Thank you for this wonderful post! Interleaving...
----- Original Message -----
From: "Bruno Marchal" <[EMAIL PROTECTED]>
Sent: Saturday, June 24, 2006 1:43 PM
Subject: Re: Only Existence is necessary?
> Dear Stephen,
>> We can go on and on about relations between states, numbers, UDs, or
>> whatever, but unless we have a consistent way to deal with the source
>> individuation and thus distinguishability, we are going nowhere...
> The source of individuation could be personal memory I think. Like a
> sequence of W and M appears in the diary of someone subjected to an
> iterated WM-self-multiplication experiment. Memory is rather easy to
> define once we assume comp. The main difficulty here is to get an idea
> of what "personal" means, and for this we need a theory of
> self-reference, ... and that is what the diagonalization posts are all
Does not the notion of "memory" carry with it some requirement of
"persistence under changes/transformations". It seems to be a lot
but one that can be read and written. Pratt's restatement of Descartes
dictum: "I think, therefore I was" can be easily seem to be equivalent to:
"I am what I remember (active reading of memory) myself to be."
Comp, I am claiming requires more than just the mere a priori existence
of AR (Platonic theory of Numbers), it requires a means to relate them to
one another. This latter requirement seems to require both a means to relate
and distinguish Numbers from each other. This is more than a linear
superposition! We need a means to explain the appearance of Interaction: I
read recently that some prominent scientist said something like that the
physical realm is the means by which Numbers interact, I agree but go
further to claim, with Pratt, that if we are required to have even some
"appearance" of a physical realm, why not go all the way and put it on equal
footing with the Ideals? (Symmetry anyone?!)
Pratt solves the problem of dualism! Why do we still demand an
incomplete and asymmetric Monism?
As to the notion of "personal", it seems to me that what we mean by such
is some means of self-referencing that is capable of "updating", this brings
in the notion of "memory"... I still do not see how any form of
diagonalization obtains self-referencing absent some means that allows the
entries in the columns and rows to both "be themselves" and "relate to each
Goedelization works because we have the tacit idea that we can write a
representation of a number as a symbol of something physical, giving it a
persistence.... Where is the Platonic "paper tape"?
> Concerning Pratt's dualism, it seems to me it is a purely mathematical
> dualism a priori coherent with number platonism, although further
> studies could refute this. Open problem. I don't see Pratt reifying
> either primary matter or primary time, it seems to me.
Pratt does not seek to reify neither a primary notion of matter or time.
His Dualism becomes a Russellerian neutral Monism in the limit of Existence
in itself. When the notion of distinguishability vanishes, so do all notions
of Predicates and Properties, all that is left is mere Existence. This is
why I am pounding hard on the apparent problem that monistic Platonism
suffers from a severe problem, that it is only a coherent theory if and only
if there is some "subject" to which the Forms have a meaning and this
"subject" can not be a Form!
Any form of Monism will have this severe incompleteness that has been
heretofore overlooked because of the continued use of the tacit assumption
of a 3rd person Point of View. Strip away the distinguishability that the
3rd person entails and Forms become exactly isomorphic to each other.
Pratt shows how the "arrow of Time" has a dual aspect, the "arrow of
logical implication" and from this a very elegant explanation of
interactions and causality follows, among other things... ;-)
(Unfortunately, most readers of his papers do not seem to get past the
> I think a similar dualism appears in Plotinus cosmogony where
> (simplifying a lot!) *from outside* the Good transforms itself
> degenerating eventually into Evil (also called Matter by the
> (neo)platonist!) and by doing so makes the soul falling inexorably in
> that matter) and *from inside* all souls extract themselves from that
> matter and are inexorably attracted by the Good and converge toward it.
> Arrows are reversed. And with comp it can be argued that the choice of
> the Categories of sets and its dual (which funnily enough gives the
> category of boolean algebras) is a genuine one, although some
> quasi-constructive alpha-categories could fit in a still more better
> way (I think). But I have neither the time nor the competence to really
> develop such approaches. Also, finding good notion of coherence here
> seems to me to be a little bit ad hoc so that I refer to you the the
> comp derivation path of those coherence conditions.
Yes, we are converging here, but with this proposed dualism the
"outside" is the *neutral* monism of Existence. BTW, it is interesting to
point out that the use of an equivalence between the notion of "points" and
"sets" gives us the basic "objects" that make up our notions of "space", all
be have to add is a liberal amount of symmetry generators. This follows the
same pattern as what is required to complete Mathematics: numbers and the
relations between them.
Bodies are the sets (as point and their interactions = Physics!) and
Minds are the Boolean algebras (information structures and their
implications = Computations!). Is this so hard to swallow?
All we are asked to do here is do stop trying to make up a static
Universe! This reminds me of Einstein's "greatest mistake", his addition of
a "cosmological constant" to make his field equation give a static solution.
Look what that has lead to!
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