Re: The Mathematico-Cognition Reality Theory (MCRT) Ver 6.0
Brent Meeker
...
> Different levels of Causality
>
> Brain processes are enacting things which are *mathematical* in nature
> - 'algorithms' (See 'Functionalism'). Mathematical entities are
> abstracted patterns. But abstracted patterns themselves (like
> 'algorithms') don't exist directly inside physical causal networks,
> only particular instances of them do. This is clear by pointing to the
> fact that many different brains could enact the *same* computation
> (algorithm) - the philosophical term is that the algorithm is 'multiply
> realizable'. So the particular physical processes in the brain can't
> be *identical* to the mathematical entity (the algorithm) itself.
But is it true that different brains can implement the same algorithm? It seems it
is only true because we abstract a certain algorithm from it's various
representation, e.g. as written on paper. Every actual realization, in brains or
computer or on paper is actually slightly different at a microscopic level at least.
We call it "the same algorithm" because we're abstracting a common functionality or
purpose.
>
> It was an argument similar to this that led to the demise of the
> original 'Identity Theory' of mind (a theory which attempted to
> identity mental states with physical processes). Again, the trouble is
> that many different brain states could be associated with the *same*
> algorithm (or have the same mental states) which shows that physical
> processes cannot be identified with mathematical entities in any simple
> way.
But this only shows that mathematical objects exist in the sense that chair exists;
as a abstraction from chairs. So chair isn't identical with any particular chair.
>The weaker 'Token Identity' theories concede this, but still
> attempt to equate mental states with physical processes. Couldn't one
> simply say that there's some general high-level properties of physical
> matter which can be equated with the algorithm, and hence dispense with
> ghostly mathematical entities? The reason one can't really say this
> boils down to Occam's razor and inference to the best explanation
> again. Attempting to replace the concept of 'algorithm' with some high
> level properties of physical matter is results in descriptions that are
> enormously complex and unwieldy.
But you can look at it the other way around. The "algorithm" is already the general
high-level property that is common to all the brains and computers implementing.
....
>
> The Mathematico-Cognition Ontology
This looks more like botany than ontology.
Brent Meeker
Bruno Marchal
Le 08-sept.-06, à 05:42, marc....@gmail.com a écrit :
<snip>
> It must consist of the 'movement' of mathematical forms through
> state space. The only conclusion that can be drawn from this is that
> mathematical truth is not fixed, but can vary with time - because
> that's exactly what 'the movement of mathematical forms through
> state space' represents... the shifting of mathematical truth.
>
> And I suggest *that Qualia are precisely these abstract processes* !!!
>
> Hope this all makes a bit more sense.
I would certainly encourage you in that direction, although I am not
sure you are aware that even "modern math" is going in a similar
direction. Seeing qualia as mathematical *motions*, as you said in
another post, can be related in a precise way with the arithmetical
hypostases (comp notions of n-person) once you realize that modal logic
is already a way to tackle notions of shifting mathematical truth: once
for each world in a multiplicity (sometimes a continuum) of worlds.
Modal logic, but also Cohen's forcing technic in set theory, have led
to a vast literature on variable truth.
The MWI itself can be seen in that context too. The whole category
approach to math and logic can also be seen as a way to study variable
notion of truth, especially through the notion of topos (boolean valued
or not). All what you say, as far as I understand it, can, and perhaps
should, be recasted in such a frame. Note that with comp, for technical
reasons which I intuit only through my "understanding" of quantum
mechanics, the quanta appears themselves to be sharable (first person
plural) qualia having relational and somehow variable truth values
attached to it too.
The advantage of modal logic and category theory is that such "variable
truth" approach can be based on common non-variable usual notion of
mathematical truth, making it possible to prevent extreme relativism
which often appears in corresponding approaches in less rigorous
philosophical works. I think this is not a problem for you, especially
seeing your today's post (with which I do agree).
Technical remark: all arithmetical hypostases (godel-lobian derived
notion of n-persons) come equipped with their own notions of
"multiverses" (not all are Kripkean one), and so they are all equipped
with a canonical notion of variable truth, but only the 1-person
hypostase (and probably the sensible matter hypostase) got a notion of
temporal-like (albeit bifurking) notion of variability. With the other
hypostases, truth varies, not in a temporal way but in a more abstract
and logical way.
With those remarks what you say makes sense for me,
Bruno
Bruno Marchal
Le 13-sept.-06, à 09:19, marc....@gmail.com a écrit :
> Oh hurrah, then there is finally light at the end of the philosophic
> tunnel for me :D Trying to learn this stuff is just a matter of
> becoming a baby again... the baby just has to keep painfullly throwing
> himself at the stuff and after enough ga-ga-goo-goo sounds the baby
> finally starts to speak a few words that make sense.
