Bruno Marchal wrote: > Le 16-août-06, à 18:36, Tom Caylor a écrit : > > > I noticed that you slipped in "infinity" ("infinite collection of > > computations") into your roadmap (even the short roadmap). In the > > "technical" posts, if I remember right, you said that at some point we > > were leaving the constructionist realm. But are you really talking > > about infinity? It is easy to slip into invoking infinity and get away > > with it without being noticed. I think this is because we are used to > > it in mathematics. In fact, I want to point out that David Nyman > > skipped over it, perhaps a case in point. But then you brought it up > > again here with aleph_zero, and 2^aleph_zero, so it seems you are > > really serious about it. I thought that infinities and singularities > > are things that physicists have dedicated their lives to trying to > > purge from the system (so far unsuccessfully ?) in order to approach a > > "true" theory of everything. Here you are invoking it from the start. > > No wonder you talk about faith. > > > > Even in the realm of pure mathematics, there are those of course who > > think it is invalid to invoke infinity. Not to try to complicate > > things, but I'm trying to make a point about how serious a matter this > > is. Have you heard about the feasible numbers of V. Sazanov, as > > discussed on the FOM (Foundations Of Mathematics) list? Why couldn't > > we just have 2^N instantiations or computations, where N is a very > > large number? > > > I would say infinity is all what mathematics is about. Take any theorem > in arithmetic, like any number is the sum of four square, or there is > no pair of number having a ratio which squared gives two, etc. > And I am not talking about analysis, or the use of complex analysis in > number theory (cf zeta), or category theory (which relies on very high > infinite) without posing any conceptual problem (no more than > 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 > sometimes under the form of potential infinity (which is all we need > for G and G* and all third person point of view, but is not enough for > having mathematical semantics, and then the first person (by UDA) is > really linked to an actual infinity. But those, since axiomatic set > theory does no more pose any interpretative problem. > True, I heard about some ultrafinitist would would like to avoid > infinity, but until now, they do have conceptual problem (like the fact > that they need notion of fuzzy high numbers to avoid the fact that for > each number has a successor. Imo, this is just philosophical play > having no relation with both theory and practice in math. > > > > The UDA is not precise enough for me, maybe because I'm a > > mathematician? > > I'm waiting for the interview, via the roadmap. > > UDA is a problem for mathematicians, sometimes indeed. The reason is > that although it is a "proof", it is not a mathematical proof. And some > mathematician have a problem with non mathematical proof. But UDA *is* > the complete proof. I have already explain on this list (years ago) > that although informal, it is rigorous. The first version of it were > much more complex and technical, and it has taken years to suppress > eventually any non strictly needed difficulties. > I have even coined an expression "the 1004 fallacy" (alluding to Lewis > Carroll), to describe argument using unnecessary rigor or abnormally > precise term with respect to the reasoning. > So please, don't hesitate to tell me what is not precise enough for > you. Just recall UDA is not part of math. It is part of cognitive > science and physics, and computer science. > The lobian interview does not add one atom of rigor to the UDA, albeit > it adds constructive features so as to make possible an explicit > derivation of the "physical laws" (and more because it attached the > quanta to extended qualia). Now I extract only the logic of the certain > propositions and I show that it has already it has a strong quantum > perfume, enough to get an "arithmetical quantum logic, and then the > rest gives mathematical conjectures. (One has been recently solved by a > young mathematician). > > Bruno > > > 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 --~--~---------~--~----~------------~-------~--~----~ You received this message because you are subscribed to the Google Groups "Everything List" group. To post to this group, send email to email@example.com To unsubscribe from this group, send email to [EMAIL PROTECTED] For more options, visit this group at http://groups.google.com/group/everything-list -~----------~----~----~----~------~----~------~--~---