numbers do not explain my existence -- explaining
> >>> how a strucuture like a physial world would emerge from
> >>> a UD if a UD existed does not explain my *existence* --
> >>> then something else does, such as matter.
> >>
> >>
> >> 1) I don't think think so at all. Even if numbers cannot explain your
> >> existence, it does not follows that matter can explain it, nor God,
> >> nor
> >> anything else a priori.
> >
> > Matter has been a succesful explanation for many centuries -- an
> > aposteriori explanation. Who said that only apriori explanations are
> > acceptable ?
> > Is that the premiss underlying your other premisses ?
>
>
> I talk about primitive or primary matter. Just show me one text where
> that notion explain anything.
> I have never find a physical theory using it, except that it is
> implicitly assume in the background, but the notion are never referred
> too.
All physics assumes "Somethingism" -- it seeks to find the one
mathemticals structure, out of all the structures "in Platonia"
that describes the universe. Since i define matter in a somethingist
way, that means all physics is materialist.
> > It can also provide support for time and qulia, and
> > explain away HP universes.
>
>
> All serious people in the philosophy of mind agree that the mind-body
> problem is not yet solved.
There is difference between providing an explanation, making
and explanation possible, and making an explanation impossible.
Matterialism per se does not provide a solution to the MBP.
Matter makes certain classes of solution possible-- e.g. property
dualism.
Immaterialism makes the MBP harder or impossible.
http://www.geocities.com/peterdjones/diagrams/matter_substrate.jpg
> Even Dennett agrees on this in the last
> chapter of his "consciousness explained". Matter makes things worst
> because, at least with comp, we have to justify it without positing it.
Computationalism alone does not justify the existnce
of an entity capable of being appeared-to; so by itself
it does not allow matter to be explained away as an appearance.
> > Everett is compatible with standard computationalism.
> > It doesn't have to assume computationalism. Any non-magical
> > theory of mind will do.
>
>
> Well, actually I do agree a bit with you here. But comp is assumed by
> almost all many-worlder. This is because comp is the only known theory
> of mind which does not posit actual infinities,
Not at all. The uncomputability of matter, qualia
or anything else does not have to be justified in mathematical
terms by their being actual infinities. It can be justified
by their being fundamentally un-mathematical. For the
non-Platonist, it is a peculiarty of abstract mathematical
structures and behaviour that they can be emulated without deficit.
Non-emulability, by contrast , is just business as usual.
. and in general people
> attracted to MW are motivated by searching a theory compatatible with
> reasonable approach to the mind.
> > Not just computationalism, because you need to
> > assume a UD exists
>
> No. The UD exists by AR, without which CT would not make sense.
AR as a claim about truth is implied by comoputationalism, and is
not enough to support the real (=as real as I am) existence
of the UD.
AR as a claim about existence is
enough to support the real (=as real as I am) existence
of the UD, but is not impied by computationalism.
Stathis Papaioannou
> Matter is a bare substrate with no properties of its own. The question
> may well be asked at this point: what roles does it perform ? Why not
> dispense with matter and just have bundles of properties -- what does
> matter add to a merely abstract set of properties? The answer is that
> not all bundles of posible properties are instantiated, that they
> exist.
> What does it mean to say something exists ? "..exists" is a meaningful
> predicate of concepts rather than things. The thing must exist in some
> sense to be talked about. But if it existed full, a statement like
> "Nessie doesn't exist" would be a contradiction ...it would amout to
> "the existing thign Nessie doesnt exist". However, if we take that the
> "some sense" in which the subject of an "...exists" predicate exists is
> only initially as a concept, we can then say whether or not the concept
> has something to refer to. Thus "Bigfoot exists" would mean "the
> concept 'Bigfoot' has a referent".
>
> What matter adds to a bundle of properties is existence. A non-existent
> bundle of properties is a mere concept, a mere possibility. Thus the
> concept of matter is very much tied to the idea of contingency or
> "somethingism" -- the idea that only certain possible things exist.
But even existence can be defined as a bundle of properties. If I am
wondering whether the pencil on my desk exists I can look at it, pick it up,
tap it and so on. If my hand passes through it when I try to pick it up
then maybe it is just an illusion. If it passes all the tests I put it through
then by definition it exists. If I want to claim that some other object exists,
like Nessie, what I actually mean is that it exists *in the same way as this
pencil exists*. The pencil is the gold standard: there is no other, more
profound standard of existence against which it can be measured.
Stathis Papaioannou
_________________________________________________________________
Be one of the first to try Windows Live Mail.
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Brent Meeker
Maybe it's a holographic projection - in which case the projection (a certain state
of photons) does exist, and other people can see it. Even an illusion must exist as
some brain process. I understand Peters objection to regarding a "mere bundle" of
properties as existent. But I don't understand why one needs a propertyless
substrate. Why not just say that some bundles of properties are instantiated and
some aren't. Anyway, current physical theory is that there is a material
"substrate" which has properties, e.g. energy, spin, momentum,...
>If it passes all the tests I put it through
> then by definition it exists. If I want to claim that some other object exists,
> like Nessie, what I actually mean is that it exists *in the same way as this
> pencil exists*. The pencil is the gold standard: there is no other, more
> profound standard of existence against which it can be measured.
I agree. But the gold standard is not just that you see and touch that pencil - you
might be hallucinating. And you can't see an electron, or even a microbe. So what
exists or not is a matter of adopting a model of the world; and the best models take
account of a consistent theory of instruments as well as direct perception.
Brent Meeker
Stathis Papaioannou
> > But even existence can be defined as a bundle of properties. If I am
> > wondering whether the pencil on my desk exists I can look at it, pick it up,
> > tap it and so on. If my hand passes through it when I try to pick it up
> > then maybe it is just an illusion.
>
> Maybe it's a holographic projection - in which case the projection (a certain state
> of photons) does exist, and other people can see it. Even an illusion must exist as
> some brain process. I understand Peters objection to regarding a "mere bundle" of
> properties as existent. But I don't understand why one needs a propertyless
> substrate. Why not just say that some bundles of properties are instantiated and
> some aren't. Anyway, current physical theory is that there is a material
> "substrate" which has properties, e.g. energy, spin, momentum,...
Saying that there is a material substrate which has certain properties is just a working
assumption to facilitate thinking about the real world. It may turn out that if we dig into
quarks very deeply there is nothing "substantial" there at all, but solid matter will still be
solid matter, because it is defined by its properties, not by some mysterious raw physical
substrate.
> >If it passes all the tests I put it through
> > then by definition it exists. If I want to claim that some other object exists,
> > like Nessie, what I actually mean is that it exists *in the same way as this
> > pencil exists*. The pencil is the gold standard: there is no other, more
> > profound standard of existence against which it can be measured.
>
> I agree. But the gold standard is not just that you see and touch that pencil - you
> might be hallucinating. And you can't see an electron, or even a microbe. So what
> exists or not is a matter of adopting a model of the world; and the best models take
> account of a consistent theory of instruments as well as direct perception.
By "gold standard" I did not mean just direct sensory experience, but every possible
empirical test or measurement. A hallucination is a hallucination because other people
don't see it, it does not register on a photograph, and so on. A hallucination which
passed every possible reality test would not be a hallucination.
Brent Meeker
> Brent meeker writes:
>
>
>>>But even existence can be defined as a bundle of properties. If I am
>>>wondering whether the pencil on my desk exists I can look at it, pick it up,
>>>tap it and so on. If my hand passes through it when I try to pick it up
>>>then maybe it is just an illusion.
>>
>>Maybe it's a holographic projection - in which case the projection (a certain state
>>of photons) does exist, and other people can see it. Even an illusion must exist as
>>some brain process. I understand Peters objection to regarding a "mere bundle" of
>>properties as existent. But I don't understand why one needs a propertyless
>>substrate. Why not just say that some bundles of properties are instantiated and
>>some aren't. Anyway, current physical theory is that there is a material
>>"substrate" which has properties, e.g. energy, spin, momentum,...
>
>
> Saying that there is a material substrate which has certain properties is just a working
> assumption to facilitate thinking about the real world. It may turn out that if we dig into
> quarks very deeply there is nothing "substantial" there at all, but solid matter will still be
> solid matter, because it is defined by its properties, not by some mysterious raw physical
> substrate.
But I don't think we ever have anything but "working assumptions"; so we might as
well call our best ones "real"; while keeping in mind we may have to change them.
>>>If it passes all the tests I put it through
>>>then by definition it exists. If I want to claim that some other object exists,
>>>like Nessie, what I actually mean is that it exists *in the same way as this
>>>pencil exists*. The pencil is the gold standard: there is no other, more
>>>profound standard of existence against which it can be measured.
>>
>>I agree. But the gold standard is not just that you see and touch that pencil - you
>>might be hallucinating. And you can't see an electron, or even a microbe. So what
>>exists or not is a matter of adopting a model of the world; and the best models take
>>account of a consistent theory of instruments as well as direct perception.
>
>
> By "gold standard" I did not mean just direct sensory experience, but every possible
> empirical test or measurement. A hallucination is a hallucination because other people
> don't see it, it does not register on a photograph, and so on. A hallucination which
> passed every possible reality test would not be a hallucination.
>
> Stathis Papaioannou
True. But if we knew enough about how brains work we might be able to detect the
processes within one having an hallucination and identify them as presenting, say an
illusion of a pencil. In that case we would say that it was a *real* hallucination -
because then we have fitted it within our model of the world.
Brent Meeker
Stathis Papaioannou
> > Saying that there is a material substrate which has certain properties is just a working
> > assumption to facilitate thinking about the real world. It may turn out that if we dig into
> > quarks very deeply there is nothing "substantial" there at all, but solid matter will still be
> > solid matter, because it is defined by its properties, not by some mysterious raw physical
> > substrate.
>
> But I don't think we ever have anything but "working assumptions"; so we might as
> well call our best ones "real"; while keeping in mind we may have to change them.
That's just what I meant. If you say, this is *not* just a working assumption, there is some
definite, basic substance called reality over and above what we can observe, that is a
metaphysical statement which can only be based on something akin to religious faith.
Bruno Marchal
Le 25-août-06, à 23:24, 1Z a écrit :
> AR as a claim about truth is implied by comoputationalism, and is
> not enough to support the real (=as real as I am) existence
> of the UD.
It is you who come up with a notion of real existence. You are reifying
I don't know which theory.
>
> AR as a claim about existence is
> enough to support the real (=as real as I am) existence
> of the UD, but is not impied by computationalism.
And my WHOLE point is that it does not have to be that way.
Bruno
Bruno Marchal
Le 26-août-06, à 22:44, Brent Meeker a écrit :
> I understand Peters objection to regarding a "mere bundle" of
> properties as existent. But I don't understand why one needs a
> propertyless
> substrate. Why not just say that some bundles of properties are
> instantiated and
> some aren't.
I guess Peter needs it for having a notion of (absolute) instantiation.
If Peter takes the relative notion of instantiation, which is number
theoretical in nature, then he would loose any motivation for his bare
matter.
> Anyway, current physical theory is that there is a material
> "substrate" which has properties, e.g. energy, spin, momentum,...
I doubt this. Yes current *interpretations* of physical theories do
suppose a material substrate, but only for having peaceful sleep (like
the collapse non-answer in QM). Anyway, the theories does not
presuppose it. They presuppose only mathematical structure and
quantitative functor between those mathematical structure and numbers
that we can measure in some communicable ways.
Bruno
1Z
Stathis Papaioannou wrote:
> Brent meeker writes:
>
> > > But even existence can be defined as a bundle of properties. If I am
> > > wondering whether the pencil on my desk exists I can look at it, pick it up,
> > > tap it and so on. If my hand passes through it when I try to pick it up
> > > then maybe it is just an illusion.
> >
> > Maybe it's a holographic projection - in which case the projection (a certain state
> > of photons) does exist, and other people can see it. Even an illusion must exist as
> > some brain process. I understand Peters objection to regarding a "mere bundle" of
> > properties as existent. But I don't understand why one needs a propertyless
> > substrate. Why not just say that some bundles of properties are instantiated and
> > some aren't. Anyway, current physical theory is that there is a material
> > "substrate" which has properties, e.g. energy, spin, momentum,...
>
> Saying that there is a material substrate which has certain properties is just a working
> assumption to facilitate thinking about the real world. It may turn out that if we dig into
> quarks very deeply there is nothing "substantial" there at all, but solid matter will still be
> solid matter, because it is defined by its properties, not by some mysterious raw physical
> substrate.
I am not using the Bare Substrate to explian "solidity", which is as
you say
a matter of properties/behaviour.
I am using it to explain contingent existence, and (A series) time.
1Z
Stathis Papaioannou wrote:
> Brent Meeker writes:
>
> > > Saying that there is a material substrate which has certain properties is just a working
> > > assumption to facilitate thinking about the real world. It may turn out that if we dig into
> > > quarks very deeply there is nothing "substantial" there at all, but solid matter will still be
> > > solid matter, because it is defined by its properties, not by some mysterious raw physical
> > > substrate.
> >
> > But I don't think we ever have anything but "working assumptions"; so we might as
> > well call our best ones "real"; while keeping in mind we may have to change them.
>
> That's just what I meant. If you say, this is *not* just a working assumption, there is some
> definite, basic substance called reality over and above what we can observe, that is a
> metaphysical statement which can only be based on something akin to religious faith.
By youur definitions, it's a straight choice between metaphysics and
solipsism.
I choose metaphsyics.
We can posit the unobservable to expalint he observable.
(BTW: it it is wrong to posit an unobserved substrate, why is it
OK to posit unobserved worlds/branches ?)
1Z
Bruno Marchal wrote:
> Le 26-août-06, à 22:44, Brent Meeker a écrit :
>
> > I understand Peters objection to regarding a "mere bundle" of
> > properties as existent. But I don't understand why one needs a
> > propertyless
> > substrate. Why not just say that some bundles of properties are
> > instantiated and
> > some aren't.
>
> I guess Peter needs it for having a notion of (absolute) instantiation.
If you think, as I do, that there is a difference between
logical and physical posibility, you need to explain instantiation.
If you think, as I do, that there is a difference between
phsyical actuality and physical posibility, you need to explain
instantiation.
if you think, as rationalists do, that everything possible
is also necessary and actual, you don't need those
distinctions.
> If Peter takes the relative notion of instantiation, which is number
> theoretical in nature, then he would loose any motivation for his bare
> matter.
I don't think something can exist in relation to what does not exist.
if that is what you mean.
> > Anyway, current physical theory is that there is a material
> > "substrate" which has properties, e.g. energy, spin, momentum,...
>
>
> I doubt this. Yes current *interpretations* of physical theories do
> suppose a material substrate, but only for having peaceful sleep (like
> the collapse non-answer in QM).
All theories assume contingency.
> Anyway, the theories does not
> presuppose it. They presuppose only mathematical structure and
> quantitative functor between those mathematical structure and numbers
> that we can measure in some communicable ways.
No physical theory needs to presuppose numbers as
having an existence of their own. Formalists
can do physics.
> Bruno
>
> http://iridia.ulb.ac.be/~marchal/
1Z
Bruno Marchal wrote:
> Le 25-août-06, à 23:24, 1Z a écrit :
>
> > AR as a claim about truth is implied by comoputationalism, and is
> > not enough to support the real (=as real as I am) existence
> > of the UD.
>
>
> It is you who come up with a notion of real existence.
I am starting with the reality my own existence.
That is an *empirical* fact.
> You are reifying
> I don't know which theory.