>
> In other words: I need to study, study, study ;)
>
> Let me just test out what I think is the key point. It's this. Three
> ontologic levels:
>
> (1) Abstract entities of universal applicability (eg Math/number)
> (2) Abstract entities of limited applicability (eg Alphabet, Chair
> concept)
> (3) Concrete instances (eg specific Chair)
>
> Only (1) is real. (2) and (3) are cognitive interpretations or
> constructs. True yes?
To be short: yes.
I could introduce nuances, but this is because I have already a utterly
precise theory. So I prefer to refer you to my papers instead, or to my
past, present, and future posts here. The risk of being precise too
early would be that we could easily be driven into useless
terminological babbling.
Just to be a little less short I would say that (1) and (2) are closer
than it seems to be with your phrasing. And then (3) refer to empirical
existence which is indeed a cognitive construct or an internal
i-person view or hypostase (assuming comp, bla-bla-bla ...). Concrete
objects or apparent tokens are just relative types.
Bruno
David Nyman
> I think that conscious experience (Qualia) is ultimately knowledge
> reflecting on itself, or, to be more precise, I think Qualia are
> *mathematics modelling itself* - a sort of 'internal model of
> mathematics'. To be even more precise, I think Qualia are symbols
> representing *ontological categories*.
I agree that qualia are ontological, rather than epistemological. I
'experience blue' in virtue of 'being blue' - i.e. myself-as-perceiver,
in specific self-relation with myself-as-percept = being blue (or
rather, blue in parts). This qualitative ontological base is the given
that differentiates into every epistemological category by internal
self-contrast - this is blue, that is red, sour, disgusting, verbal,
mathematical, sexy, whatever. Hence this ontological base cannot itself
be - for example - the physics, because the physics, like all
relationally expressed and acquired information, is part of
epistemology.
If one's ontology is grounded in Arithmetical Realism (e.g. the UD
arithemetically instantiating the infinities of programs generated by
infinities of infinite bitstrings) it then follows that qualia must
indeed be 'internal models of mathematics'. The Arithmetical plenitude
of 'zero-information' self-isolates into islands of non-zero 1st-person
information through anthropic and counter-factual self-selection. The
Library of Babel generates readers to peruse itself. We must therefore
accept that the sense in which we wish this ontological base to be
considered real must be granted to be the same sense, mutatis mutandis
- i.e. the self-isolation of self-aware 1st-persons from the plenitude
- in which we ourselves wish to be considered real.
David
> Interesting what you said about modal and category theory. I don't
> know much about category theory and I'd be interested to know how you
> would define it. So: what is category theory? As far as I can make
> out it's a highly advanced branch of algebra concerned with the
> classification of mathematical structures. Very interesting that you
> put Category Theory and Modal logic together!
>
> I feel the whole area of non-classical logic is underdeveloped. Things
> like modal logic, paraconsistent logic, fuzzy logic, possibility theory
> - perhaps these logics are actually the proper logic for dealing with
> 'reflection' and consciousness?
>
> I think that conscious experience (Qualia) is ultimately knowledge
> reflecting on itself, or, to be more precise, I think Qualia are
> *mathematics modelling itself* - a sort of 'internal model of
> mathematics'. To be even more precise, I think Qualia are symbols
> representing *ontological categories*. Could Category theory be
> exactly the type of math we need to understand this? How does category
> theory fit in with the other non-classical logics mentioned above?
>
> We're closing in Bruno. We're closing in on the answers. I feel I
> vaguely understand the general principles behind everything now and
> it's just a matter of 'working out the math'. If course, all the devil
> is in 'working out the math' , and it could take decades. But I feel
> there's hope now. Real hope for answers in our lifetime. It might
> just be that one of us will break through and then all the powers of
> the universe will be humanities to hold...
