Dear Stephen,
<snip>
>
> 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.
Numbers are related by addition and multiplication. With Church thesis
(+ Godel or Matiyasevich) that is enough. The "observer" says more and
relates infinities of numbers through induction.
Of course comp is more than just AR, you need Church Thesis and, in
practice, the "yes doctor" faith.
> This latter requirement seems to require both a means to relate
> and distinguish Numbers from each other.
Only the observer or the intellect will do that, although only the soul
will appreciate.
(Technical note: Observer, intellect and the soul are given by
intensional (modal) variants of the Godel provability predicate; this
gives the notions of person or the arithmetical interpretation of
Plotinus hypostases.)
> 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?
I am not sure comp leads to asymmetric monism. But if you accept AR,
third person incompleteness is not a matter of choice. We have to take
it into account. The collection of "everything computable" is not
itself computable.
>
>
>
> 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
> other".
It depends only of you. Normally the diagonalization post will go
through that problem. Just be patient.
>
> Goedelization works because we have the tacit idea that we can
> write a
> representation of a number as a symbol of something physical,
Here I disagree. Frankly. Godelization works for purely number
theoretical reasons.
> giving it a
> persistence....
With AR (Arithmetical realism) numbers and their relation persists per
se, or better does not need to persist at all, because persistence is
only relative to change and numbers are beyond time and space, and
change (assuming AR).
> Where is the Platonic "paper tape"?
In Platonia. And if a platonic universal machine lacks platonic tape,
she will continue her computations on platonics walls :-)
>
>
>> ***
>> [BM]
>> 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.
>
> [SPK]
>
>
>
> 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!
I agree one hundred percent!
With comp this can already be justified in many ways:
1) The (counter)-intuitive comp level: no 1-soul or first person can
recognize herself in any third person description done at any level.
The 1-soul has no description, no name, it is indeed not a Form.
2) The limit of the self-extending self cannot be defined by
him/her/itself.
3) When I interview the lobian machine, I define the first person by
the knower, and I take the Theaetetical definitions of knowledge, and
this gives thanks, to incompleteness, a non nameable, by any person,
person. Technical reasons show how 1 2 and 3 are related. We can come
back on this when people get some familarization with the
diagonalization stuff.
>
> 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.
? It is not tacit. Science prose have to be third person
communicable.As Judson Webb argues the "severe incompleteness" is a
lucky event for mechanist. First it makes Church thesis consistent.
Indeed Church thesis entails incompleteness, so without incompleteness
Church Thesis would be refutable (on this normally we will arrive
soon).
> 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
> abstract...)
>
>
>
> http://chu.stanford.edu/guide.html#concur02
>
> http://chu.stanford.edu/guide.html#ratmech
>
> http://chu.stanford.edu/guide.html#P5
Most of those papers are very interesting. By the way, Stephen, I
realize you are the only one I thank in my last (Elsevier paper) and
this indeed for having make me read some of Pratt's papers.
(The others in the list disappears from the paper when, for reason of
conciseness I drop the "related works" section. Sorry).
But Pratt, and Girard (and Abramsky) react to the failure of Hilbert
program by mainly weakening logic, at first. I believe that if a
mathematical theorem, like Godel's incompleteness, forces us to weaken
(or enriche) the logic, then an analysis of the incompleteness
phenomenon should help us to chose the exact way of weakening the
logic. I would only criticize Girard and Pratt for not providing enough
motivation. I have still some hope to get an arithmetical *linear
logic* and extract the relevant "Chu transforms", in the long run. I
appreciate very much those papers, but in this list the closer I have
been to that approach is in the combinator posts (prematurely too much
technical, I would say now.). But see my Elsevier paper for more on
this.
>> [BM]
>> 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.
>
> [SPK]
>
>
>
> 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.
Yes.
>
>
>
> 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?
I totally agree and swallow this with pleasure :-) (although this is a
very abstract immaterial view of "bodies")
More can be said: the quantum appears through parallelizing the boolean
algebras, and generates the many locally classical bodies. No problem.
Pratt would be more convincing about those mind/body issue if he could
apply it to the mind/body issues explicitly addressed by the mind/body
researchers, also, I think.
>
>
>
> All we are asked to do here is do stop trying to make up a static
> Universe!
If you talk about the mental or physical Universes, I agree with you.
Now the "theological universe" from which mind and bodies derive and
begin to play the many dual and relative games, well, it does not makes
sense for me to get an outside non static view of it. Dynamics and
spaces are first person views (assuming comp or weaker).
> 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!
Mmmmmmm...... Perhaps a good reason for not doing physics when
interested in the ultimate invariants .... Observations distract us
.... (I am not 100% serious here :)
Bruno
http://iridia.ulb.ac.be/~marchal/
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Received on Mon Jun 26 2006 - 04:30:21 PDT