That's because it is empirical! Whatever theory explains
or doesn't explain my existence, I exist.
> >
> > AR as a claim about existence is
> > enough to support the real (=as real as I am) existence
> > of the UD, but is not impied by computationalism.
>
>
> And my WHOLE point is that it does not have to be that way.
But you don't really address the existence question. You just loosely
assume it is the
same thing as truth.
Brent Meeker
> Brent Meeker writes:
>
>
>>>Saying that there is a material substrate which has certain properties is just a working
>>>assumption to facilitate thinking about the real world. It may turn out that if we dig into
>>>quarks very deeply there is nothing "substantial" there at all, but solid matter will still be
>>>solid matter, because it is defined by its properties, not by some mysterious raw physical
>>>substrate.
>>
>>But I don't think we ever have anything but "working assumptions"; so we might as
>>well call our best ones "real"; while keeping in mind we may have to change them.
>
>
> That's just what I meant. If you say, this is *not* just a working assumption, there is some
> definite, basic substance called reality over and above what we can observe, that is a
> metaphysical statement which can only be based on something akin to religious faith.
>
> Stathis Papaioannou
I put "working assumption" in scare quotes because I think the fact that we can
create models of the world that are successful over a wide domain of phenomena is
evidence for an underlying reality. It's not conclusive evidence, but reality is
more than just an assumption.
Brent Meeker
jam...@prodigy.net
----- Original Message -----
From: "Stathis Papaioannou" <stathispa...@hotmail.com>
To: "Brent Meeker" <everyth...@googlegroups.com>
Sent: Sunday, August 27, 2006 7:52 AM
Subject: RE: Rép: ROADMAP (well, not yet really...
Brent Meeker writes:
> > Saying that there is a material substrate which has certain properties
is just a working
> > assumption to facilitate thinking about the real world. It may turn out
that if we dig into
> > quarks very deeply there is nothing "substantial" there at all, but
solid matter will still be
> > solid matter, because it is defined by its properties, not by some
mysterious raw physical
> > substrate.
>
> But I don't think we ever have anything but "working assumptions"; so we
might as
> well call our best ones "real"; while keeping in mind we may have to
change them.
SP reply:
"That's just what I meant. If you say, this is *not* just a working
assumption, there is some
definite, basic substance called reality over and above what we can observe,
that is a
metaphysical statement which can only be based on something akin to
religious faith.
Stathis Papaioannou"
JM:
Brent can call it anything he likes, as long as he does not consider it a
"reality" and Stathis can call it anything he likes, as long as he does not
considers it a "faith".
I work with "narratives" - consider them working assumptions (hypotheses)
with an open mind for getting contradictions and so changing their
conditions. This prevents me from calling it "reality" and developing a
"faith" in it, which (both) assign absolute truth to the idea(s) involved.
John M
David Nyman
Could I appeal to Bruno at this juncture to address this point
directly?! At several places in our own dialogues, Bruno, you've
implied that your 'number theology' was an 'as if' postulate, because
(if I've understood) you are concerned to see how much can be explained
by starting from this particular set of assumptions. I don't believe
that you are claiming they are 'true' in an exclusive sense, rather
that they are enlightening. Is this a correct interpretation of your
position, or is there further nuance?
David
Stathis Papaioannou
> > Saying that there is a material substrate which has certain properties is just a working
> > assumption to facilitate thinking about the real world. It may turn out that if we dig into
> > quarks very deeply there is nothing "substantial" there at all, but solid matter will still be
> > solid matter, because it is defined by its properties, not by some mysterious raw physical
> > substrate.
>
>
> I am not using the Bare Substrate to explian "solidity", which is as
> you say
> a matter of properties/behaviour.
>
> I am using it to explain contingent existence, and (A series) time.
We could say that matter is that which feels solid, reflects light, distorts spacetime etc.
and leave it at that. Having these properties is necessary and sufficient for what we call
existence, and it doesn't add anything to postulate a "bare substrate", any more than it
adds anything to postulate an undetectable ether.
Stathis Papaioannou
> By youur definitions, it's a straight choice between metaphysics and
> solipsism.
> I choose metaphsyics.
> We can posit the unobservable to expalint he observable.
Solipsism is a metaphysical position.
> (BTW: it it is wrong to posit an unobserved substrate, why is it
> OK to posit unobserved worlds/branches ?)
It's debatable, but perhaps MWI is a better and simpler explanation of
the facts of quantum mechanics than is CI, for example. Similarly (but
much more strongly) believing there is a world out there is a better
explanation of the facts than solipsism. But some explanations of physical
phenomena, such as an undetectable ether through which light propagates
have been dropped as unnecessary. And perhaps the propertyless
substrate is more like the ether than the many worlds, in that we can at
least imagine travelling to other branches or detecting them in some way,
whereas the ether and the propertyless substrate are undetectable as
a part of their definition - i.e. if we found evidence of the propertyless
substrate it wouldn't be a propertyless substrate any more.
Stathis Papaioannou
> Stathis Papaioannou wrote:
> > Brent Meeker writes:
> >
> >
> >>>Saying that there is a material substrate which has certain properties is just a working
> >>>assumption to facilitate thinking about the real world. It may turn out that if we dig into
> >>>quarks very deeply there is nothing "substantial" there at all, but solid matter will still be
> >>>solid matter, because it is defined by its properties, not by some mysterious raw physical
> >>>substrate.
> >>
> >>well call our best ones "real"; while keeping in mind we may have to change them.
> >
> >
> > definite, basic substance called reality over and above what we can observe, that is a
> > metaphysical statement which can only be based on something akin to religious faith.
> >
> > Stathis Papaioannou
>
> create models of the world that are successful over a wide domain of phenomena is
> evidence for an underlying reality. It's not conclusive evidence, but reality is
> more than just an assumption.
>
> Brent Meeker
There is good reason to believe that there is some sort of reality out there as opposed to the
solipsistic alternative, but there is less reason to believe that there is some basic material substrate
on which the various properties of physical objects are hung. The two ideas are not the same.
1Z
Stathis Papaioannou wrote:
> Peter Jones writes:
>
> > > Saying that there is a material substrate which has certain properties is just a working
> > > assumption to facilitate thinking about the real world. It may turn out that if we dig into
> > > quarks very deeply there is nothing "substantial" there at all, but solid matter will still be
> > > solid matter, because it is defined by its properties, not by some mysterious raw physical
> > > substrate.
> >
> >
> > I am not using the Bare Substrate to explian "solidity", which is as
> > you say
> > a matter of properties/behaviour.
> >
> > I am using it to explain contingent existence, and (A series) time.
>
> We could say that matter is that which feels solid, reflects light, distorts spacetime etc.
> and leave it at that.
However, that is mere behaviour. I need a defiition
which digs deeper than behaviour,and I have one.
> Having these properties is necessary and sufficient for what we call
> existence, and it doesn't add anything to postulate a "bare substrate",
Solidity and light-reflection are not instantiated at every point in
space
time. There is contingent existence, i.e materiality.
1Z
Stathis Papaioannou wrote:
> Peter Jones writes:
>
> > By youur definitions, it's a straight choice between metaphysics and
> > solipsism.
> > I choose metaphsyics.
> > We can posit the unobservable to expalint he observable.
>
> Solipsism is a metaphysical position.
A minimal one, that refuses to posit anything beyond
that for which there is direct evidence.
> > (BTW: it it is wrong to posit an unobserved substrate, why is it
> > OK to posit unobserved worlds/branches ?)
>
> It's debatable, but perhaps MWI is a better and simpler explanation of
> the facts of quantum mechanics than is CI, for example.
Presumably for reason more complex than "we cannot posit the
unobservable".
> Similarly (but
> much more strongly) believing there is a world out there is a better
> explanation of the facts than solipsism. But some explanations of physical
> phenomena, such as an undetectable ether through which light propagates
> have been dropped as unnecessary. And perhaps the propertyless
> substrate is more like the ether than the many worlds, in that we can at
> least imagine travelling to other branches or detecting them in some way,
> whereas the ether and the propertyless substrate are undetectable as
> a part of their definition - i.e. if we found evidence of the propertyless
> substrate it wouldn't be a propertyless substrate any more.
Since the propertyless substrate is needed to explain time and
contingency, time and contingency are evidence for it.
1Z
Stathis Papaioannou wrote:
> There is good reason to believe that there is some sort of reality out there as opposed to the
> solipsistic alternative, but there is less reason to believe that there is some basic material substrate
> on which the various properties of physical objects are hung. The two ideas are not the same.
Materialism has stood up for centuries.
Bruno Marchal
Le 27-août-06, à 19:36, 1Z a écrit :
>
>
> Bruno Marchal wrote:
>> Le 26-août-06, à 22:44, Brent Meeker a écrit :
>>
>>> I understand Peters objection to regarding a "mere bundle" of
>>> properties as existent. But I don't understand why one needs a
>>> propertyless
>>> substrate. Why not just say that some bundles of properties are
>>> instantiated and
>>> some aren't.
>>
>> I guess Peter needs it for having a notion of (absolute)
>> instantiation.
>
> If you think, as I do, that there is a difference between
> logical and physical posibility, you need to explain instantiation.
I do think indeed that there is a difference between logical and
physical possibility.
The logico-arithmetical possibility for a machine are given by the G
and G* logics of self-reference. G is for what the machine can tell us
about that, and G* is for the whole truth (unexpectedly, at the
propositional level, this is completely captured by G*).
The physical possibilities are given by the box and diamond of the Z(*)
and X(*) logics,
The "COMP" physical possibilities are given by the box and diamond of
the Z1(*) and X1(*) logics. A case can still be given that S4Grz1 plays
some role there too, but that would make physics closer to the David
Lyman, George Levy conception; this is testable in principle, but for
some reason I doubt that this could be possible).
>
> If you think, as I do, that there is a difference between
> phsyical actuality and physical posibility, you need to explain
> instantiation.
The difference belongs to the person views.
>
> if you think, as rationalists do, that everything possible
> is also necessary and actual, you don't need those
> distinctions.
It is grosso modo, the motto of the everything list!
Of course the comp hyp put restriction on what we can take as possible,
and it is mainly given by the "true" or "consistent" or both
restriction. This leads naturally to the hypostases.
>
>> If Peter takes the relative notion of instantiation, which is number
>> theoretical in nature, then he would loose any motivation for his bare
>> matter.
>
> I don't think something can exist in relation to what does not exist.
Nor do I.
> if that is what you mean.
I guess you are doing the confusion I describe in my preceding post.
>
>>> Anyway, current physical theory is that there is a material
>>> "substrate" which has properties, e.g. energy, spin, momentum,...
>>
>>
>> I doubt this. Yes current *interpretations* of physical theories do
>> suppose a material substrate, but only for having peaceful sleep (like
>> the collapse non-answer in QM).
>
> All theories assume contingency.
? (very vague, I can agree, disagree ...)
>
>> Anyway, the theories does not
>> presuppose it. They presuppose only mathematical structure and
>> quantitative functor between those mathematical structure and numbers
>> that we can measure in some communicable ways.
>
> No physical theory needs to presuppose numbers as
> having an existence of their own. Formalists
> can do physics.
But they cannot interpret their theory. Now, you can be formalist with
respect to the lobian interview, but then you should try to understand
formally the theory (at least).
But frankly I have no clues about how a formalist can apply any theory
without accepting some interpretation of the formula in the theory.
Bruno
Bruno Marchal
Le 27-août-06, à 19:41, 1Z a écrit :
> But you don't really address the existence question. You just loosely
> assume it is the
> same thing as truth.
I just assume that the "existence of a number" is equivalent with the
intended truth of an existential
proposition written in a theory about numbers.
I identify propositions like "there exist a perfect number" with "it is
true that there exist a perfect number".
I am dialoguing with PA (Peano Arithmetic theorem prover). When PA
tells me "there exist perfect numbers", I take it as an existential
proposition. It is a way, for PA, to make an ontological commitment,
which I do too.
Of course, I don't interpret this as "there exist a physical world, and
numbers exist there physically".
I don't assume there is a physical world, and I doubt very much there
is a physical primary world. Indeed the UDA shows such an assumption to
be useless concerning the possible explanations of both quanta and
qualia.
Bruno
Bruno Marchal
Le 27-août-06, à 21:41, Brent Meeker a écrit :
> I put "working assumption" in scare quotes because I think the fact
> that we can
> create models of the world that are successful over a wide domain of
> phenomena is
> evidence for an underlying reality. It's not conclusive evidence, but
> reality is
> more than just an assumption.
I agree that "reality" is more than an assumption.
I agree even that "physical reality" is more than an assumption. I have
few doubt about the existence of a physical reality.
Now to assume the existence of a "primary" physical reality, or to
believe that physics is obviously or necessarily the fundamental
science, well that is a big assumption, and I would say that such an
assumption is even unclear in front of QM, and then useless in front of
comp.
I realize that even Aristotle, in his metaphysics, is much more prudent
on this, than the standard Christian (especially catholic)
interpretation of Aristotle.
Bruno
Bruno Marchal
Le 27-août-06, à 23:17, David Nyman wrote to Peter (1Z) :
>> 1Z: But you don't really address the existence question. You just
>> loosely
>> assume it is the
>> same thing as truth.
>
> Could I appeal to Bruno at this juncture to address this point
> directly?! At several places in our own dialogues, Bruno, you've
> implied that your 'number theology' was an 'as if' postulate, because
> (if I've understood) you are concerned to see how much can be explained
> by starting from this particular set of assumptions. I don't believe
> that you are claiming they are 'true' in an exclusive sense, rather
> that they are enlightening. Is this a correct interpretation of your
> position, or is there further nuance?
As a scientist, or if you prefer as a "willing to be a consistent
scientist" (you never know), I would say that *all* theories are third
person discourses which have to be taken with an "as if" proviso. Even
the grandmother physics (with propositions like 'objects fall', or
'the sun rise in the morning', etc.) is like that. Even our unconscious
theories that we have probably inherited from our ancestors are like
that.
Of course, given a theory, we can harbor doubts about it, and we can
harbor those doubts differentially, that is more or less doubts on some
part of it.
"My" theory is a digital version of the very old mechanist theory,
saying that we are sort of natural machine. It is already explained by
Nagarjuna in the "Milinda's Questions" for example, or by Plato in some
place, and it has been developed by Descartes concerning animals (and
perhaps concerning humans too in some hidden way, if you take the
context of Descartes epoch).
I make that digital version more precise so as to be able to drive
precise conclusions. I have called in this list that more precise
version: COMP (but I called it digital mechanism in some places). Note
that what you call "number theology" belongs to the conclusion of comp
(I don't assume it).
The precise comp version is given by
a) the "yes doctor" act of faith YD
b) Church (Hypo) Thesis CT
c) Arithmetical Realism hypothesis AR
Now I can imagine "a)" to be false. In three ways actually: For example
I say yes to the doctor but the digital reconstitution of me remains
inanimate, or, I say yes to the doctor, and the digital reconstitution
is a zombie, or I say yes to the doctor, and the reconstitution is
alive but is not me. This I can logically conceived, and that would
make "a)" wrong.
Note that in the lobian interview we do not need anymore the "yes
doctor", except for giving a general sense to the *goal* of the
interview.