>
> Pink Floyd
> 'High Hopes'
> by David Gilmour / Polly Samson
>
> Beyond the horizon of the place we lived when we were young
> In a world of magnets and miracles
> Our thoughts strayed constantly and without boundary
> The ringing of the division bell had begun
>
> Along the Long Road and on down the Causeway
> Do they still meet there by the Cut
>
> There was a ragged band that followed in our footsteps
> Running before times took our dreams away
> Leaving the myriad small creatures trying to tie us to the ground
> To a life consumed by slow decay
>
> The grass was greener
> The light was brighter
> When friends surrounded
> The nights of wonder
>
> Looking beyond the embers of bridges glowing behind us
> To a glimpse of how green it was on the other side
> Steps taken forwards but sleepwalking back again
> Dragged by the force of some inner tide
> At a higher altitude with flag unfurled
> We reached the dizzy heights of that dreamed of world
>
> Encumbered forever by desire and ambition
> There's a hunger still unsatisfied
> Our weary eyes still stray to the horizon
> Though down this road we've been so many times
>
> The grass was greener
> The light was brighter
> The taste was sweeter
> The nights of wonder
> With friends surrounded
> The dawn mist glowing
> The water flowing
> The endless river
>
> Forever and ever
David Nyman
> So I think integrated patches of Knowledge-Information (logical-depth
> complexity) are the 'islands' in the 'sea' of raw Information (Shannon
> or statistical type complexity). And I think there's a third kind of
> information associated with Qualia which isn't understood yet.
Would you care to speculate?
David
> David Nyman wrote:
>
> >
> > I agree that qualia are ontological, rather than epistemological. I
> > 'experience blue' in virtue of 'being blue' - i.e. myself-as-perceiver,
> > in specific self-relation with myself-as-percept = being blue (or
> > rather, blue in parts). This qualitative ontological base is the given
> > that differentiates into every epistemological category by internal
> > self-contrast - this is blue, that is red, sour, disgusting, verbal,
> > mathematical, sexy, whatever. Hence this ontological base cannot itself
> > be - for example - the physics, because the physics, like all
> > relationally expressed and acquired information, is part of
> > epistemology.
> >
> > If one's ontology is grounded in Arithmetical Realism (e.g. the UD
> > arithemetically instantiating the infinities of programs generated by
> > infinities of infinite bitstrings) it then follows that qualia must
> > indeed be 'internal models of mathematics'. The Arithmetical plenitude
> > of 'zero-information' self-isolates into islands of non-zero 1st-person
> > information through anthropic and counter-factual self-selection. The
> > Library of Babel generates readers to peruse itself. We must therefore
> > accept that the sense in which we wish this ontological base to be
> > considered real must be granted to be the same sense, mutatis mutandis
> > - i.e. the self-isolation of self-aware 1st-persons from the plenitude
> > - in which we ourselves wish to be considered real.
> >
> > David
> >
>
> Whoa dude. That is some heavy-duty 'reality theory' speak ;)
>
> One point. I wouldn't say that 'the Arithmetical plentitude' has 'zero
> information'. There is Shannon information there - I'd say it's a sea
> of Shannon information. Of course strings of random gibbrish are
> Shannon information.
>
> We should perhaps distinguish between several different kinds of
> information. I agree that the 'plentitude' , to quote you, does
> 'self-isolate into islands of non-zero 1st person information'. This
> kind of information could be 'logical depth' type complexity (or
> roughly 'knowledge').
>
> So I think integrated patches of Knowledge-Information (logical-depth
> complexity) are the 'islands' in the 'sea' of raw Information (Shannon
> or statistical type complexity). And I think there's a third kind of
> information associated with Qualia which isn't understood yet.
Bruno Marchal
Le 19-sept.-06, à 11:50, marc....@gmail.com a écrit :
>
> Interesting what you said about modal and category theory. I don't
> know much about category theory and I'd be interested to know how you
> would define it. So: what is category theory? As far as I can make
> out it's a highly advanced branch of algebra concerned with the
> classification of mathematical structures.
You can put it in that way. A category is a collection of objects
together with collections of arrows between each object. The arrows are
supposed to follow some rules, like the existence of an identity arrow
for each objects, and arrows should be composable (i.e. if there is an
arrow f from A to B, and g from B to C, then there is an arrow gf from
A to C.
The amazing and interesting thing is that you can learn a lot about the
objects just by the arrows coming in and out of the objects. It leads
to a sort of purely functional view of math.
Typical categories are those where the objects are mathematical
structures and arrows are the morphism (or homomorphism) between those
objects. Ex: category of set (objects = sets, arrows = functions),
category of groups, category of topological spaces. Categories of
categories play the basic role, by supplying functor (morphism of
categories) which can be used for translating
Unfortunately categories occuring in recursion theory are hard to
handle, and my opinion is that we should use category when we cannot
avoid them (but I am confident that this is the case in all
mathematical fields up to some advanced point).
The third hypostases has already a free topos associated to it (a topos
is a generalisation the the category of set, it is a category of
"variable set" actuallly).
