Cantor's Diagonal?
in [Math]
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From: FF on 10 Feb 2010 07:58 On Wed, 10 Feb 2010 04:40:57 -0800 (PST), FredJeffries wrote: [...]. >>> Transfer Principle <lwal...(a)lausd.net> wrote: >>>> Therefore, _ultra_finitists such as WM and ... Note idiot (not you FJ), WM explicitly _rejects_ to be considered a (representative of) ultrafinitism! Just for the record. FF
From: Aatu Koskensilta on 10 Feb 2010 08:41 Transfer Principle <lwalke3(a)lausd.net> writes: > I believe that Yessenin-Volpin is a "crank" if and only if WM is a > "crank." Yessenin-Volpin is a great humorist. His musings on logic and mathematics are wonderful stuff, quite unlike the tepid twaddle we get from WM. -- Aatu Koskensilta (aatu.koskensilta(a)uta.fi) "Wovon man nicht sprechan kann, dar�ber muss man schweigen" - Ludwig Wittgenstein, Tractatus Logico-Philosophicus
From: Aatu Koskensilta on 10 Feb 2010 08:58 Transfer Principle <lwalke3(a)lausd.net> writes: > Consider the thread in the link above. In this thread, Nguyen used > mostly symbolic language, which according to criterion III above, > suggests that he is standard. You do realize that in passages such as this you come off as extremely silly? -- Aatu Koskensilta (aatu.koskensilta(a)uta.fi) "Wovon man nicht sprechan kann, dar�ber muss man schweigen" - Ludwig Wittgenstein, Tractatus Logico-Philosophicus
From: Aatu Koskensilta on 10 Feb 2010 09:04 Transfer Principle <lwalke3(a)lausd.net> writes: > I agree with Webb here -- in the end, it's a wash as to which side > physics really favors, so perhaps it's best just to avoid physics in > any discussion of set theory. The point that I was making is that > members of both sides _do_ make physical-based arguments, not that > such arguments are actually valid. Setting aside the rather fantastic notion that the axiom of choice, say, could have any physical consequences, we may note that as regards logical strength the mathematics used in physics is rather wimpy -- PA, and even PRA, suffices just fine, with some tedious coding and massaging of the mathematical machinery. Of course, we can't draw from this purely logical observation any conclusion about whether it would be humanly possible to do mathematical physics using only weak mathematical principles. -- Aatu Koskensilta (aatu.koskensilta(a)uta.fi) "Wovon man nicht sprechan kann, dar�ber muss man schweigen" - Ludwig Wittgenstein, Tractatus Logico-Philosophicus
From: Gc on 10 Feb 2010 09:17
On 10 helmi, 16:04, Aatu Koskensilta <aatu.koskensi...(a)uta.fi> wrote: > Transfer Principle <lwal...(a)lausd.net> writes: > > I agree with Webb here -- in the end, it's a wash as to which side > > physics really favors, so perhaps it's best just to avoid physics in > > any discussion of set theory. The point that I was making is that > > members of both sides _do_ make physical-based arguments, not that > > such arguments are actually valid. > > Setting aside the rather fantastic notion that the axiom of choice, say, > could have any physical consequences, we may note that as regards > logical strength the mathematics used in physics is rather wimpy -- PA, > and even PRA, suffices just fine, with some tedious coding and massaging > of the mathematical machinery. Of course, we can't draw from this purely > logical observation any conclusion about whether it would be humanly > possible to do mathematical physics using only weak mathematical > principles. Are you sure about this? I think you need at least borel measure to define a Hilbert space which is used in Quantum mechanics, but in the other hand Hilbert space probably contains functions which have no physical meaning, not differentiable anywhere etc. Anyway you probably need some axiom of choice like stuff in functional analysis, operator algebras etc. I agree (if that is what you are saying) that doing things rigorously as in mathematical physics you probably will need more stronger mathematics. Implicitly ordinary physicist also us those notions. |