It is much harder for me to conceive that Church thesis could be false,
but this is due to more than many years of reflection on it. I am not
so much impress by the empirical evidence (all attempt to define
computable function lead to the same class of function, despite
completely different definitions and motivations), but I am infinitely
impressed by the closure for the diagonalization of the class of
partial computable functions. This is a quite convincing argument for
CT, as I try to explain periodically on this list. Still I can
"logically" doubt about CT. It is enough that someone comes up with a
function and a way to explain me how to compute and a proof that the
function cannot be programmed in Java (say), and CT would be refuted. I
would say that this is unlikely.
Now, it is still much more harder for me to doubt about AR. It is about
AR that I often say that I would have the feeling to lie to myself in
case I would pretend harboring doubt about it. AR just says that
elementary number theoretical statements (including existential one)
are true or false in a way which does not depend on me. Actually I am
even using a weaker version of AR, in the sense that for the ontic part
of the theory, I need only the independent truth of the formula with
the shape ExP(x), i.e. "it exist a number verifying the property P",
where P is an easily verifiable statement (like being prime, being odd,
etc.). I don't need universal (with the "for all" quantifier)
independent truth, only the simpler formula among the existential one.
(of course I don't believe at all in Peter Jones heavy form of magical
platonism).
I have also never met someone doubting about AR, although I met
regularly people who pretend to doubt AR, but like Peter, they put in
it things which I don't put in it at all.
Somehow, to believe in NON-AR you have to believe in the possibility
that there is a proposition of arithmetic, stating the existence of a
number having some verifiable property, which truth value is capable of
changing according to the fact that you are alive or not. You need to
make a stronger and much weirder ontological commitment to get it.
Some people ask me: but if AR is so obvious, why do you postulate it?
I postulate it for reason of completeness, but also because I am aware
of contradicting 1500 years of implicit theological aristotelian
belief, and so I need to be quite explicit about what I assume.
Although very simple to believe, AR does play a key role, if not *the*
key role in the UDA proof.
AR eventually provides the whole comp ontology, although it has nothing
to do with any commitment with a substantial reality.
Hope this helps,
Bruno
1Z
Bruno Marchal wrote:
> AR eventually provides the whole comp ontology, although it has nothing
> to do with any commitment with a substantial reality.
If it makes no commitments about existence,. it can prove nothing about
ontology.
Brent Meeker
> Peter Jones writes:
>
>
>>>Saying that there is a material substrate which has certain properties is just a working
>>>assumption to facilitate thinking about the real world. It may turn out that if we dig into
>>>quarks very deeply there is nothing "substantial" there at all, but solid matter will still be
>>>solid matter, because it is defined by its properties, not by some mysterious raw physical
>>>substrate.
>>
>>
>>I am not using the Bare Substrate to explian "solidity", which is as
>>you say
>>a matter of properties/behaviour.
>>
>>I am using it to explain contingent existence, and (A series) time.
>
>
> We could say that matter is that which feels solid, reflects light, distorts spacetime etc.
> and leave it at that. Having these properties is necessary and sufficient for what we call
> existence, and it doesn't add anything to postulate a "bare substrate", any more than it
> adds anything to postulate an undetectable ether.
>
> Stathis Papaioannou
I agree with your conclusion. But matter isn't that which feels solid, etc (as I'm
sure you know). One defintion is, "Matter is what kicks back if you kick it." or
less colorfully it is what you can manipulate. This changes depending on our
theories of physics. Before Einstein space could be regarded as purely relational -
it didn't kick back. Now we think it does.
Brent Meeker
Brent Meeker
> Peter Jones writes:
>
>
>>By youur definitions, it's a straight choice between metaphysics and
>>solipsism.
>>I choose metaphsyics.
>>We can posit the unobservable to expalint he observable.
>
>
> Solipsism is a metaphysical position.
>
>
>>(BTW: it it is wrong to posit an unobserved substrate, why is it
>>OK to posit unobserved worlds/branches ?)
>
>
> It's debatable, but perhaps MWI is a better and simpler explanation of
> the facts of quantum mechanics than is CI, for example.
Multiple-worlds are a consequence of dropping the collapse of the wave function,
which was inexplicable and ad hoc. I'm not fond of it either, but it does have the
support of being based on an good empirical model. Similarly for multiple-universes;
they are implied by our best theory.
>Similarly (but
> much more strongly) believing there is a world out there is a better
> explanation of the facts than solipsism. But some explanations of physical
> phenomena, such as an undetectable ether through which light propagates
> have been dropped as unnecessary.
The lumineferous aether was not only undetectable, it had to have contrdictory
properties to remain undetected in both Michelson-Morley and stellar aberration.
Brent Meeker
1Z
Brent Meeker wrote:
> Stathis Papaioannou wrote:
> > Peter Jones writes:
> >
> >
> >>By youur definitions, it's a straight choice between metaphysics and
> >>solipsism.
> >>I choose metaphsyics.
> >>We can posit the unobservable to expalint he observable.
> >
> >
> > Solipsism is a metaphysical position.
> >
> >
> >>(BTW: it it is wrong to posit an unobserved substrate, why is it
> >>OK to posit unobserved worlds/branches ?)
> >
> >
> > It's debatable, but perhaps MWI is a better and simpler explanation of
> > the facts of quantum mechanics than is CI, for example.
>
> Multiple-worlds are a consequence of dropping the collapse of the wave function,
> which was inexplicable and ad hoc.
It's neither. If anything there is an embarassment of explanations for
it,
and number of motivations for positing it.
A genuine problem with MWI: it starts with the assumption that the
universe is in a 'pure' state. However, unitary evolution under the SWE
is unable to fully transform a pure state into a genuine mixture. It
can generate (by mechanisms similar to environmental decoherence) an
approximate mixture -- For All Practical Purposes. Since collapse does,
by stipulation, produce orthogonal states, there is a difference
between collapse interpretations and MW. The residual interferences
could be detectable. (It is also believed by many that collapse itself
is detectable).
"In fact it turns out that in the general case , there will be a unique
pair of orthogonal perception states accompanying a pair of orthogonal
cat states. This is something known as the Schmidt decomposition of an
entangled state. However this is not much use for resolving the
measurement paradox (...) because gernerally this mathematically
preferred pair of cat states (..) would not be the desired |live cat> +
| dead cat> at all, but some linear superposition of these! [...] Since
the mathematics alone will not single out the |live cat> and |dead cat>
states as being in any way 'preferred' we still need a theory of
perception before we can make sense of [MWI] and such a theory is
lacking.Moreover the onus on such a theory would be not only to explain
why superpositions of dead and alive cats (or anything else
macroscopic) occur in do not occur in the physical world but also why
the wonderous and extraordinarily precise squared-modulus rule actually
gives the right answers for probabilities in quantum mechanics!"
R. Penrose, Road to Reality p809
Is MWI a complete solution to the paradoxes of QM? Is an Universal Wave
Function feasible ?
A genuine problem with MWI: Reasonableness of all-embracing unitary
evolution. MWI-ers claim that the unitary evolution of the SWE (or some
variation) is the single all-embracing law of the universe -- the other
main part of the QM universe, the process of collapse (AKA reduction)
is not needed. However, QM itself is not an all-encompassing physical
theory because it does not include gravity and relativity. It might be
possible to include gravity in an extended WE, but the conventional SWE
requires a derivative against time, wich is difficult to achieve in a
way that is compatible with the requirements of relativity. There is
also a more conceptual argument against large-scale branching; since
all branches co-exist in the same space-time, and since the disposition
of matter determines how space bends in general relativity, large-scale
differences between the branches would leave space not "knowing" which
way to bend.
Brent Meeker
I'm well aware of the problems of MWI. But I think Roger is too pessimistic about
the potential of a theory of einselection. There's an excellent review paper
available on arXiv.org:
Decoherence, the measurement problem, and interpretations of quantum mechanics
Authors: Maximilian Schlosshauer
Comments: 41 pages. Final published version
Journal-ref: Rev. Mod. Phys. 76, 1267-1305 (2004)
DOI: 10.1103/RevModPhys.76.1267
Environment-induced decoherence and superselection have been a subject of
intensive research over the past two decades, yet their implications for the
foundational problems of quantum mechanics, most notably the quantum measurement
problem, have remained a matter of great controversy. This paper is intended to
clarify key features of the decoherence program, including its more recent results,
and to investigate their application and consequences in the context of the main
interpretive approaches of quantum mechanics.
It discusses the sucesses and problems of the decoherence program and their relation
to other intepretations. I think you are wrong in saying the are plenty of
explanations for collapse of the wave-function. Penrose's is the only one that comes
close to being an explanation, i.e. something with a physical basis that could be
tested. The others are just hueristic models. Decoherence is experimentally tested
and provides "collapse FAPP"; but the "FAPP" still leaves some problems.
Personally, I like Omnes' viewpoint, which is that QM is a probabilistic theory, so
it predicts probabilities and probability implies that some things happen and some
don't. But that still leaves a problem in interpreting those (vanishingly small) off
diagonal terms in the density matrix.
Brent Meeker
Stathis Papaioannou
> > > > Saying that there is a material substrate which has certain properties is just a working
> > > > assumption to facilitate thinking about the real world. It may turn out that if we dig into
> > > > quarks very deeply there is nothing "substantial" there at all, but solid matter will still be
> > > > solid matter, because it is defined by its properties, not by some mysterious raw physical
> > > > substrate.
> > >
> > >
> > > I am not using the Bare Substrate to explian "solidity", which is as
> > > you say
> > > a matter of properties/behaviour.
> > >
> > > I am using it to explain contingent existence, and (A series) time.
> >
> > We could say that matter is that which feels solid, reflects light, distorts spacetime etc.
> > and leave it at that.
>
> However, that is mere behaviour. I need a defiition
> which digs deeper than behaviour,and I have one.
All I see is mere behaviour. When I say that something is as real as this desk in front of me, I am
saying that it is as real as the mere mere behaviour in front of me - as opposed to the desk in my
dreams, which lacks such behaviour. Do you think we really disagree about desks? If it looks like a
desk, feels like a desk etc., then it's a desk. It doesn't add anything to say that it also contains
"essence of real desk" to distinguish it from dream desks, because dream desks differ from real
desks in other ways.
Bruno Marchal
Le 28-août-06, à 16:47, 1Z a écrit :
Absolutely so. But I said that comp makes no commitment about primary
physical stuff. As I said more than 10 times to you is that comp,
through AR makes a commitment about the existence of (non substantial)
numbers.
You tend to beg the question through your assumption that only primary
physical matter exists.
But then comp is false or the UDA reasoning is false, but then just
show where, please.
Tell me also this, if you don't mind: are you able to doubt about the
existence of "primary matter"? I know it is your main fundamental
postulate. Could you imagine that you could be wrong?
> Bruno Marchal wrote:
>
>> In both comp and the quantum, a case can be made that the
>> irreversibility of memory (coming from usual thermodynamics, or big
>> number law) can explain, through physical or comp-physical
>> interactions, the first person feeling of irreversibility.
>> But with comp we do start from a basic "irreversibility": 0 has a
>> successor but no predecessors.
>
> ...among the natural numbers. Does COMP really prove
> that negative numebrs don't exist ?
Who said that? You can already define the negative integer in Robinson
Arithmetic, and prove the existence of each negative integer. The
common algebraical construction of the integer as couple of natural
number togeteher with the genuine equivalence relation can be done in
RA. RA or PA proves only that 0 has no predecessor among the natural
numbers.
Actually, as I have said, RA can already define all partial recursive
functions, i.e. all function which are programmable in your favorite
programming language. (No need of CT here, unless your favorite
programming language belongs to the future).
Despite this RA is very weak and has almost no ability to generalize.
Peano Arithmetic PA, which is just RA + the induction axioms, is much
clever, and most usual mathematics (including Ramanujan's work) can be
done by PA.
Bruno
1Z
Bruno Marchal wrote:
> Le 28-août-06, à 16:47, 1Z a écrit :
>
> >
> >
> > Bruno Marchal wrote:
> >
> >> AR eventually provides the whole comp ontology, although it has
> >> nothing
> >> to do with any commitment with a substantial reality.
> >
> > If it makes no commitments about existence,. it can prove nothing about
> > ontology.
>
>
>
>
> Absolutely so. But I said that comp makes no commitment about primary
> physical stuff.
It makes no other ontological commitment.
>As I said more than 10 times to you is that comp,
> through AR makes a commitment about the existence of (non substantial)
> numbers.
The version of AR that is supported by comp
only makes a commitment about mind-independent *truth*. The idea
that the mind-independent truth of mathematical propositions
entails the mind-independent *existence* of mathematical objects is
a very contentious and substantive claim.
> You tend to beg the question through your assumption that only primary
> physical matter exists.
AFAICS, I am only asuming that *I* exist.
(I could also you tend to beg the guqestio that ruth is existence...)
> But then comp is false or the UDA reasoning is false, but then just
> show where, please.
Where is it shown the UD exists ?
> Tell me also this, if you don't mind: are you able to doubt about the
> existence of "primary matter"? I know it is your main fundamental
> postulate. Could you imagine that you could be wrong?
It is possible that I am wrong. It is possible that I am right.
But you are -- or were -- telling me matter is impossible.
> > Bruno Marchal wrote:
> >
> >> In both comp and the quantum, a case can be made that the
> >> irreversibility of memory (coming from usual thermodynamics, or big
> >> number law) can explain, through physical or comp-physical
> >> interactions, the first person feeling of irreversibility.
> >> But with comp we do start from a basic "irreversibility": 0 has a
> >> successor but no predecessors.
> >
> > ...among the natural numbers. Does COMP really prove
> > that negative numebrs don't exist ?
>
>
> Who said that? You can already define the negative integer in Robinson
> Arithmetic, and prove the existence of each negative integer. The
> common algebraical construction of the integer as couple of natural
> number togeteher with the genuine equivalence relation can be done in
> RA. RA or PA proves only that 0 has no predecessor among the natural
> numbers.
But the negative integers exist (or "exist"), so it has
an existing predecessor.
All you are aying is that in Platoia
there are structures with the same one-way quality as time,
well, of course there are. Every structure exists in Platonia,
if Paltonia exists.
That doesn't explain why we see only one particular structure
(which is still only B-series).
uv
> The version of AR that is supported by comp
> only makes a commitment about mind-independent *truth*. The idea
> that the mind-independent truth of mathematical propositions
> entails the mind-independent *existence* of mathematical objects is
> a very contentious and substantive claim.
I'm very late in reading this thread. I assume AR is "Arithmetical
Realism" and that *truth* in this thread implies alethic qualification
of some sort. To me, a statement like "only use batteries with the
same rated voltage" would seem only to be qualifiable as true or
otherwise if related to factual content. Such a statement would not be
meaningless and would contain information which could be worth
preserving or using.
I am wondering how much semantic loading Bruno's ideas of
quantification are obliged to carry here. Quantifiers always worry me
as they often seem to come up at a very early stage and they do always
seem to carry with them a similar pattern to "only use batteries with
the same rated voltage" and their meaning if any is never absolutely
clear or clarifiable. Perhaps they cannot entail the aforementioned
"mind-independent *existence* of mathematical objects". Or, at least,
not without further qualification, rendering his theory possibly
incomplete as theories tend to be.
This is not the same as people saying "in spite of all we know about
electricity, we do not know what electricity is", because of course we
do know what electricity is, in context if not in metaphysics.
[Bruno's defintiion of Arithmetic Realism I understand to be
" Arithmetical Realism.