> Very interesting that you
> put Category Theory and Modal logic together!
They are many links. See Goldblat book (ref in my url).
>
> I feel the whole area of non-classical logic is underdeveloped. Things
> like modal logic, paraconsistent logic, fuzzy logic, possibility theory
> - perhaps these logics are actually the proper logic for dealing with
> 'reflection' and consciousness?
In my opinion they are overdeveloped. That is why I like to see them
unified by ... classical logic and classical (platonist) consideration.
>
> I think that conscious experience (Qualia) is ultimately knowledge
> reflecting on itself, or, to be more precise, I think Qualia are
> *mathematics modelling itself* - a sort of 'internal model of
> mathematics'.
I am more or less OK with that, although I would link them to their
"mathematics modelling itself" features that are non 3-communicable.
> To be even more precise, I think Qualia are symbols
> representing *ontological categories*.
?
> Could Category theory be
> exactly the type of math we need to understand this? How does category
> theory fit in with the other non-classical logics mentioned above?
This is almost a branch of logic by itself. Intuitionist logic fits
nicely with the toposes.
Symmetrical monoidal categories have something to say about quantal
algebra and quantum logic (but this leads to many technical
difficulties).
But if you have a taste for algebra, don't hesitate to dig ...
Categories are very useful in topology, knot theory, ...
They can be used in computation theory, but not really in computability
theory. I have used them in "Conscience et mecanisme", but abandon them
in subsequent work, if only because there are already too much "hard
math" to swallow before.
>
> We're closing in Bruno. We're closing in on the answers. I feel I
> vaguely understand the general principles behind everything now and
> it's just a matter of 'working out the math'. If course, all the devil
> is in 'working out the math' , and it could take decades. But I feel
> there's hope now. Real hope for answers in our lifetime. It might
> just be that one of us will break through and then all the powers of
> the universe will be humanities to hold...
We can hope ;)
Bruno
David Nyman
> Whoa dude. That is some heavy-duty 'reality theory' speak ;)
Yes indeedy. But my point is that qualia are an ontological category,
not an epistemological one. This is crucial, because it entails that we
can't *know* qualia, we can only instantiate them - *be* them. What we
know - epistemology - is possible only in terms of the ontological
categories that instantiate information, and qualia are examples of
these categories that we personally instantiate, and in terms of which
we 'know' seeing, tasting, touching, and all the rest. Consequently we
cannot communicate such categories directly, but we can invite others
to instantiate them - by communicating the necessary information - and
consequently achieve commensurable dialogue by indicating the relevant
parts of our personal instantiations.
This implies that there are ontological categories, in the equivalent
sense, for all orders of being, in terms of which their informational
structure is expressed. This has great significance for 'yes doctor',
zombies, and other thought experiments (and actual ones) when conducted
in a manner that (may) attempt to analyse the informational structure
of reality (epistemology) without considering its instantiation
(ontology). If your mathematical conjectures re qualia are correct,
they will have to show precisely how such 'internal models of
mathematics' provide an *instantiation* (substrate) in terms of which
information can then - and only then - be expressed.
> One point. I wouldn't say that 'the Arithmetical plentitude' has 'zero
> information'. There is Shannon information there - I'd say it's a sea
> of Shannon information. Of course strings of random gibbrish are
> Shannon information.
Yes, of course. But my point (like Russell's in his book) is that the
totality adds up to zero information in a looser (but extremely
significant) sense because, like in the Library of Babel, there is no
'external' crib to tell you what's what. Only the self-selecting view
from inside delineates what's useful from what's garbage.
David
> David Nyman wrote:
>
> >
> > I agree that qualia are ontological, rather than epistemological. I
> > 'experience blue' in virtue of 'being blue' - i.e. myself-as-perceiver,
> > in specific self-relation with myself-as-percept = being blue (or
> > rather, blue in parts). This qualitative ontological base is the given
> > that differentiates into every epistemological category by internal
> > self-contrast - this is blue, that is red, sour, disgusting, verbal,
> > mathematical, sexy, whatever. Hence this ontological base cannot itself
> > be - for example - the physics, because the physics, like all
> > relationally expressed and acquired information, is part of
> > epistemology.
> >
> > If one's ontology is grounded in Arithmetical Realism (e.g. the UD
> > arithemetically instantiating the infinities of programs generated by
> > infinities of infinite bitstrings) it then follows that qualia must
> > indeed be 'internal models of mathematics'. The Arithmetical plenitude
> > of 'zero-information' self-isolates into islands of non-zero 1st-person
> > information through anthropic and counter-factual self-selection. The
> > Library of Babel generates readers to peruse itself. We must therefore
> > accept that the sense in which we wish this ontological base to be
> > considered real must be granted to be the same sense, mutatis mutandis
> > - i.e. the self-isolation of self-aware 1st-persons from the plenitude
> > - in which we ourselves wish to be considered real.
