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From: Tom Caylor <Daddycaylor.domain.name.hidden>

Date: Wed, 06 Sep 2006 12:23:26 -0700

Bruno Marchal wrote:

*> Le 16-août-06, à 18:36, Tom Caylor a écrit :
*

*>
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*> > I noticed that you slipped in "infinity" ("infinite collection of
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*> > computations") into your roadmap (even the short roadmap). In the
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*> > "technical" posts, if I remember right, you said that at some point we
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*> > were leaving the constructionist realm. But are you really talking
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*> > about infinity? It is easy to slip into invoking infinity and get away
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*> > with it without being noticed. I think this is because we are used to
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*> > it in mathematics. In fact, I want to point out that David Nyman
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*> > skipped over it, perhaps a case in point. But then you brought it up
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*> > again here with aleph_zero, and 2^aleph_zero, so it seems you are
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*> > really serious about it. I thought that infinities and singularities
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*> > are things that physicists have dedicated their lives to trying to
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*> > purge from the system (so far unsuccessfully ?) in order to approach a
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*> > "true" theory of everything. Here you are invoking it from the start.
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*> > No wonder you talk about faith.
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*> >
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*> > Even in the realm of pure mathematics, there are those of course who
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*> > think it is invalid to invoke infinity. Not to try to complicate
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*> > things, but I'm trying to make a point about how serious a matter this
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*> > is. Have you heard about the feasible numbers of V. Sazanov, as
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*> > discussed on the FOM (Foundations Of Mathematics) list? Why couldn't
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*> > we just have 2^N instantiations or computations, where N is a very
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*> > large number?
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*>
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*>
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*> I would say infinity is all what mathematics is about. Take any theorem
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*> in arithmetic, like any number is the sum of four square, or there is
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*> no pair of number having a ratio which squared gives two, etc.
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*> And I am not talking about analysis, or the use of complex analysis in
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*> number theory (cf zeta), or category theory (which relies on very high
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*> infinite) without posing any conceptual problem (no more than
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*> elsewhere).
*

When you say infinity is what math is all about, I think this is the

same thing as I mean when I say that invariance is what math is all

about. But in actuality we find only local invariance, because of our

finiteness. You have said a similar thing recently about comp. But

here you seem to be talking about induction, concluding something about

*all* numbers. Why is this needed in comp? Is not your argument based

on Robinson's Q without induction?

*> Even constructivist and intuitionist accept infinity, although
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*> sometimes under the form of potential infinity (which is all we need
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*> for G and G* and all third person point of view, but is not enough for
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*> having mathematical semantics, and then the first person (by UDA) is
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*> really linked to an actual infinity. But those, since axiomatic set
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*> theory does no more pose any interpretative problem.
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*> True, I heard about some ultrafinitist would would like to avoid
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*> infinity, but until now, they do have conceptual problem (like the fact
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*> that they need notion of fuzzy high numbers to avoid the fact that for
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*> each number has a successor. Imo, this is just philosophical play
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*> having no relation with both theory and practice in math.
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*>
*

*>
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*> > The UDA is not precise enough for me, maybe because I'm a
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*> > mathematician?
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*> > I'm waiting for the interview, via the roadmap.
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*>
*

*> UDA is a problem for mathematicians, sometimes indeed. The reason is
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*> that although it is a "proof", it is not a mathematical proof. And some
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*> mathematician have a problem with non mathematical proof. But UDA *is*
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*> the complete proof. I have already explain on this list (years ago)
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*> that although informal, it is rigorous. The first version of it were
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*> much more complex and technical, and it has taken years to suppress
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*> eventually any non strictly needed difficulties.
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*> I have even coined an expression "the 1004 fallacy" (alluding to Lewis
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*> Carroll), to describe argument using unnecessary rigor or abnormally
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*> precise term with respect to the reasoning.
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*> So please, don't hesitate to tell me what is not precise enough for
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*> you. Just recall UDA is not part of math. It is part of cognitive
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*> science and physics, and computer science.
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*> The lobian interview does not add one atom of rigor to the UDA, albeit
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*> it adds constructive features so as to make possible an explicit
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*> derivation of the "physical laws" (and more because it attached the
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*> quanta to extended qualia). Now I extract only the logic of the certain
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*> propositions and I show that it has already it has a strong quantum
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*> perfume, enough to get an "arithmetical quantum logic, and then the
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*> rest gives mathematical conjectures. (One has been recently solved by a
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*> young mathematician).
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*>
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*> Bruno
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*>
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*>
*

*> http://iridia.ulb.ac.be/~marchal/
*

What is the non-mathematical part of UDA? The part that uses Church

Thesis? When I hear "non-mathematical" I hear "non-rigor". Define

rigor that is non-mathematical. I guess if you do then you've been

mathematical about it. I don't understand.

Tom

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Received on Wed Sep 06 2006 - 15:25:20 PDT

Date: Wed, 06 Sep 2006 12:23:26 -0700

Bruno Marchal wrote:

When you say infinity is what math is all about, I think this is the

same thing as I mean when I say that invariance is what math is all

about. But in actuality we find only local invariance, because of our

finiteness. You have said a similar thing recently about comp. But

here you seem to be talking about induction, concluding something about

*all* numbers. Why is this needed in comp? Is not your argument based

on Robinson's Q without induction?

What is the non-mathematical part of UDA? The part that uses Church

Thesis? When I hear "non-mathematical" I hear "non-rigor". Define

rigor that is non-mathematical. I guess if you do then you've been

mathematical about it. I don't understand.

Tom

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Received on Wed Sep 06 2006 - 15:25:20 PDT

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