All proposition pertaining on natural numbers
with the form Qx Qy Qz Qt Qr ... Qu P(x,y,z,t,r, ...,u) are true
independently
of me. Q represents a universal or existential quantifier, and P
represents a
decidable (recursive) predicate. That is, proposition like the
Fermat-Wiles
theorem, or Goldbach conjecture, or Euclide's infinity of primes
theorem are
either true or false, and this independently of the proposition "Bruno
Marchal
exists". It amounts to accept, for the sake of my argument, that
classical logic is correct in the realm of positive integers. Nothing
more."]
Bruno Marchal
Le 29-août-06, à 20:45, 1Z a écrit :
> The version of AR that is supported by comp
> only makes a commitment about mind-independent *truth*. The idea
> that the mind-independent truth of mathematical propositions
> entails the mind-independent *existence* of mathematical objects is
> a very contentious and substantive claim.
You have not yet answered my question: what difference are you making
between "there exist a prime number in platonia" and "the truth of the
proposition asserting the *existence* of a prime number is independent
of me, you, and all contingencies" ?
> Where is it shown the UD exists ?
If you agree that the number 0, 1, 2, 3, 4, ... exist (or again, if you
prefer, that the truth of the propositions:
Ex(x = 0),
Ex(x = s(0)),
Ex(x = s(s(0))),
...
is independent of me), then it can proved that the UD exists. It can be
proved also that Peano Arithmetic (PA) can both define the UD and prove
that it exists.
>
>> Tell me also this, if you don't mind: are you able to doubt about the
>> existence of "primary matter"? I know it is your main fundamental
>> postulate. Could you imagine that you could be wrong?
>
> It is possible that I am wrong. It is possible that I am right.
> But you are -- or were -- telling me matter is impossible.
Only when I use Occam. Without Occam I say only that the notion of
primary matter is necessarily useless i.e. without explanatory purposes
(even concerning just the belief in the physical proposition only) .
This is a non trivial consequence of the comp hyp. (cf UDA).
> But the negative integers exist (or "exist"), so it has
> an existing predecessor.
Yes. But the axiom Q1 "Ax ~(0 = s(x)" is not made wrong just because
you define the negative integer in Robinson Arithmetic. The "x" are
still for "natural number". The integer are new objects defined from
the natural number. All right? To take another example, you can define
in RA all partial recursive functions, but obviously they does not obey
to the Q axioms, they are just constructs, definable in RA.
Bruno
1Z
Stathis Papaioannou wrote:
> Peter Jones writes:
>
> > > > > Saying that there is a material substrate which has certain properties is just a working
> > > > > assumption to facilitate thinking about the real world. It may turn out that if we dig into
> > > > > quarks very deeply there is nothing "substantial" there at all, but solid matter will still be
> > > > > solid matter, because it is defined by its properties, not by some mysterious raw physical
> > > > > substrate.
> > > >
> > > >
> > > > I am not using the Bare Substrate to explian "solidity", which is as
> > > > you say
> > > > a matter of properties/behaviour.
> > > >
> > > > I am using it to explain contingent existence, and (A series) time.
> > >
> > > We could say that matter is that which feels solid, reflects light, distorts spacetime etc.
> > > and leave it at that.
> >
> > However, that is mere behaviour. I need a defiition
> > which digs deeper than behaviour,and I have one.
>
> All I see is mere behaviour.
All you see is phenomena in your own mimd, says the solipsist..
>When I say that something is as real as this desk in front of me, I am
> saying that it is as real as the mere mere behaviour in front of me
How do you know it is really in front of you ?
> - as opposed to the desk in my
> dreams, which lacks such behaviour. Do you think we really disagree about desks? If it looks like a
> desk, feels like a desk etc., then it's a desk. It doesn't add anything to say that it also contains
> "essence of real desk" to distinguish it from dream desks, because dream desks differ from real
> desks in other ways.
Well, what is the difference ? How do you escape solipsism without
embracing materialism ?
Quentin Anciaux
> Stathis Papaioannou wrote:
> > Peter Jones writes:
> > > > > > Saying that there is a material substrate which has certain
> > > > > > properties is just a working assumption to facilitate thinking
> > > > > > about the real world. It may turn out that if we dig into quarks
> > > > > > very deeply there is nothing "substantial" there at all, but
> > > > > > solid matter will still be solid matter, because it is defined by
> > > > > > its properties, not by some mysterious raw physical substrate.
> > > > >
> > > > > I am not using the Bare Substrate to explian "solidity", which is
> > > > > as you say
> > > > > a matter of properties/behaviour.
> > > > >
> > > > > I am using it to explain contingent existence, and (A series) time.
> > > >
> > > > We could say that matter is that which feels solid, reflects light,
> > > > distorts spacetime etc. and leave it at that.
> > >
> > > However, that is mere behaviour. I need a defiition
> > > which digs deeper than behaviour,and I have one.
> >
> > All I see is mere behaviour.
>
> All you see is phenomena in your own mimd, says the solipsist..
"There is no other solipsist than me" he would say... As the solipsist is the
only real... but it is a disgression and as usual you answer by question or
opinion which are not yours.
> >When I say that something is as real as this desk in front of me, I am
> > saying that it is as real as the mere mere behaviour in front of me
>
> How do you know it is really in front of you ?
This is still a language babeling... define real (for you) then we can
discuss... But I'll try to do it for you.
What is real is what is material. Materiality define what is real... Don't
forget to byte the snake.
> > - as opposed to the desk in my
> > dreams, which lacks such behaviour. Do you think we really disagree about
> > desks? If it looks like a desk, feels like a desk etc., then it's a desk.
> > It doesn't add anything to say that it also contains "essence of real
> > desk" to distinguish it from dream desks, because dream desks differ from
> > real desks in other ways.
>
> Well, what is the difference ? How do you escape solipsism without
> embracing materialism ?
How do you escape the circle without leaving materialism ?
Quentin
1Z
Quentin Anciaux wrote:
> Le Wednesday 30 Août 2006 21:26, 1Z a écrit :
> > Stathis Papaioannou wrote:
> > > Peter Jones writes:
> > > > > > > Saying that there is a material substrate which has certain
> > > > > > > properties is just a working assumption to facilitate thinking
> > > > > > > about the real world. It may turn out that if we dig into quarks
> > > > > > > very deeply there is nothing "substantial" there at all, but
> > > > > > > solid matter will still be solid matter, because it is defined by
> > > > > > > its properties, not by some mysterious raw physical substrate.
> > > > > >
> > > > > > I am not using the Bare Substrate to explian "solidity", which is
> > > > > > as you say
> > > > > > a matter of properties/behaviour.
> > > > > >
> > > > > > I am using it to explain contingent existence, and (A series) time.
> > > > >
> > > > > We could say that matter is that which feels solid, reflects light,
> > > > > distorts spacetime etc. and leave it at that.
> > > >
> > > > However, that is mere behaviour. I need a defiition
> > > > which digs deeper than behaviour,and I have one.
> > >
> > > All I see is mere behaviour.
> >
> > All you see is phenomena in your own mimd, says the solipsist..
>
> "There is no other solipsist than me" he would say... As the solipsist is the
> only real... but it is a disgression and as usual you answer by question or
> opinion which are not yours.
I am making the point that if you apply the "I don't believe in a
anything
I can't see" principle *consistently*, you don't just abandon matter,
you also abandon Other Minds.
> > >When I say that something is as real as this desk in front of me, I am
> > > saying that it is as real as the mere mere behaviour in front of me
> >
> > How do you know it is really in front of you ?
>
> This is still a language babeling... define real (for you) then we can
> discuss... But I'll try to do it for you.
> What is real is what is material. Materiality define what is real... Don't
> forget to byte the snake.
What is real is what Quentin can see..what Quentin can see is real...
two can play at the snake-biting game.
> > > - as opposed to the desk in my
> > > dreams, which lacks such behaviour. Do you think we really disagree about
> > > desks? If it looks like a desk, feels like a desk etc., then it's a desk.
> > > It doesn't add anything to say that it also contains "essence of real
> > > desk" to distinguish it from dream desks, because dream desks differ from
> > > real desks in other ways.
> >
> > Well, what is the difference ? How do you escape solipsism without
> > embracing materialism ?
>
> How do you escape the circle without leaving materialism ?
What you have is a choice of circles.
> Quentin
1Z
Bruno Marchal wrote:
> Le 29-août-06, à 20:45, 1Z a écrit :
>
>
>
> > The version of AR that is supported by comp
> > only makes a commitment about mind-independent *truth*. The idea
> > that the mind-independent truth of mathematical propositions
> > entails the mind-independent *existence* of mathematical objects is
> > a very contentious and substantive claim.
>
>
> You have not yet answered my question: what difference are you making
> between "there exist a prime number in platonia" and "the truth of the
> proposition asserting the *existence* of a prime number is independent
> of me, you, and all contingencies" ?
"P is true" is not different to "P". That is not the difference I
making.
I'm making a difference between what "exists" means in mathematical
sentences and what it means in empiricial sentences (and what it means
in fictional contexts...)
The logical case for mathematical Platonism is based on the idea
that mathematical statements are true, and make existence claims.
That they are true is not disputed by the anti-Platonist, who
must therefore claim that mathematical existence claims are somehow
weaker than other existence claims -- perhaps merely metaphorical.
That the the word "exists" means different things in different contexts
is easily established.
For one thing, this is already conceded by Platonists! Platonists think
Platonic existence is eternal, immaterial non-spatial, and so on,
unlike the Earthly existence of material bodies. For another,
we are already used to contextualising the meaning of "exists".
We agree with both: "helicopters exist"; and "helicopters
don't exist in Middle Earth". (People who base their entire
anti-Platonic philosophy are called fictionalists. However,
mathematics is not a fiction because it is not a free creation.
Mathematicians are constrained by consistency and non-contradiction
in a way that authors are not. Dr Watson's fictional existence
is intact despite the fact that he is sometimes called John
and sometimes James in Conan Doyle's stories).
The epistemic case for mathematical Platonism is be argued on the
basis of the
objective
nature of mathematical truth. Superficially, it seems persuasive that
objectivity requires objects.
However, the basic case for the objectivity of mathematics is the
tendency
of mathematicians to
agree about the answers to mathematical problems; this can be explained
by
noting that mathematical logic is based on axioms and rules of
inference, and
different mathematicians following the same rules will tend to get the
same
answers , like different computers running the same problem.
(There is also disagreement about some axioms, such as the Axiom of
Choice,
and different mathematicians with different attitudes about the AoC
will
tend to get different answers -- a phenomenon which is easily explained
by the formalist view I am taking here).
The semantic case for mathematical Platonism is based on the idea
that the terms in a mathematical sentence must mean something,
and therefore must refer to objects. It can be argued on
general linguistic grounds that not all meaning is reference
to some kind of object outside the head. Some meaning is sense,
some is reference. That establishes the possibility that mathematical
terms do not have references. What establishes it is as likely
and not merely possible is the obeservation that nothing like
empirical investigation is needed to establish the truth
of mathematical statements. Mathematical truth is arrived at by a
purely
conceptual process, which is what would be expected if mathematical
meaning were restricted to the
Sense, the "in the head" component of meaning.
A possible counter argument by the Platonist is that the downgrading of
mathematical existence to a mere metaphor is arbitrary. The
anti-Platonist must
show that a consistent standard is being applied. This it is possible
to do; the standard is to take the meaning of existence in the context
of
a particular proposition to relate to the means of justification of the
proposition.
Since ordinary statements are confirmed empirically, "exists" means
"can
be perceived" in that context. Since sufficient grounds for asserting
the
existence of mathematical objects are that it is does not contradict
anything else
in mathematics, mathematical existence just amounts to concpetual
non-contradictoriness.
(Incidentally, this approach answers a question about mathematical and
empirical
truth. The anti-Platonists want sthe two kinds of truth to be
different, but
also needs them to be related so as to avoid the charge that one class
of
statement is not true at all. This can be achieved because empirical
statements rest on non-contradiction in order to achive correspondence.
If an empricial observation fails co correspond to a statemet, there
is a contradiction between them. Thus non-contradiciton is a necessary
but insufficient justification for truth in empircal statements, but
a sufficient one for mathematical statements).
> > Where is it shown the UD exists ?
>
>
> If you agree that the number 0, 1, 2, 3, 4, ... exist (or again, if you
> prefer, that the truth of the propositions:
>
> Ex(x = 0),
> Ex(x = s(0)),
> Ex(x = s(s(0))),
> ...
>
> is independent of me), then it can proved that the UD exists. It can be
> proved also that Peano Arithmetic (PA) can both define the UD and prove
> that it exists.
But again this is just "mathematical existence". You need some
reason to assert that mathematical existence is not a mere
metaphor implying no real existence, as anti-Platonist
mathematicians claim. I do not think that is given by computationalism.
> >> Tell me also this, if you don't mind: are you able to doubt about the
> >> existence of "primary matter"? I know it is your main fundamental
> >> postulate. Could you imagine that you could be wrong?
> >
> > It is possible that I am wrong. It is possible that I am right.
> > But you are -- or were -- telling me matter is impossible.
>
>
> Only when I use Occam.
Occam does not support conclusions of impossibility. It could
be a brute fact that the universe is more complicated than
strcitly necessary.
> Without Occam I say only that the notion of
> primary matter is necessarily useless i.e. without explanatory purposes
> (even concerning just the belief in the physical proposition only) .
> This is a non trivial consequence of the comp hyp. (cf UDA).
As is the way with these things, we anti-Platonists appeal
to Occam as well (although not qua impossibilia).
All the facts about mathematical truth and methodology can be
established
without appeal to the actual existence of mathematical objects.
In fact, the lack of such objects actually explains the
objectivity and necessity of maths. Mathematical statements
are necessarily true because there are no possible circumstances
that make them false; there are no possible circumstances that
would make them false because they do not refer to anything
external. This is much simpler than the Platonist
alternative that mathematical statements :
1) have referents
which are
2) unchanging and eternal, unlike anything anyone has actuall seen
and thereby
3) explain the necessity (invariance) of mathematical statements
without
4) performing any other role -- they are not involved in
mathematical proof.
> > But the negative integers exist (or "exist"), so it has
> > an existing predecessor.
>
>
> Yes. But the axiom Q1 "Ax ~(0 = s(x)" is not made wrong just because
> you define the negative integer in Robinson Arithmetic. The "x" are
> still for "natural number". The integer are new objects defined from
> the natural number. All right? To take another example, you can define
> in RA all partial recursive functions, but obviously they does not obey
> to the Q axioms, they are just constructs, definable in RA.
So the specialness of Time depends on the specialness of nautral
numbers, depends on the specialness of Robinson Arithemtic ?
> Bruno
>
>
> http://iridia.ulb.ac.be/~marchal/
Bruno Marchal
Le 31-août-06, à 22:20, 1Z a écrit :
>
>
> Bruno Marchal wrote:
>
>> Le 29-août-06, à 20:45, 1Z a écrit :
>>
>>
>>
>>> The version of AR that is supported by comp
>>> only makes a commitment about mind-independent *truth*. The idea
>>> that the mind-independent truth of mathematical propositions
>>> entails the mind-independent *existence* of mathematical objects is
>>> a very contentious and substantive claim.
>>
>>
>> You have not yet answered my question: what difference are you making
>> between "there exist a prime number in platonia" and "the truth of the
>> proposition asserting the *existence* of a prime number is independent
>> of me, you, and all contingencies" ?
>
> "P is true" is not different to "P". That is not the difference I
> making.
I am glad to hear this.
>
> I'm making a difference between what "exists" means in mathematical
> sentences and what it means in empiricial sentences (and what it means
> in fictional contexts...)
Of course I do that difference too! Each hypostase has its own notion
of existence.
