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Topic: Matheology § 179
Replies: 4   Last Post: Dec 13, 2012 3:29 PM

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Posts: 18,076
Registered: 1/29/05
Re: Matheology § 179
Posted: Dec 13, 2012 8:03 AM
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On 13 Dez., 10:22, Virgil <> wrote:
> In article
> <>,
>  WM <> 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)
> > 45-49]
> >
> > ?

> 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

Regards, WM

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