Search All of the Math Forum:
Views expressed in these public forums are not endorsed by
Drexel University or The Math Forum.



Re: Matheology § 179
Posted:
Dec 13, 2012 8:03 AM


On 13 Dez., 10:22, Virgil <vir...@ligriv.com> wrote: > In article > <055bfb01cdd04df2a0bb117e2dc52...@gu9g2000vbb.googlegroups.com>, > > > > > > WM <mueck...@rz.fhaugsburg.de> wrote: > > Matheology § 179 > > > The great fascination that contemporary mathematical logic has for its > > devotees is due, in large measure, to the ever increasing > > sophistication of its techniques rather than to any definitive > > contribution to our understanding of the foundations of mathematics. > > Nevertheless, the achievements of logic in recent years are relevant > > to foundational questions and it behooves the logician, at least once > > in a while, to reflect on the basic nature of his subject and perhaps > > even to report his conclusions. In an address given some years ago the > > present writer stated a point of view on the foundations of > > mathematics which may be summed up as follows. (1) Infinite totalities > > do not exist and any purported reference to them is, literally, > > meaningless; (2) this should not prevent us from developing > > mathematics in the classical vein involving the free use of infinitary > > concepts; and (3) although an infinitary framework such as set theory, > > or even only Peano number theory cannot be regarded as the ultimate > > foundation for mathematics, it appears that we have to accept at least > > a rudimentary form of logic and arithmetic as common to all > > mathematical reasoning. > > [A. Robinson: "From a formalist's point of view", Dialectica 23 (1969) > > 4549] > >http://onlinelibrary.wiley.com/doi/10.1111/j.17468361.1969.tb01177.x... > > ? > > Considering Robinson's use of infinity and infinite sets in his > Nonstandard Analysis, one should not take his objections to infinite > sets and infinite totalities very seriously. > > Note points 2 "this should not prevent us from developing mathematics > in the classical vein involving the free use of infinitary concepts" > > So that WM here has cited a obvious proponent of all WM objects to re > "infinitary concepts".
You are in error. I quote and support Robinson's standpoint in all my books. https://portal.dnb.de/opac.htm;jsessionid=206ED1BB2341642E4152416386313FA5.prodworker4?query=Wolfgang+M%C3%BCckenheim&method=simpleSearch
Regards, WM