When I say that a number exists, it is in the usual sense of a realist
arithmetician.
But physical existence is a completely different things having a logic
of its own. The UDA shows that the logic of the physical propositions
should emerge from the logic of what will be true in all accessible
worlds. The world correspond to the relative consistent extension and
are eventually characterized by the discourse which remain invariant
through world-transition, themselves eventually given by the interview
of the lobian machine.
I am certainly not identifying many different notion of existence, on
the contrary. Recall perhaps that each hypostase (that is "notion of
person") defines some "canonical" Kripke "multiverses".
Perhaps search on "Kripke" in the archive, but I guess we will go back
to this at some point.
>
>
> The logical case for mathematical Platonism is based on the idea
> that mathematical statements are true, and make existence claims.
> That they are true is not disputed by the anti-Platonist, who
> must therefore claim that mathematical existence claims are somehow
> weaker than other existence claims -- perhaps merely metaphorical.
> That the the word "exists" means different things in different contexts
> is easily established.
>
> <snip; ok but not completely relevant or premature>
>
> (Incidentally, this approach answers a question about mathematical and
> empirical
> truth. The anti-Platonists want sthe two kinds of truth to be
> different, but
> also needs them to be related so as to avoid the charge that one class
> of
> statement is not true at all. This can be achieved because empirical
> statements rest on non-contradiction in order to achive correspondence.
> If an empricial observation fails co correspond to a statemet, there
> is a contradiction between them. Thus non-contradiciton is a necessary
> but insufficient justification for truth in empircal statements, but
> a sufficient one for mathematical statements).
Even for math, non contradiction is not a sufficient criteria. This
follows immediately from the second incompleteness theorem. PA cannot
prove its own consistency (PA does not prove ~Bf). This means you will
not get a contradiction by adding to PA the formula stating that PA is
inconsistent (Bf). Sp PA + Bf, although quite insane in some sense, is
actually consistent, but mathematically unreasonable (but useful in
self-reference theory for getting a simple example of arithmetically
unsound but consistent machine).
>
>
>
>>> Where is it shown the UD exists ?
>>
>>
>> If you agree that the number 0, 1, 2, 3, 4, ... exist (or again, if
>> you
>> prefer, that the truth of the propositions:
>>
>> Ex(x = 0),
>> Ex(x = s(0)),
>> Ex(x = s(s(0))),
>> ...
>>
>> is independent of me), then it can proved that the UD exists. It can
>> be
>> proved also that Peano Arithmetic (PA) can both define the UD and
>> prove
>> that it exists.
>
> But again this is just "mathematical existence". You need some
> reason to assert that mathematical existence is not a mere
> metaphor implying no real existence, as anti-Platonist
> mathematicians claim. I do not think that is given by computationalism.
When I say that there is an infinity of prime number, it is not a
metaphor.
I am not saying that prime numbers exists like electrons, only that the
"physical existence of electron" emerge in the stable dreams of the
lobian machines, and those dreams are reducible to relative and local
finite computations which, relatively to universal numbers (which exist
by CT), exist then, in the same sense than the prime number, that is
the interpretation of formula like "ExP(x,y)" in the standard model of
arithmetic (the one we learn at school).
>
>>>> Tell me also this, if you don't mind: are you able to doubt about
>>>> the
>>>> existence of "primary matter"? I know it is your main fundamental
>>>> postulate. Could you imagine that you could be wrong?
>>>
>>> It is possible that I am wrong. It is possible that I am right.
>>> But you are -- or were -- telling me matter is impossible.
>>
>>
>> Only when I use Occam.
>
> Occam does not support conclusions of impossibility. It could
> be a brute fact that the universe is more complicated than
> strcitly necessary.
With comp the universe is more complicated than necessary. Once lobian
machines appear relatively to themselves, complexity grows locally, in
an unbounded way.
>
>> Without Occam I say only that the notion of
>> primary matter is necessarily useless i.e. without explanatory
>> purposes
>> (even concerning just the belief in the physical proposition only) .
>> This is a non trivial consequence of the comp hyp. (cf UDA).
>
> As is the way with these things, we anti-Platonists appeal
> to Occam as well (although not qua impossibilia).
Please I have never said that primary matter is impossible. Just that I
have no idea what it is, no idea what use can it have, nor any idea how
it could helps to explain quanta or qualia.
So I am happy that with comp it has necessarily no purpose, and we can
abandon "weak materialism", i.e. the doctrine of primary matter, like
the biologist have abandon the vital principle, or like the abandon of
ether by most physicist.
But with comp it is shown how to retrieve the appearance of it, by
taking into account the differences between the notions of n-person
(and of n-existence) the universal machine cannot avoid.
>
> All the facts about mathematical truth and methodology can be
> established
> without appeal to the actual existence of mathematical objects.
I am not *that* platonist.
But I can revert your sentence: All the facts about *physical* truth
and methodology can be established (and with comp: *have to* be
established) without appeal to the actual existence of physical object.
> In fact, the lack of such objects actually explains the
> objectivity and necessity of maths. Mathematical statements
> are necessarily true because there are no possible circumstances
> that make them false;
Not really .....
> there are no possible circumstances that
> would make them false because they do not refer to anything
> external.
It depends what you mean by "external". You beg the question because
you talk like if we *knew* there is a "primary material reality" out
there.
> This is much simpler than the Platonist
> alternative that mathematical statements :
> 1) have referents
> which are
> 2) unchanging and eternal, unlike anything anyone has actuall seen
> and thereby
> 3) explain the necessity (invariance) of mathematical statements
> without
> 4) performing any other role -- they are not involved in
> mathematical proof.
I am not *that* platonist at all!!!!! (Neither Plato or Plotinus, ...)
>
>>> But the negative integers exist (or "exist"), so it has
>>> an existing predecessor.
>>
>>
>> Yes. But the axiom Q1 "Ax ~(0 = s(x)" is not made wrong just because
>> you define the negative integer in Robinson Arithmetic. The "x" are
>> still for "natural number". The integer are new objects defined from
>> the natural number. All right? To take another example, you can define
>> in RA all partial recursive functions, but obviously they does not
>> obey
>> to the Q axioms, they are just constructs, definable in RA.
>
> So the specialness of Time depends on the specialness of nautral
> numbers, depends on the specialness of Robinson Arithemtic ?
Robinson Arithmetic is Turing-universal, and, unlike just any UTM, RA
can easily be extended into Peano Arithmetic, which is not only turing
universal, but which, in some precise sense, know that she is turing
universal.
Mathematician does this all the time. They show that what they want to
prove about some mathematical object O does not depend on the choice of
representations used to represent O, so, after, they choose a special
representation in which O appears as something as simple as possible
for reasoning about it and then they can conclude by statements true on
O in all representations.
For the math you are far more platonist than I am. My position is just
that propositions like :"all non negative integers can be written as
the sum of four squares", [which was already known by Diophantus
(probably a contemporary of Plotinus), but proved much later by
Lagranges], are true independently of me or of any cognition abilities.
... If only because "cognition" has to be defined or isolate by number
relations, once the comp hyp is taken seriously enough.
And then physics will reappear as "relation between cognitions", higher
order "meta" relation between numbers ...
What I say is far more concrete than what you try to ascribe to me, I
think. I could say more: the standard comp-particles are probably
related to the irreducible presentation of permutation groups operating
on the roots of some (any?) universal diophantine polynomial(s), or
something like that. Why waves? I am still asking the lobian machine.
But thanks to Godel, Lob, Solovay ... it is possible to manage the
difference between quanta and qualia, intelligible matter and sensible
matter, sharable and unsharable truth, and many other n-person notions,
etc.
Don't forget I propose an empirically testable theory.
Bruno
David Nyman
> Please I have never said that primary matter is impossible. Just that I
> have no idea what it is, no idea what use can it have, nor any idea how
> it could helps to explain quanta or qualia.
> So I am happy that with comp it has necessarily no purpose, and we can
> abandon "weak materialism", i.e. the doctrine of primary matter, like
> the biologist have abandon the vital principle, or like the abandon of
> ether by most physicist.
> But with comp it is shown how to retrieve the appearance of it, by
> taking into account the differences between the notions of n-person
> (and of n-existence) the universal machine cannot avoid.
Are we not trying to discriminate two possible starting assumptions
here?
1) Necessity
2) Contingency
Assumption 1 makes no appeal to fundamental contingency, but posits
only 'necessarily true' axioms (e.g. AR). In this sense there could
never be "nothing instead of something" because the 'necessary truth'
of AR is deemed independent of contingency - indeed 'contingency' would
be seen to emerge from it (hence its 'empiricism' Bruno?)
Assumption 2 posits by contrast the ultimate contingency of 'existence'
- there might indeed have been 'nothing'. The apparent 'necessity' of
AR must consequently be illusory - i.e. AR, CT etc. derive their
'existence' and characteristics from the prior facts of brute
contingency.
Under assumption 2, therefore, the semantics of 'bare substrate' boil
down to a fundamental assertion of 'non-relative contingent existence',
and 'primary matter' to 'relative contingent processes/ structures'.
Starting from assumption 2 we could see comp as a schema of relative
contingent process/ structure within which 'primary matter' is deemed
to be 'instantiated', or vice versa (i.e. the 'usual assumption' of
physical instantiation).
But are assumptions 1 and 2 ineluctably 'theological preferences', or
can we discriminate them empirically?
David
1Z
David Nyman wrote:
> Bruno Marchal wrote:
>
> > Please I have never said that primary matter is impossible. Just that I
> > have no idea what it is, no idea what use can it have, nor any idea how
> > it could helps to explain quanta or qualia.
> > So I am happy that with comp it has necessarily no purpose, and we can
> > abandon "weak materialism", i.e. the doctrine of primary matter, like
> > the biologist have abandon the vital principle, or like the abandon of
> > ether by most physicist.
> > But with comp it is shown how to retrieve the appearance of it, by
> > taking into account the differences between the notions of n-person
> > (and of n-existence) the universal machine cannot avoid.
>
> Are we not trying to discriminate two possible starting assumptions
> here?
>
> 1) Necessity
> 2) Contingency
>
> Assumption 1 makes no appeal to fundamental contingency, but posits
> only 'necessarily true' axioms (e.g. AR).
Things don't become necessarily true just
because someone says so. The truths
of mathematics may be necessarily true, but
that does not make AR a s aclaim about
existence necessarily true. AR as a claim
about existence is metaphysics, and highly debatable.
> In this sense there could
> never be "nothing instead of something" because the 'necessary truth'
> of AR is deemed independent of contingency - indeed 'contingency' would
> be seen to emerge from it (hence its 'empiricism' Bruno?)
Necessary truth doesn't entail necessary existence unless
the claims in question are claims about existence.
Whether mathematical truths are about existence is debatable
and not "necessary".
> Assumption 2 posits by contrast the ultimate contingency of 'existence'
> - there might indeed have been 'nothing'. The apparent 'necessity' of
> AR must consequently be illusory
Not if AR is only a claim about truth. Necessary truth
can exist in a world of contingent existence -- providing
all necessary truths in such a world are ontologically non-commital.
As non-Platonists indded take mathematical statements to be.
> - i.e. AR, CT etc. derive their
> 'existence' and characteristics from the prior facts of brute
> contingency.
>
> Under assumption 2, therefore, the semantics of 'bare substrate' boil
> down to a fundamental assertion of 'non-relative contingent existence',
> and 'primary matter' to 'relative contingent processes/ structures'.
> Starting from assumption 2 we could see comp as a schema of relative
> contingent process/ structure within which 'primary matter' is deemed
> to be 'instantiated', or vice versa (i.e. the 'usual assumption' of
> physical instantiation).
>
> But are assumptions 1 and 2 ineluctably 'theological preferences', or
> can we discriminate them empirically?
That's what White Rabbits are all about.
There is also an apriori argument against Pythagoreanism (=everything
is numbers). If it is a *contingent* fact that non-mathematical
entities
don't exist, Pythagoreanism cannot be justified by rationalism (=-
all truths are necessary and apriori). Therefore the
Pythagorean-ratioanlist
must believe matter is *impossible*.
(BTW, empiricists can accept *some* apriori arguments).
David Nyman
> Necessary truth doesn't entail necessary existence unless
> the claims in question are claims about existence.
If one claims (which I don't BTW) that something is 'necessarily true'
*independent of contingent existence* then I think for this to be in
any way coherent, one must be making some sort of existence claim for
'necessary truth'. By contrast, within contingent existence, some
things may seem 'necessarily true', but this truth can only be derived
from aspects of contingency (i.e. in virtue of the concept and its
referents being contingently instantiated).
> Not if AR is only a claim about truth. Necessary truth
> can exist in a world of contingent existence -- providing
> all necessary truths in such a world are ontologically non-commital.
> As non-Platonists indded take mathematical statements to be.
I agree insofar as you mean what I'm saying above: i.e. the 'existence'
of 'necessary truth' in a world of contingent existence must itself be
'contingently instantiated'. 'Necessity' in this sense is restricted to
'necessary under ceratin contingencies'. In a world of contingent
existence the behaviour of a logical system must reduce ultimately to
the behaviour of a contingently instantiated system.
> There is also an apriori argument against Pythagoreanism (=everything
> is numbers). If it is a *contingent* fact that non-mathematical
> entities
> don't exist, Pythagoreanism cannot be justified by rationalism (=-
> all truths are necessary and apriori). Therefore the
> Pythagorean-ratioanlist
> must believe matter is *impossible*.
Yes, I agree. That's what I mean about the 'existence' claim of
'necessary truth' - since it rules out 'contingent instantiation', it
must replace it with 'necessary instantiation', or be incoherent as to
ontology.
David
1Z
David Nyman wrote:
> 1Z wrote:
>
> > Necessary truth doesn't entail necessary existence unless
> > the claims in question are claims about existence.
>
> If one claims (which I don't BTW) that something is 'necessarily true'
> *independent of contingent existence* then I think for this to be in
> any way coherent, one must be making some sort of existence claim for
> 'necessary truth'.
But only the sort of abstract "exisence" that
numbers have in the first place, which is
not genuine existence at all for anti-Platonists.
> By contrast, within contingent existence, some
> things may seem 'necessarily true', but this truth can only be derived
> from aspects of contingency (i.e. in virtue of the concept and its
> referents being contingently instantiated).
What things ? Are they really necessarily true,
or only seemingly so ?
> > Not if AR is only a claim about truth. Necessary truth
> > can exist in a world of contingent existence -- providing
> > all necessary truths in such a world are ontologically non-commital.
> > As non-Platonists indded take mathematical statements to be.
>
> I agree insofar as you mean what I'm saying above: i.e. the 'existence'
> of 'necessary truth' in a world of contingent existence must itself be
> 'contingently instantiated'.
Statements, concepts and beliefs must
be contingently instantiated. That doesn't
mean that their truths-values are logially
contingent.
> 'Necessity' in this sense is restricted to
> 'necessary under ceratin contingencies'. In a world of contingent
> existence the behaviour of a logical system must reduce ultimately to
> the behaviour of a contingently instantiated system.
But physical possibility is a subset
of logical possibility, so the physical
systems can't do anything its abstract counterpart
cannot do, so what is true of the abstract system
is true of any phsycial systems that really instantiates it.
David Nyman
> Statements, concepts and beliefs must
> be contingently instantiated. That doesn't
> mean that their truths-values are logially
> contingent.