> >
> > David
> >
>
David Nyman
> I don't totally agree. I think qualia have a dual-aspect: they are
> *both* Ontological (the fabric of reality itself) *and* Epistemological
> (the means through which reality is experienced).
But I think we *do* agree - I would put it precisely as you have above.
> I wouldn't read much into the fact that humans can't communicate qualia
> directly.
I think we are experiencing terminological difficulties. In fact we
don't communicate *anything* 'directly' (i.e. without mediation) - this
is simply not what we mean by 'communication' (i.e. the mediated
distribution of information). Information is distributed on the basis
of which we construct analogs of a source experience - i.e. we
instantiate them: equivalently we experience them. The ontic/ epistemic
distinction is simply the 'role' (medium/ content) being played in a
given narrative by different aspects of a 'fabric' (which in your
analysis is a mathematical metaphysics) at a given level. And in the
case of qualia, the role is to mediate the communication, but by that
same token not to be part of the *information* thus communicated. So in
'experiencing' qualia, we gain access to information *mediated by
qualia*; or equivalently: we *instantiate* such information and thus
represent it 'to ourselves directly' (i.e. without further mediation).
> I maintain that a mind which *could* directly represent
> mathematical concepts in its consciousness would no longer be confused
> about Qualia in the slightest.
But I'm saying precisely that qualia *are* the direct (i.e. immediate)
representation of such concepts, if those concepts are indeed
ontological categories as you suggest. And to follow your 'blindsight'
analogy, if instead of this we had the machinery to 'see' the
underlying structure of our present qualia in some more directly
accessible way, this would be *qualitatively different*, not 'lacking
qualities'. To 'have qualities' = to experience immediately = to
instantiate.
So I agree that were we able to be 'conscious' at another level about
'qualia' we would be unconfused about their structure - but this new
consciousness would itself take place in terms of a novel level of
'qualia' to whose internal structure we would be equally blind. This is
entailed by the necessity for any 'fabric of reality' to differentiate
situationally into perceiver-roles and percept-roles. This generates
both the many povs, their perceptual capabilities and contents, and by
the same differentiation, their ineliminable 'blindspots'.
David
> David Nyman wrote:
> > marc....@gmail.com wrote:
> >
> > > Whoa dude. That is some heavy-duty 'reality theory' speak ;)
> >
> > Yes indeedy. But my point is that qualia are an ontological category,
> > not an epistemological one. This is crucial, because it entails that we
> > can't *know* qualia, we can only instantiate them - *be* them. What we
> > know - epistemology - is possible only in terms of the ontological
> > categories that instantiate information, and qualia are examples of
> > these categories that we personally instantiate, and in terms of which
> > we 'know' seeing, tasting, touching, and all the rest. Consequently we
> > cannot communicate such categories directly, but we can invite others
> > to instantiate them - by communicating the necessary information - and
> > consequently achieve commensurable dialogue by indicating the relevant
> > parts of our personal instantiations.
>
>
> I don't totally agree. I think qualia have a dual-aspect: they are
> *both* Ontological (the fabric of reality itself) *and* Epistemological
> (the means through which reality is experienced). See what I said in
> the other thread: for the ontological categories which are universal in
> scope (i.e the objectively real math concepts) I think there is *no*
> difference between Cognitive categories and Metaphysical ones. Math is
> both the fabric of reality (metaphysics) *and* the means through which
> reality is experienced and categorized (epistemology).
>
> I wouldn't read much into the fact that humans can't communicate qualia
> directly. I see this as a limitation of the human mind rather than a
> fundamental limitation. The reason we're so horribly confused about
> Qualia is that the human brain is not capable of consciously
> representing mathematical concepts. As regards mathematics we humans
> are like someone suffering from 'blind-sight' : we can reason about
> math indirectly in an abstract, intellectual sense (we can have
> abstract mathematical knowledge), but we humans have no direct
> *conscious* representations of mathematical concepts.
>
> This is why I keep pointing out my theory that phenomal properties are
> identical to mathematical properties. The fact that the human mind
> cannot consiously represent mathematical concepts is the source of all
> our confusion. I maintain that a mind which *could* directly represent
> mathematical concepts in its consciousness would no longer be confused
> about Qualia in the slightest.