[FOM] sad news

Kreinovich, Vladik vladik at utep.edu
Wed Mar 16 13:54:27 EDT 2016


Alexander Esenin-Volpin, one of the passionate promoters of ultrafinitist approach to foundations of mathematics, died today

Here is from the Wikipedia article:

Most of his later work was on the foundations of mathematics, where he introduced ultrafinitism<https://en.wikipedia.org/wiki/Ultrafinitism>, an extreme form of constructive mathematics that casts doubt on the existence of not only infinite sets, but even of large integers such as 1012. He sketched a program for proving the consistency of Zermelo-Fraenkel set theory<https://en.wikipedia.org/wiki/Zermelo%E2%80%93Fraenkel_set_theory> using ultrafinitistic techniques in (Ésénine-Volpine 1961<https://en.wikipedia.org/wiki/Alexander_Esenin-Volpin#CITEREF.C3.89s.C3.A9nine-Volpine1961>), (Yessenin-Volpin 1970<https://en.wikipedia.org/wiki/Alexander_Esenin-Volpin#CITEREFYessenin-Volpin1970>) and (Yessenin-Volpin 1981<https://en.wikipedia.org/wiki/Alexander_Esenin-Volpin#CITEREFYessenin-Volpin1981>).

Mathematical publications
Ésénine-Volpine, A. S. (1961), "Le programme ultra-intuitionniste des fondements des mathématiques", Infinitistic Methods (Proc. Sympos. Foundations of Math., Warsaw, 1959), Oxford: Pergamon, pp. 201-223, MR<https://en.wikipedia.org/wiki/Mathematical_Reviews> 0147389<https://www.ams.org/mathscinet-getitem?mr=0147389>  Reviewed by Kreisel, G.; Ehrenfeucht, A. (1967), "Le Programme Ultra-Intuitionniste des Fondements des Mathematiques by A. S. Ésénine-Volpine", The Journal of Symbolic Logic (Association for Symbolic Logic) 32 (4): 517, doi<https://en.wikipedia.org/wiki/Digital_object_identifier>:10.2307/2270182<https://dx.doi.org/10.2307%2F2270182>, JSTOR<https://en.wikipedia.org/wiki/JSTOR> 2270182<https://www.jstor.org/stable/2270182>

  *   Yessenin-Volpin, A. S. (1970), "The ultra-intuitionistic criticism and the antitraditional program for foundations of mathematics", in Kino, A.; Myhill, J.; Vesley, R. E., Intuitionism and proof theory (Proc. Conf., Buffalo, N.Y., 1968), Studies in Logic and the Foundations of Mathematics, Amsterdam: North-Holland, pp. 3-45, MR<https://en.wikipedia.org/wiki/Mathematical_Reviews> 0295876<https://www.ams.org/mathscinet-getitem?mr=0295876>  Reviewed by Geiser, James R. (1975), "The Ultra-Intuitionistic Criticism and the Antitraditional Program for Foundations of Mathematics. by A. S. Yessenin-Volpin", The Journal of Symbolic Logic (Association for Symbolic Logic) 40 (1): 95-97, doi<https://en.wikipedia.org/wiki/Digital_object_identifier>:10.2307/2272294<https://dx.doi.org/10.2307%2F2272294>, JSTOR<https://en.wikipedia.org/wiki/JSTOR> 2272294<https://www.jstor.org/stable/2272294>
  *   Yessenin-Volpin, A. S. (1981), "About infinity, finiteness and finitization (in connection with the foundations of mathematics)", in Richman, Fred, Constructive mathematics (Las Cruces, N.M., 1980), Lecture Notes in Math. 873, Berlin-New York: Springer, pp. 274-313, doi<https://en.wikipedia.org/wiki/Digital_object_identifier>:10.1007/BFb0090740<https://dx.doi.org/10.1007%2FBFb0090740>, ISBN<https://en.wikipedia.org/wiki/International_Standard_Book_Number> 3-540-10850-5<https://en.wikipedia.org/wiki/Special:BookSources/3-540-10850-5>, MR<https://en.wikipedia.org/wiki/Mathematical_Reviews> 0644507<https://www.ams.org/mathscinet-getitem?mr=0644507>
I have seen some ultrafinitists go so far as to challenge the existence of 2100 as a natural number, in the sense of there being a series of "points" of that length. There is the obvious "draw the line" objection, asking where in 21, 22, 23, ... , 2100 do we stop having "Platonistic reality"? Here this ... is totally innocent, in that it can be easily be replaced by 100 items (names) separated by commas. I raised just this objection with the (extreme) ultrafinitist Yessenin-Volpin during a lecture of his. He asked me to be more specific. I then proceeded to start with 21 and asked him whether this is "real" or something to that effect. He virtually immediately said yes. Then I asked about 22, and he again said yes, but with a perceptible delay. Then 23, and yes, but with more delay. This continued for a couple of more times, till it was obvious how he was handling this objection. Sure, he was prepared to always answer yes, but he was going to take 2100 times as long to answer yes to 2100 then he would to answering 21. There is no way that I could get very far with this.
Harvey M. Friedman "Philosophical Problems in Logic"
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