>
I'm not sure that in a world of strictly contingent existence one can
establish a 'logical necessity' that is independent of 'contingent
instantiation' and thus escapes restriction to 'necessary under certain
contingencies' (even if these are equivalent to 'any that I can
imagine'). If one is going to be a 'contingentist', then one might as
well be a thoroughgoing one.
> But physical possibility is a subset
> of logical possibility, so the physical
> systems can't do anything its abstract counterpart
> cannot do, so what is true of the abstract system
> is true of any phsycial systems that really instantiates it.
I agree. However what I'm saying is that in a world of contingent
existence *everything* is contingently instantiated. Consequently,
neither 'physical possibility' nor 'logical possibility' can escape
dependency on such instantiation. In a world of contingent existence
the elevation of any 'necessary truth' above contingency is dubious and
possibly incoherent. To be coherent AFAICS one would need to be making
ontic claims for 'necessary truth' that would constrain 'contingent
possibility'.
David
1Z
David Nyman wrote:
> 1Z wrote:
>
> > Statements, concepts and beliefs must
> > be contingently instantiated. That doesn't
> > mean that their truths-values are logially
> > contingent.
> >
>
> I'm not sure that in a world of strictly contingent existence one can
> establish a 'logical necessity' that is independent of 'contingent
> instantiation'
Why should the *truth* of a statement be dependent on
the *existence* of an instance of it ?
Moreover, the necessary truth of mathematical statements
follows from their lack or real referents:-
Mathematical statements
are necessarily true because there are no possible circumstances
that make them false; there are no possible circumstances that
would make them false because they do not refer to anything
external. This is much simpler than the Platonist
alternative that mathematical statements:
1) have referents
which are
2) unchanging and eternal, unlike anything anyone has actually seen
and thereby
3) explain the necessity (invariance) of mathematical statements
without
4) performing any other role -- they are not involved in
mathematical proof.
> and thus escapes restriction to 'necessary under certain
> contingencies' (even if these are equivalent to 'any that I can
> imagine').
If one is going to be a 'contingentist', then one might as
> well be a thoroughgoing one.
>
> > But physical possibility is a subset
> > of logical possibility, so the physical
> > systems can't do anything its abstract counterpart
> > cannot do, so what is true of the abstract system
> > is true of any phsycial systems that really instantiates it.
>
> I agree. However what I'm saying is that in a world of contingent
> existence *everything* is contingently instantiated.
What does instantiation have to do with truth ?
> Consequently,
> neither 'physical possibility' nor 'logical possibility' can escape
> dependency on such instantiation.
Logical possibility is defined in terms of contradiciton.
Why should it turn out to be nonetheless dependent
on instantiation ?
> In a world of contingent existence
> the elevation of any 'necessary truth' above contingency is dubious and
> possibly incoherent.
I don't see why. You just seem to be treating
truth and existence as interchangeable, which
begs the questions AFAICS.
> To be coherent AFAICS one would need to be making
> ontic claims for 'necessary truth' that would constrain 'contingent
> possibility'.
I have no idea what you mean by that. Why would a claim about
necessary truth be ontic rather than epistemic, for instance ?
David Nyman
> Why should the *truth* of a statement be dependent on
> the *existence* of an instance of it ?
What I mean is that - for a 'thoroughgoing contingentist' -
'statements', 'concepts', 'truths', 'referents' and anything else
whatsoever can exist solely in virtue of their actual contingent
instantiation (i.e. there literally isn't any other sort of
'existence'). Within such a world-view, even apparently inescapable
logical truths are 'necessary' only within a relational system
instantiated solely in terms of a contingent world. They cannot
'transcend' present contingencies, and under different contingencies
(about which we can know nothing) they could be different. This
establishes an 'epistemic horizon' for a contingent world.
> What does instantiation have to do with truth ?
Everything. 'Truth' in contingent terms is (very loosely) something
like:
1) dispositions to believe that certain statements correspond with
putative sets of 'facts'.
2) sets of 'facts'
3) logical/ empirical processes of judgement
4) conclusions as to truths asserted
5) behaviour consequent on this
6) etc.
If any element of this - from soup to nuts - fails to be instantiated
in some form it cannot exist in a purely contingent world. In this
view, 'conceptual existence' is just the instantiated existence of a
concept. AFAICS any other view would have to assert some sort of
transcendent 'conceptual existence' that subsumes 'contingent
existence'.
> Logical possibility is defined in terms of contradiciton.
> Why should it turn out to be nonetheless dependent
> on instantiation ?
Because 'contradiction' itself depends on instantiation. A statement is
'contradictory' because its referent is impossible to instantiate under
present contingencies. In this world-view, answering such questions is
easy - *everything* depends on such instantiation. Conceptual
'existence' is simply the sum of the instantiations of all (agreed)
instances of a concept - IOW they're all apples if we agree they are.
Any other view is surely already 'Platonic'?
> I don't see why. You just seem to be treating
> truth and existence as interchangeable, which
> begs the questions AFAICS.
No, I'm saying (above) that 'truth' in a contingent world can only be
*derived* from present contingencies. By this token, truth in any
'transcendent' sense is either impossible (if one believes in a
contingent world), or alternatively *must* be a de facto 'existence'
claim that rules out 'primary contingency' - i.e. the world 'in the
sense that I exist' is supposed to emerge from 'necessity'. So I'm
agreeing with you (I think) in your contention that 'number theology',
to be ontically coherent, must be an existence claim for a priori truth
in this 'strong' sense.
> > To be coherent AFAICS one would need to be making
> > ontic claims for 'necessary truth' that would constrain 'contingent
> > possibility'.
>
> I have no idea what you mean by that. Why would a claim about
> necessary truth be ontic rather than epistemic, for instance ?
For the reasons you yourself have argued - i.e. that claims based on
'Platonic numbers' must be regarded as ontic in a strong sense if they
are supposed to account for a world that exists 'in the sense that I
exist'. Epistemic claims would then follow from this.
David
1Z
David Nyman wrote:
> 1Z wrote:
>
> > Why should the *truth* of a statement be dependent on
> > the *existence* of an instance of it
> What I mean is that - for a 'thoroughgoing contingentist' -
> 'statements', 'concepts', 'truths', 'referents' and anything else
> whatsoever can exist solely in virtue of their actual contingent
> instantiation (i.e. there literally isn't any other sort of
> 'existence').
Indeed, but the contingentist doesn't have to regard truth
as something that exists.
> Within such a world-view, even apparently inescapable
> logical truths are 'necessary' only within a relational system
> instantiated solely in terms of a contingent world.
That would indicate that logical possibility is a subset
of physical possibility, which is counterintuitive. That
is one motivation for sayign that truth (along with other
abstracta such as numbers) doesn't exist at all.
> They cannot
> 'transcend' present contingencies, and under different contingencies
> (about which we can know nothing) they could be different.
No they couldn't, because they do not refer to external
contingencies ITFP. Where there is no relation, there
is no variation. Invariance is necessity.
> This
> establishes an 'epistemic horizon' for a contingent world.
> > What does instantiation have to do with truth ?
>
> Everything. 'Truth' in contingent terms is (very loosely) something
> like:
>
> 1) dispositions to believe that certain statements correspond with
> putative sets of 'facts'.
That is belief, not truth.
> 2) sets of 'facts'
Facts exist. Statements are true. Which do you mean ?
> 3) logical/ empirical processes of judgement
What is judged may be true, since it
may be a statement or proposition.
Processes of judgement are neither true nor false.
> 4) conclusions as to truths asserted
Defining truth in terms of truth.
> 5) behaviour consequent on this
Behaviour is neither true nr false. It is not a
statement or proposition.
> 6) etc.
You seem to be intent on defining truth in
the most baggy way possible.
> If any element of this - from soup to nuts - fails to be instantiated
> in some form it cannot exist in a purely contingent world.
Hardly anything in your list actually has anythig to
do with truth. The possible exception is (2), "facts".
But "fact" is a notoriously[*] ambiguous word.
[*] Not notoriously *enough* , though.
> In this
> view, 'conceptual existence' is just the instantiated existence of a
> concept.
What has that got to do with truth ?
> AFAICS any other view would have to assert some sort of
> transcendent 'conceptual existence' that subsumes 'contingent
> existence'.
No, because truth and existence are different.
Thus, a proposition can both exist contingently and
have a necessary truth-value.
> > Logical possibility is defined in terms of contradiciton.
> > Why should it turn out to be nonetheless dependent
> > on instantiation ?
>
> Because 'contradiction' itself depends on instantiation.
No it doesn't.
> A statement is
> 'contradictory' because its referent is impossible to instantiate under
> present contingencies.
No, it is contradictory becuase it contains a clause of
the form [A & ~A] (A and not-A). Contradiciton is a formal,
logical property.
> In this world-view, answering such questions is
> easy - *everything* depends on such instantiation. Conceptual
> 'existence' is simply the sum of the instantiations of all (agreed)
> instances of a concept - IOW they're all apples if we agree they are.
> Any other view is surely already 'Platonic'?
Nope.
> > I don't see why. You just seem to be treating
> > truth and existence as interchangeable, which
> > begs the questions AFAICS.
>
> No, I'm saying (above) that 'truth' in a contingent world can only be
> *derived* from present contingencies.
It can also be derived from the interrelation of concepts.
> By this token, truth in any
> 'transcendent' sense
Could you specify a "transcendent sense" ?
> is either impossible (if one believes in a
> contingent world), or alternatively *must* be a de facto 'existence'
> claim that rules out 'primary contingency' - i.e. the world 'in the
> sense that I exist' is supposed to emerge from 'necessity'.
I couldn't make sense of that.
Necessity is an abstract logical property, not a thing.
> So I'm
> agreeing with you (I think) in your contention that 'number theology',
> to be ontically coherent, must be an existence claim for a priori truth
> in this 'strong' sense.
Platonists feel they must reify the supposed referents
of necessarily true statements in order to explain
their necessity.
Number theologians only need to reify numbers. I have no
idea why you are so keen on reifying truth.
> > > To be coherent AFAICS one would need to be making
> > > ontic claims for 'necessary truth' that would constrain 'contingent
> > > possibility'.
> >
> > I have no idea what you mean by that. Why would a claim about
> > necessary truth be ontic rather than epistemic, for instance ?
>
> For the reasons you yourself have argued - i.e. that claims based on
> 'Platonic numbers' must be regarded as ontic in a strong sense if they
> are supposed to account for a world that exists 'in the sense that I
> exist'.
If you want to finish with the conclusion that we
are in Plato's heaven, you must start with the
assumption that Plato's heaven exists. But I
don't see what that has to with being coherent.
One can simply deny that we are in Plato's heaven.
Then we don't need to make ontological
assumptions about mathematical statements.
Nothing else prompts us to, either,
David Nyman
> Indeed, but the contingentist doesn't have to regard truth
> as something that exists.
Fair enough, but even the contingentist needs to express herself
intelligibly without recourse to a constant blizzard of scare quotes.
So she still needs something that FAPP corresponds to 'instantiated
truth', and we can indeed discover such analogs in a contingent world.
> That would indicate that logical possibility is a subset
> of physical possibility, which is counterintuitive. That
> is one motivation for sayign that truth (along with other
> abstracta such as numbers) doesn't exist at all.
Agreed, with the above proviso.
> No they couldn't, because they do not refer to external
> contingencies ITFP. Where there is no relation, there
> is no variation. Invariance is necessity.
Well, at the level of metaphor you are correct, but in a strictly
contingentist sense, they implicitly refer to external contingencies,
because 'conceptual' contingencies must be instantiated in terms of
those selfsame 'external' ones. IOW, 'reference', 'externality' and the
entire conceptual armamentarium are instantiated in a given contingent
state of affairs and consequently are dependent on it for their
'logic'. Were these contingencies different, white rabbits might become
quite mundane.
> You seem to be intent on defining truth in
> the most baggy way possible.
Yes, but I'm just trying to point out that we can pragmatically deploy
a variety of means to establish agreement to some level of accuracy
without having to believe in the 'transcendent existence' of truth.
> > In this
> > view, 'conceptual existence' is just the instantiated existence of a
> > concept.
>
> What has that got to do with truth ?
Well, the existence of truth is just the instantiated existence of a
truth, in the contingentist view. Actually, I don't really want to push
all this too far. FAPP the distinctions you make are valid, and I'd
much rather agree to deploy a metaphorical sense of the 'existence' of
truth rather than chase about looking for its multifarious
contingentist instantiations. I was originally trying to contrast the
contingent vs. necessary ontic assumptions that seemed to me implicit
in your dialogue with Bruno. As it happens, my own preference lies on
the side of contingency.
Conceptual
> > 'existence' is simply the sum of the instantiations of all (agreed)
> > instances of a concept - IOW they're all apples if we agree they are.
> > Any other view is surely already 'Platonic'?
>
> Nope.
Why isn't it? Do you mean that we can ascribe metaphorical 'existence'
to a conceptual framework that transcends any or all particular
instantiated examples, without ascribing literal existence to it? In
this case, as with 'truth', I would concur.
David
1Z
David Nyman wrote:
> 1Z wrote:
>
> > Indeed, but the contingentist doesn't have to regard truth
> > as something that exists.
>
> Fair enough, but even the contingentist needs to express herself
> intelligibly without recourse to a constant blizzard of scare quotes.
> So she still needs something that FAPP corresponds to 'instantiated
> truth', and we can indeed discover such analogs in a contingent world.
Finding something that corresponds to instantiated
truth -- such as knowledge -- does not make truth contingent.
> > That would indicate that logical possibility is a subset
> > of physical possibility, which is counterintuitive. That
> > is one motivation for sayign that truth (along with other
> > abstracta such as numbers) doesn't exist at all.
>
> Agreed, with the above proviso.
>
> > No they couldn't, because they do not refer to external
> > contingencies ITFP. Where there is no relation, there
> > is no variation. Invariance is necessity.
>
> Well, at the level of metaphor you are correct, but in a strictly
> contingentist sense, they implicitly refer to external contingencies,
No. They don't refer at all. Maths isn't empirical.
> because 'conceptual' contingencies must be instantiated in terms of
> those selfsame 'external' ones.
Instantiation isn't reference.
> IOW, 'reference', 'externality' and the
> entire conceptual armamentarium are instantiated in a given contingent
> state of affairs
if they are instantiated at all.
> and consequently are dependent on it for their
> 'logic'.
Clearly not, since we are able to concive physically
impossible worlds. The virtual "logic" isn't determined
by physics. A computer running on real phsyics can
simulate a world where graivity is an inverse cube law.
> Were these contingencies different, white rabbits might become
> quite mundane.
Yes. It is logically possible for what is physically
(im)possible to have been different. Physical
possibillity is a subset of logical possibility.
Logical possibility isn't determined by physical possibility.
> > You seem to be intent on defining truth in
> > the most baggy way possible.
>
> Yes, but I'm just trying to point out that we can pragmatically deploy
> a variety of means to establish agreement to some level of accuracy
> without having to believe in the 'transcendent existence' of truth.
That is tangential to the discussion. The point
is that anti-Plaotonists can agree with Platonists
100% about the mind-independence of mathemaical
trth, whilst agreeing 0% about the mind-independent
existence of mathematical objects."Transcendent" truth does not
have to be sacrificed to ontological contingency.
> > > In this
> > > view, 'conceptual existence' is just the instantiated existence of a
> > > concept.
> >
> > What has that got to do with truth ?
