Cantor's Diagonal?
in [Logic]
|
Prev: The set theoretic content of the transfinite recursion theorem
Next: Geometry surface area Contact; related to "flatness"; Pedestal-Geometry #386 Correcting Math
From: MoeBlee on 10 Feb 2010 11:20 On Feb 9, 10:52 pm, Transfer Principle <lwal...(a)lausd.net> wrote: > standard theorist MoeBlee I'm a standard theorist now? This should give my parents such naches! > Typical of the standard theorists, MoeBlee desires a theory > in which calculus can be axiomatized. It matters little to > such standard theorists what "extra" can be axiomatized in > theory I NEVER said that it matters little what else is proven. In fact, I've posted that being ontologically (if you will) conservative may be a desideratum. In fact, IF you ASKED me about this instead of PUTTING WORDS IN MY MOUTH, you'd find that I even have some (I stress 'some') sympathy for "V=L" as an axiom. > The standard theorist MoeBlee > says to include calculus in the foundational theory (no > matter what else gets included). I NEVER said the parenthetical portion or implied it. You're plain lying about me again. Stop it. Also, I've allowed that the calculus doesn't necessarily have to be classical but could be constructivist instead. MoeBlee
From: MoeBlee on 10 Feb 2010 11:22 On Feb 10, 12:34 am, Virgil <Vir...(a)home.esc> wrote: > In article > <a8554fc6-0b17-44e5-88dc-4543a9338...(a)s33g2000prm.googlegroups.com>, > "Ross A. Finlayson" <ross.finlay...(a)gmail.com> wrote: > > The equivalency function, though, that works in general models of the > > reals, and variously as I show in the proof machinery of results about > > uncountability of the reals not similarly to any other function you > > describe, by proof, still sees that you are selecting a different by > > the symmetry of the diagonal, with respect to EF's about the other. > > Would you translate that into comprehensible English please. Might as well ask a pastrami sandwhich to do the backstroke. MoeBlee
From: William Hughes on 10 Feb 2010 12:38 On Feb 9, 6:01 pm, Transfer Principle <lwal...(a)lausd.net> wrote: > On Feb 9, 8:14 am, FredJeffries <fredjeffr...(a)gmail.com> wrote: > > > On Feb 7, 10:55 pm, Transfer Principle <lwal...(a)lausd.net> wrote: > > > Therefore, _ultra_finitists such as WM and > > > Yessenin-Volpin will now be considered cranks (and that's > > > _without_ the scare quotes, since the label is deserved). > > That you consider Alexander Yessenin-Volpin a crank does not say much > > for your method of classification. > > I believe that Yessenin-Volpin is a "crank" if and only if WM > is a "crank." (For this post, I return to scare quotes until > the "crank"-hood of WM and Y-V is settled.) I do not. Indeed my view of WM as a crank has very little to do with his views on ultrafinitism. > > Recall that Yessenin-Volpin is the mathematician famous for, > upon being asked "Is n a natural number?" (for the standard > or Peano natural n), waiting until a time proportional to the > magnitude of n has passed before answering "yes." In other > words, he waits until time nt has passed (for some fixed > constant time t) before answering the question. > > There are many similarities between Yessenin-Volpin and WM > that lead me to believe that each deserves to be a "crank" if > the other so deserves. These similarities include: > > 1. Both are ultrafinitists. Except for WM who actively denies the existence of a largest integer. > 2. Neither actually has a fixed upper bound on the magnitude > of a permissible natural number. Thus Y-V can't answer the > question "What is the largest number?" He may, however, be able to answer the question "Is there a largest number" The answers "yes" (but it is not possible to know what it is", "no" (I have not constructed such a beast) and "this question is meaningless" would all be consistent with what I do know. > WM has also stated > that although some Peano natural numbers "don't exist," there > is no largest permissible natural number. And I consider this inconsistent with his arguments that there are a limited number of natural numbers. (Though I think it is possible to make this consistent by saying that the question "Are there a limited number of natural numbers" has meaning and "Is there a largest natural number" does not.) However, in of itself, I do not think that espousing a view I find to be inconsistent makes someone a crank. Y-V may or may not be a crank. I do not know (my limited exposure would lead me to think not). In my opinion WM is a crank because of the way he argues. E.g. - he mostly refuses to give definitions, and many of the definitions he does use (generally implicitly) are idiosyncratic in the extreme. - he changes the subject frequently. If you challenge a "proof" that X is true, you will not get a reply to your challenge, but another "proof" of X. - many discussions with him follow the pattern WM: A is true and A implies B. O: A is true but A does not imply B. WM: Clearly you do not understand. Here is another proof that A is true. [Note that your categorization of crank only applies to construction of mathematics. E.g. your stuff does not apply to JSH.] - William Hughes
From: Tonico on 10 Feb 2010 14:08 On Feb 10, 12:01 am, Transfer Principle <lwal...(a)lausd.net> wrote: > On Feb 9, 8:14 am, FredJeffries <fredjeffr...(a)gmail.com> wrote: > > > On Feb 7, 10:55 pm, Transfer Principle <lwal...(a)lausd.net> wrote: > > > Therefore, _ultra_finitists such as WM and > > > Yessenin-Volpin will now be considered cranks (and that's > > > _without_ the scare quotes, since the label is deserved). > > That you consider Alexander Yessenin-Volpin a crank does not say much > > for your method of classification. > > I believe that Yessenin-Volpin is a "crank" if and only if WM > is a "crank." (For this post, I return to scare quotes until > the "crank"-hood of WM and Y-V is settled.) > ****Sigh**** Of all the nonsenses you've written in this forum, either "deffending" (against what or whom?) people like Tommy or speaking in the name of others about stuff you don't know, this last one must surely be one of the highest peaks of them all: you actually dare to compare in any sense an actual mathematician, and a great logician, thinker, poet and even philosopher, as Essenin-Volpin, with a megacrank like WM...do you have some nerve or what! You better check yourself...with a shrink, preferably. Tonio Ps. Unbelievable...! As you've
From: Virgil on 10 Feb 2010 15:23
In article <779fde9f-45bb-4be1-a012-7bc05e3b1260(a)z19g2000yqk.googlegroups.com>, MoeBlee <jazzmobe(a)hotmail.com> wrote: > On Feb 10, 12:34�am, Virgil <Vir...(a)home.esc> wrote: > > In article > > <a8554fc6-0b17-44e5-88dc-4543a9338...(a)s33g2000prm.googlegroups.com>, > > �"Ross A. Finlayson" <ross.finlay...(a)gmail.com> wrote: > > > > The equivalency function, though, that works in general models of the > > > reals, and variously as I show in the proof machinery of results about > > > uncountability of the reals not similarly to any other function you > > > describe, by proof, still sees that you are selecting a different by > > > the symmetry of the diagonal, with respect to EF's about the other. > > > > �Would you translate that into comprehensible English please. > > Might as well ask a pastrami sandwhich to do the backstroke. > > MoeBlee Conceded. But every once in a while he should be given a chance to show whether he can improve. |