>
> Well, the existence of truth is just the instantiated existence of a
> truth, in the contingentist view. Actually, I don't really want to push
> all this too far. FAPP the distinctions you make are valid, and I'd
> much rather agree to deploy a metaphorical sense of the 'existence' of
> truth rather than chase about looking for its multifarious
> contingentist instantiations. I was originally trying to contrast the
> contingent vs. necessary ontic assumptions that seemed to me implicit
> in your dialogue with Bruno. As it happens, my own preference lies on
> the side of contingency.
OK.
> Conceptual
> > > 'existence' is simply the sum of the instantiations of all (agreed)
> > > instances of a concept - IOW they're all apples if we agree they are.
> > > Any other view is surely already 'Platonic'?
> >
> > Nope.
>
> Why isn't it? Do you mean that we can ascribe metaphorical 'existence'
> to a conceptual framework that transcends any or all particular
> instantiated examples, without ascribing literal existence to it? In
> this case, as with 'truth', I would concur.
Mathematical "existence" operates under constraints of logical
coherence,
non-contradicition, consistency. It is not just a case of conceiving
something.
Bruno Marchal
Le 02-sept.-06, à 16:03, David Nyman a écrit :
>
> Bruno Marchal wrote:
>
>> Please I have never said that primary matter is impossible. Just that
>> I
>> have no idea what it is, no idea what use can it have, nor any idea
>> how
>> it could helps to explain quanta or qualia.
>> So I am happy that with comp it has necessarily no purpose, and we can
>> abandon "weak materialism", i.e. the doctrine of primary matter, like
>> the biologist have abandon the vital principle, or like the abandon of
>> ether by most physicist.
>> But with comp it is shown how to retrieve the appearance of it, by
>> taking into account the differences between the notions of n-person
>> (and of n-existence) the universal machine cannot avoid.
>
> Are we not trying to discriminate two possible starting assumptions
> here?
>
> 1) Necessity
> 2) Contingency
>
> Assumption 1 makes no appeal to fundamental contingency, but posits
> only 'necessarily true' axioms (e.g. AR). In this sense there could
> never be "nothing instead of something" because the 'necessary truth'
> of AR is deemed independent of contingency - indeed 'contingency' would
> be seen to emerge from it (hence its 'empiricism' Bruno?)
All right.
>
> Assumption 2 posits by contrast the ultimate contingency of 'existence'
> - there might indeed have been 'nothing'. The apparent 'necessity' of
> AR must consequently be illusory - i.e. AR, CT etc. derive their
> 'existence' and characteristics from the prior facts of brute
> contingency.
>
> Under assumption 2, therefore, the semantics of 'bare substrate' boil
> down to a fundamental assertion of 'non-relative contingent existence',
> and 'primary matter' to 'relative contingent processes/ structures'.
> Starting from assumption 2 we could see comp as a schema of relative
> contingent process/ structure within which 'primary matter' is deemed
> to be 'instantiated', or vice versa (i.e. the 'usual assumption' of
> physical instantiation).
>
> But are assumptions 1 and 2 ineluctably 'theological preferences', or
> can we discriminate them empirically?
Like you can test the Everett MW from a first person point of view by
quantum suicide, you can get first person confirmation of comp by comp
suicide. But this is trivial and not so interesting. Now my point is
that comp gives enough constraint by itself so that you can derive the
physical *law-like* propositions from it, so you can compare them with
empiry. So you can get first person plural confirmation (of a purely
third person communicable theory).
Bruno
Bruno Marchal
Le 30-août-06, à 16:37, uv a écrit :
> [Bruno's defintiion of Arithmetic Realism I understand to be
> " Arithmetical Realism.
> All proposition pertaining on natural numbers
> with the form Qx Qy Qz Qt Qr ... Qu P(x,y,z,t,r, ...,u) are true
> independently
> of me. Q represents a universal or existential quantifier, and P
> represents a
> decidable (recursive) predicate. That is, proposition like the
> Fermat-Wiles
> theorem, or Goldbach conjecture, or Euclide's infinity of primes
> theorem are
> either true or false, and this independently of the proposition "Bruno
> Marchal
> exists". It amounts to accept, for the sake of my argument, that
> classical logic is correct in the realm of positive integers. Nothing
> more."]
Indeed. Good summary, thanks. Third person necessity and contingency
will then be defined by the (Sigma1) provability predicate of
Godel-Lob, and the n-version persons by intensional (modal) variants of
it.
Note that Fermat-Wiles, Riemann, Godlbach, Euclide's are all Sigma1.
Arithmetical realism bears also on the independence of the truth of
Pi1, Sigma2, Pi2, ...SigmaN, PiN ..., sentences, but I have no problem
with the lobian machine which have also "realist" analytical beliefs
(where we can quantify on sets).
Nice example of non P1 or Sigma1 conjectures is given by the famous
Syracuse question:
http://www.cecm.sfu.ca/organics/papers/lagarias/
Bruno
Bruno Marchal
Le 30-août-06, à 21:26, 1Z (Peter D. Jones) a écrit :
> How do you escape solipsism without embracing materialism ?
You can escape solipsism by embracing *any* kind of *objective*
idealism (inspired by mathematical structures or not).
Objective idealisms are not in fashion today, I know, but fashion is
not an argument, hope you agree ...
Bruno
1Z
Bruno Marchal wrote:
> Le 30-août-06, à 21:26, 1Z (Peter D. Jones) a écrit :
>
>
> > How do you escape solipsism without embracing materialism ?
>
>
>
>
> You can escape solipsism by embracing *any* kind of *objective*
> idealism (inspired by mathematical structures or not).
Why should a belief in other minds (which I do not directly experience)
be more reasonable thant a belief in unexperienced primary matter ?
It's a question of consistency.
Bruno Marchal
Le 02-sept.-06, à 17:26, 1Z a écrit :
> Things don't become necessarily true just
> because someone says so. The truths
> of mathematics may be necessarily true, but
> that does not make AR a s aclaim about
> existence necessarily true. AR as a claim
> about existence is metaphysics, and highly debatable.
Yes. So let us never do it.
> Necessary truth doesn't entail necessary existence unless
> the claims in question are claims about existence.
Exactly.
> Whether mathematical truths are about existence is debatable
> and not "necessary".
Existential mathematical statement are about existence.
> Not if AR is only a claim about truth.
AR is about the truth of arithmetical statements, and among
arithmetical statements, many are existential, so AR makes claim about
the independent truth of existential statements. No need to add
metaphysics at this stage (nor at any other stage by the way, except
the yes doctor, which I prefer to range in "theology" than in
"metaphysics").
> Necessary truth
> can exist in a world of contingent existence -- providing
> all necessary truths in such a world are ontologically non-commital.
I don't understand.
> As non-Platonists indded take mathematical statements to be.
AR does not ask you for believing in some metaphysical (still less
physical) existence of numbers. It ask you to agree that a proposition
of the type ExP(x) is true or false independently of any cognitive
faculty. Cognitive abilities are needed to believe or know that ExP(x)
is true (or false), but that's all.
> That's what White Rabbits are all about.
>
> There is also an apriori argument against Pythagoreanism (=everything
> is numbers). If it is a *contingent* fact that non-mathematical
> entities
> don't exist,
It is not even a fact. It is an assumption. Nobody has proved that
something non mathematical exists, although comp is quite close in
proving this. Indeed comp shows that no first person can be described
mathematically by herself. So *relatively* to a machine first person,
many things will *appear* non mathematical. It is a consequence of
incompleteness + the theaetetical-plotinian definition of knowledge.
> Pythagoreanism cannot be justified by rationalism (=-
> all truths are necessary and apriori). Therefore the
> Pythagorean-ratioanlist
> must believe matter is *impossible*.
Not impossible. Just useless.
Bruno
Bruno Marchal
Le 04-sept.-06, à 02:56, 1Z a écrit :
>
> Why should a belief in other minds (which I do not directly experience)
> be more reasonable thant a belief in unexperienced primary matter ?
> It's a question of consistency.
Attributing mind to others explains many things. There are rich (albeit
vague) theories about those other mind (treated in Psychology (cf
jealousy, shame, fear, ...) and Theology (does other minds go to
paradise?). Although I have no direct experience of other minds I have
many indirect evidences.
Unexperienced primary matter? I have not even indirect experiences, and
with comp and/or the quantum I can not even ascribe a simple meaning to
the concept. Why should I postulate something I don't understand?
Of course I believe in the existence of fermions and bosons, of stars
and galaxies, ... I believe also in the existence of Bridge and Chess,
Nations and humans, etc... I see only relatively stable patterns and
histories.
Bruno
1Z
Bruno Marchal wrote:
> Le 02-sept.-06, à 17:26, 1Z a écrit :
>
>
> > Things don't become necessarily true just
> > because someone says so. The truths
> > of mathematics may be necessarily true, but
> > that does not make AR a s aclaim about
> > existence necessarily true. AR as a claim
> > about existence is metaphysics, and highly debatable.
>
> Yes. So let us never do it.
Debate is what we are here for.
> > Necessary truth doesn't entail necessary existence unless
> > the claims in question are claims about existence.
>
> Exactly.
>
>
> > Whether mathematical truths are about existence is debatable
> > and not "necessary".
>
>
> Existential mathematical statement are about existence.
And Sherlock Holmes lives because Sherlock Holmes lives
at 221b Baker Street.
> > Not if AR is only a claim about truth.
>
> AR is about the truth of arithmetical statements, and among
> arithmetical statements, many are existential, so AR makes claim about
> the independent truth of existential statements.
Arithmetical statements use the word "exists", or the symbolic
euivalen thereof. However, it is not to be taken literally
in all contexts.
> No need to add
> metaphysics at this stage
Yes there is. You need metaphysics to answer the question
of whether the existence-claims of mathematics shouldbe takne
literally.
> (nor at any other stage by the way, except
> the yes doctor, which I prefer to range in "theology" than in
> "metaphysics").
Is theology better-foudned as a discipline ?
> > Necessary truth
> > can exist in a world of contingent existence -- providing
> > all necessary truths in such a world are ontologically non-commital.
>
>
> I don't understand.
If necessary truths don't refer to contingently
existing things, they cannot be "infected" by their contingency.
> > As non-Platonists indded take mathematical statements to be.
>
> AR does not ask you for believing in some metaphysical (still less
> physical) existence of numbers.
Then it does not show the UD exist, and it cannot follow
that I part of its output.
> It ask you to agree that a proposition
> of the type ExP(x) is true or false independently of any cognitive
> faculty.
It may well be true. It may well mean nothing more
than "P(x) is non-contradictory"
> Cognitive abilities are needed to believe or know that ExP(x)
> is true (or false), but that's all.
Quite. So nothing in the argument can tell me about the nature of my
existence.
> > That's what White Rabbits are all about.
> >
> > There is also an apriori argument against Pythagoreanism (=everything
> > is numbers). If it is a *contingent* fact that non-mathematical
> > entities
> > don't exist,
>
> It is not even a fact. It is an assumption.
I already said "if"...
> Nobody has proved that
> something non mathematical exists, although comp is quite close in
> proving this.
That isn't the point. The point is the consistency
Pythagorean rationalism as a hypothesis.
> Indeed comp shows that no first person can be described
> mathematically by herself. So *relatively* to a machine first person,
> many things will *appear* non mathematical. It is a consequence of
> incompleteness + the theaetetical-plotinian definition of knowledge.
> > Pythagoreanism cannot be justified by rationalism (=-
> > all truths are necessary and apriori). Therefore the
> > Pythagorean-ratioanlist
> > must believe matter is *impossible*.
>
> Not impossible. Just useless.
The Pythagorean rationalist *must* believe mater
is impossible -- the argument becomes inconsistent otherwise.
The argument that matter is "useless" is more akin
to empiricism than rationalism.
> Bruno
>
>
> http://iridia.ulb.ac.be/~marchal/
1Z
Bruno Marchal wrote:
> Le 04-sept.-06, à 02:56, 1Z a écrit :
>
> >
> > Why should a belief in other minds (which I do not directly experience)
> > be more reasonable thant a belief in unexperienced primary matter ?
> > It's a question of consistency.
>
> Attributing mind to others explains many things.
And the project of expaling things with matter has been going strong
for
many centuries.
> There are rich (albeit
> vague) theories about those other mind (treated in Psychology (cf
> jealousy, shame, fear, ...) and Theology (does other minds go to
> paradise?). Although I have no direct experience of other minds I have
> many indirect evidences.
Yes, that;s the problem. What stands between your mind and
other minds is your body and other bodies.
> Unexperienced primary matter? I have not even indirect experiences,
No experience of time and change ?
> and
> with comp and/or the quantum I can not even ascribe a simple meaning to
> the concept.
Quantum mechanics is a theory *of* matter.
Bruno Marchal
Le 04-sept.-06, à 16:08, 1Z a écrit :
> Arithmetical statements use the word "exists", or the symbolic
> euivalen thereof. However, it is not to be taken literally
> in all contexts.
>
>> No need to add
>> metaphysics at this stage
>
> Yes there is. You need metaphysics to answer the question
> of whether the existence-claims of mathematics shouldbe takne
> literally.
"Metaphysics" is provided through the "yes doctor", which you have no
choice not to take literally.
I mean you would not say "yes" to a doctor who tells you that you will
survive the comp-substitution and then add: don't take this literally.
But even this is strictly speaking suppressed when defining the many
notion of contingency and necessity from the intensional (modal)
variant of the Godel Lob self-referential provability notions.
Recall the UDA and AUDA difference (AUDA = Arithmetical UDA = lobian
interview).
>
>> (nor at any other stage by the way, except
>> the yes doctor, which I prefer to range in "theology" than in
>> "metaphysics").
>
> Is theology better-foudned as a discipline ?
When done by rational theologians, like most of the greek one, it is.
Of course in our civilization "theology" has been appropriated by
"politics" since a long time. Still many Christian theologians have
been "rigorous" or "modest" or "scientific" since, but are generally
put on the margins, if not burned alive or ignored. Today the
aristotelian primary matter hypothesis is defended by the atheist and
the Christian, mainly.
> And Sherlock Holmes lives because Sherlock Holmes lives
> at 221b Baker Street.
Really? Could you give me his phone number please? I will verify.
Come on Peter, this is a diversion which has nothing to do with the
notion of existence of numbers.
You refer to possibly interesting nuances, but those are out of topics
here.
> Arithmetical statements use the word "exists", or the symbolic
> euivalen thereof. However, it is not to be taken literally
> in all contexts.
I don't care. The point is that with comp, the existence of an
electron, or of anything, cannot be taken literally too. The point is
that with comp you can derive from PEANO, why numbers have to believe
in electron, although electron existence is less literal than the
existence of 417.
You keep doing the 1004 fallacy. The question are not metaphysical at
all, and does not address any notion of metaphysical existence in which
I am not interested at all. The point is that the computationalist
hypothesis generates many different notion of existence, and the
interesting thing to do (with respect of explaining quanta, qualia,
where do we come from etc.) consists in finding the relation between
those form of existence, not some intrinsic meaning that they would
have.
Now the simplest notion of existence is the standard interpretation of
"Ex" in first order logic presentation of arithmetic, if only to begin
with. All other notion of existence (psychological, physical,
theological, etc.) are derived from it.
>
>>> Necessary truth
>>> can exist in a world of contingent existence -- providing
>>> all necessary truths in such a world are ontologically non-commital.
>>
>>
>> I don't understand.
>
> If necessary truths don't refer to contingently
> existing things, they cannot be "infected" by their contingency.
I don't understand. A necessary truth could refer to contingently
existing things. If you take (like we will do in the Lobian interview)
"provability B" for "necessity", and consistency D or "possibility",
Godel's second incompleteness theorem is already an example of
necessity about contingencies: it is necessary that if a tautology is
consistent then it is consistent that a falsity is necessary
G proves Dt->DBf, or G* proves B(Dt->DBf). Also B(Ex(x=x)) which is
enough.
>> AR does not ask you for believing in some metaphysical (still less
>> physical) existence of numbers.
>
> Then it does not show the UD exist, and it cannot follow
> that I part of its output.
You should have written: "Then it does not show the UD exists
physically, and it cannot follow
that I am a physical part of its output."
And I agree with you given that I already do not believe you exist
physically in any genuine (applicable) sense of the word (assuming
comp). BTW I have already makes long answer of this, and you did not
reply.
>
>> It ask you to agree that a proposition
>> of the type ExP(x) is true or false independently of any cognitive
>> faculty.
>
> It may well be true. It may well mean nothing more
> than "P(x) is non-contradictory"
No. ExP(x) means that it exist a natural number verifying the property
P.
"P(x) is non-contradictory" is the proposition DP(x),or ~B~P(x), i.e.
~Bew('P(x)') which is a completely different proposition. This one is
even undecidable by *any* lobian machine.
Example: Bf is false but is also non-contradictory for any sound theory
of arithmetic.
Contradictory
>
>> Cognitive abilities are needed to believe or know that ExP(x)
>> is true (or false), but that's all.
>
> Quite. So nothing in the argument can tell me about the nature of my
> existence.
?
> The Pythagorean rationalist *must* believe mater
> is impossible -- the argument becomes inconsistent otherwise.
Could you elaborate?
>
> The argument that matter is "useless" is more akin
> to empiricism than rationalism.
I agree.
But don't see your point unless you believe I am not an empiricist,
which of course I am, given that one of my main point in my PhD thesis
is that comp is empirically testable.
True, sometimes some people believe that I am not empiricist because I
show that if comp is correct the physics is entirely "in our head". But
I have never said that everything "in our head" should necessarily be
taken for granted. We can and must, from comp, extract the physics
which is in our head, and then compare it with the empirical physics,
and so we can test comp. OK?
(Again this is something I have already explain, I repeat the
explanation because I suspect others could still be confused, but I am
not sure I will repeat this an infinity of times, if only because I
will be more buzy. I will begin to concentrate myself on the
presentation of the "roadmap/hypostases". This should help you to
reevaluate more constructively your critics perhaps, imo.
Bruno
Bruno Marchal
Le 04-sept.-06, à 16:12, 1Z a écrit :
>
>
> Bruno Marchal wrote:
>> Le 04-sept.-06, à 02:56, 1Z a écrit :
>>
>>>
>>> Why should a belief in other minds (which I do not directly
>>> experience)
>>> be more reasonable thant a belief in unexperienced primary matter ?
>>> It's a question of consistency.
>>
>> Attributing mind to others explains many things.
>
>
> And the project of expaling things with matter has been going strong
> for
> many centuries.
But if you know the literature in "philosophy of mind" you know that
the notion of "matter" has never been successful. It has ease the
progress in *quantitative physics", but only by paying the price of
hiding the fundamental mind/body question. Of course the fundamental
questions has been appropriated by the fake-authoritative "religion"
people. And as I have said often, if you look at the literature in
physics, primary matter never play an explicit role. It just help to
interpret formula without jeopardizing common sense.
>
>> There are rich (albeit
>> vague) theories about those other mind (treated in Psychology (cf
>> jealousy, shame, fear, ...) and Theology (does other minds go to
>> paradise?). Although I have no direct experience of other minds I have
>> many indirect evidences.
>
> Yes, that;s the problem. What stands between your mind and
> other minds is your body and other bodies.
Yes. But we can believe in bodies without attributing to them primary
matters.
>
>> Unexperienced primary matter? I have not even indirect experiences,
>
> No experience of time and change ?
Sure. So what? Time and change can be explained by the third hypostase
which appears naturally when you define the first person in terms of
the provability logics.
>
>> and
>> with comp and/or the quantum I can not even ascribe a simple meaning
>> to
>> the concept.
>
> Quantum mechanics is a theory *of* matter.
Yes. But it is even less a theory of primary matter than Newtonian
physics, where we can still imagine matter is composed of real "atomos"
(non splitable entities).
1Z
Bruno Marchal wrote:
> Le 29-août-06, à 20:45, 1Z a écrit :
>
>
>
> > The version of AR that is supported by comp
> > only makes a commitment about mind-independent *truth*. The idea
> > that the mind-independent truth of mathematical propositions
> > entails the mind-independent *existence* of mathematical objects is
> > a very contentious and substantive claim.
>
>
> You have not yet answered my question: what difference are you making
> between "there exist a prime number in platonia" and "the truth of the
> proposition asserting the *existence* of a prime number is independent
> of me, you, and all contingencies" ?
"P is true" is not different to "P". That is not the difference I
making.
I'm making a difference between what "exists" means in mathematical
sentences and what it means in empiricial sentences (and what it means
in fictional contexts...)
The logical case for mathematical Platonism is based on the idea
that mathematical statements are true, and make existence claims.
That they are true is not disputed by the anti-Platonist, who
must therefore claim that mathematical existence claims are somehow
weaker than other existence claims -- perhaps merely metaphorical.
That the the word "exists" means different things in different contexts
is easily established.
For one thing, this is already conceded by Platonists! Platonists think
(Incidentally, this approach answers a question about mathematical and
empirical
truth. The anti-Platonists want sthe two kinds of truth to be
different, but
also needs them to be related so as to avoid the charge that one class
of
statement is not true at all. This can be achieved because empirical
statements rest on non-contradiction in order to achive correspondence.
If an empricial observation fails co correspond to a statemet, there
is a contradiction between them. Thus non-contradiciton is a necessary
but insufficient justification for truth in empircal statements, but
a sufficient one for mathematical statements).
> > Where is it shown the UD exists ?
>
>
> If you agree that the number 0, 1, 2, 3, 4, ... exist (or again, if you
> prefer, that the truth of the propositions:
>
> Ex(x = 0),
> Ex(x = s(0)),
> Ex(x = s(s(0))),
> ...
>
> is independent of me), then it can proved that the UD exists. It can be
> proved also that Peano Arithmetic (PA) can both define the UD and prove
> that it exists.
But again this is just "mathematical existence". You need some
reason to assert that mathematical existence is not a mere
metaphor implying no real existence, as anti-Platonist
mathematicians claim. I do not think that is given by computationalism.
> >> Tell me also this, if you don't mind: are you able to doubt about the
> >> existence of "primary matter"? I know it is your main fundamental
> >> postulate. Could you imagine that you could be wrong?
> >
> > It is possible that I am wrong. It is possible that I am right.
> > But you are -- or were -- telling me matter is impossible.
>
>
> Only when I use Occam.
Occam does not support conclusions of impossibility. It could
be a brute fact that the universe is more complicated than
strcitly necessary.
> Without Occam I say only that the notion of
> primary matter is necessarily useless i.e. without explanatory purposes
> (even concerning just the belief in the physical proposition only) .
> This is a non trivial consequence of the comp hyp. (cf UDA).
As is the way with these things, we anti-Platonists appeal
to Occam as well (although not qua impossibilia).
All the facts about mathematical truth and methodology can be
established
without appeal to the actual existence of mathematical objects.
In fact, the lack of such objects actually explains the
objectivity and necessity of maths. Mathematical statements
are necessarily true because there are no possible circumstances
that make them false; there are no possible circumstances that
would make them false because they do not refer to anything
external. This is much simpler than the Platonist
alternative that mathematical statements :
1) have referents
which are
2) unchanging and eternal, unlike anything anyone has actuall seen
and thereby
3) explain the necessity (invariance) of mathematical statements
without
4) performing any other role -- they are not involved in
mathematical proof.
> > But the negative integers exist (or "exist"), so it has
> > an existing predecessor.
>
>
> Yes. But the axiom Q1 "Ax ~(0 = s(x)" is not made wrong just because
> you define the negative integer in Robinson Arithmetic. The "x" are
> still for "natural number". The integer are new objects defined from
> the natural number. All right? To take another example, you can define
> in RA all partial recursive functions, but obviously they does not obey
> to the Q axioms, they are just constructs, definable in RA.
So the specialness of Time depends on the specialness of nautral
numbers, depends on the specialness of Robinson Arithemtic ?
> Bruno
>
>
> http://iridia.ulb.ac.be/~marchal/
Bruno Marchal
Le 12-sept.-06, à 19:20, 1Z a écrit :
>>
>> You have not yet answered my question: what difference are you making
>> between "there exist a prime number in platonia" and "the truth of the
>> proposition asserting the *existence* of a prime number is independent
>> of me, you, and all contingencies" ?
>
> "P is true" is not different to "P". That is not the difference I
> making.
All right then. It is an important key point for what will follow.
It will help me to represent the modality "True(p)" by just "p"; that
is useful because correct machine cannot represent their notion of
truth (by Tarski theorem).
> I'm making a difference between what "exists" means in mathematical
> sentences and what it means in empiricial sentences (and what it means
> in fictional contexts...)
OK. So with this phrasing, the consequence of the UDA (including either
the movie-graph argument, or the use of the "comp-physics" already
extracted + OCCAM) can be put in this way:
The appearance of "empirical existence" is explain without ontological
empirical commitment from the mathematical existence of numbers. Indeed
empirical existence, assuming comp, has to be an internal arithmetical
modality.
> The logical case for mathematical Platonism is based on the idea
> that mathematical statements are true, and make existence claims.
Yes.
> That they are true is not disputed by the anti-Platonist, who
> must therefore claim that mathematical existence claims are somehow
> weaker than other existence claims -- perhaps merely metaphorical.
But the whole point is that if you take the "yes doctor" idea seriously
enough, then "empirical existence" appears to be more metaphorical than
mathematical existence.
> That the the word "exists" means different things in different contexts
> is easily established.
Right. Now a TOE is supposed to explain all those notion of existence
and to explain also how they are related.
I take the "simple" math existence as primitive, and explain all other
notion of existence from it. Perhaps you should wait for it, or peruse
in the archive or in my url to see how that works.
> However,
> mathematics is not a fiction because it is not a free creation.
> Mathematicians are constrained by consistency and non-contradiction
> in a way that authors are not.
OK. But after Godel, mathematicians know, (or should know) that the
consistency constrained is not enough.
Simple example: all sufficiently rich and consistent theory T remains
consistent when you add the axiom asserting that T is inconsistent. You
get a consistent but unreasonable and incorrect theory.
Yes: Godel's second incompleteness result is admittedly amazing.
> (Incidentally, this approach answers a question about mathematical and
> empirical
> truth. The anti-Platonists want sthe two kinds of truth to be
> different, but
> also needs them to be related so as to avoid the charge that one class
> of
> statement is not true at all. This can be achieved because empirical
> statements rest on non-contradiction in order to achive correspondence.
> If an empricial observation fails co correspond to a statemet, there
> is a contradiction between them. Thus non-contradiciton is a necessary
> but insufficient justification for truth in empircal statements, but
> a sufficient one for mathematical statements).
Alas no. After Godel's second incompleteness theorem (or Lob extension
of it) non-contradiction is insufficient even for the mathematical
reality. Any machine/theory can be consistent and false with respect to
the intended arithmetical reality.
Like Chaitin is aware, even pure arithmetic has some objective
"empirical" features.
>> If you agree that the number 0, 1, 2, 3, 4, ... exist (or again, if
>> you
>> prefer, that the truth of the propositions:
>>
>> Ex(x = 0),
>> Ex(x = s(0)),
>> Ex(x = s(s(0))),
>> ...
>>
>> is independent of me), then it can proved that the UD exists. It can
>> be
>> proved also that Peano Arithmetic (PA) can both define the UD and
>> prove
>> that it exists.
>
> But again this is just "mathematical existence". You need some
> reason to assert that mathematical existence is not a mere
> metaphor implying no real existence, as anti-Platonist
> mathematicians claim. I do not think that is given by computationalism.
It is not given by comp per se. It follows from the UD Argument. Don't
hesitate to ask question about any step where you feel not being
convinced.
> Occam does not support conclusions of impossibility. It could
> be a brute fact that the universe is more complicated than
> strcitly necessary.
You are *trivially* right. This could kill ANY theory. You can say to a
string theorist : what about the particles which we have not yet
discover and which would behave in a way contradicting the theory.
> All the facts about mathematical truth and methodology can be
> established
> without appeal to the actual existence of mathematical objects.
I believe that what you want to say here is this:
[All the facts about mathematical truth and methodology can be
established without appeal to the empirical (or metaphysical, ...)
existence of mathematical object"].
And I agree with this. But you still need mathematical existence. Then
I explain why (UDA) and how (arithmetical UDA, lobian interview) to
extract the other notion of more contextual form of existence.
My problem here is pedagogical (if not sometimes diplomatic): you have
to possess some good understanding of mathematical logic. Even just
concerning the arithmetical propositions p, you have to realize the
differences between
p (p is true, or satisfied by the school-learned mathematical
structure (N, +, *, 0, 1));
Bp (p is provable by the lobian machine M, fixed once and for all)
Bp & p (p is provable by M and p is true in (N, +, *, 0, 1))
Bp & Dp (p is provable by M and p is consistent with M's other
belief/theorems)
Bp & Dp & p (p is provable, consistent and true).
Now if M is a sufficiently simple correct lobian machine compared to
you (like Peano Arithmetic), then *you* can prove that Bp, Bp & p, Bp
& Dp, Bp & Dp & p are all equivalent with respect to the arithmetical
sentences p. But then you can also prove that this equivalence cannot
be proved (Bp) nor known (Bp & p) nor observed (Bp & Dp) nor "felt" (Bp
& Dp & p) by the machine M, or by any correct machine when "B" is its
own provability predicate.
> So the specialness of Time depends on the specialness of nautral
> numbers, depends on the specialness of Robinson Arithemtic ?
You are right and wrong.
Right because RA is a very precise machine/theory which has the
advantage of being both a subset of all rich lobian machine, and at the
same time a turing-complete or universal machine, and this makes it
possible to identify computability with provability in RA, or
Sigma1-provability.
You are wrong because any other machine or language could have been use
instead. Any theory capable or representing the FI and the Wi would
work. I have already try to sell the ontic SK combinator theory which
has other advantage (relating computation theory with computability
theory), but people didn't react to the posts I have send(*) about
them, and I guess the choice of RA will just make things easier if only
by allowing us to treat computability as a special case of provability.
The lobian machine we have to interview are just the extensions of RA
by induction axioms: for any formula F we accept that
[F(0) & An(F(n) -> F(n+1))] -> AnF(n).
This gives PA tremendous introspective ability, making her, not only
able to compute all the Fi and Wi like RA or any universal machine, but
able mainly to reason deeply about those things.
Perhaps this links could help:
http://www.ltn.lv/~podnieks/gt3.html
An excellent book is the one by Eliot Mendelson:
http://www.amazon.com/Introduction-Mathematical-Fourth-Elliott-
Mendelson/dp/0412808307
Book on the modal logics of provability are the one by Smorynski and
the one by Boolos. Reference:
Smoryński, P. (1985). Self-Reference and Modal Logic. Springer Verlag,
New York.
Boolos, G. (1993). The Logic of Provability. Cambridge University
Press, Cambridge
Bruno
(*) http://www.mail-archive.com/everyth...@eskimo.com/msg05961.html