Re: Name the thesis: "Formal sentences capture informal ones"

From: Torkel Franzen (torkel_at_sm.luth.se)
Date: 01/30/05 

Date: 30 Jan 2005 16:51:31 +0100

Helene.Boucher@wanadoo.fr writes:

> Presumably you would mean by 'ordinary mathematics'
> something which includes the truth of the successor axiom, so your
> additional phrase answers the question "Why is it trivially true...?"
> in a trivial way (the answer being, "because it's true by the
> definition of 'ordinary' mathematics") or turns the question into one
> of causality instead of grounds ("why has ordinary mathematics come to
> include the successor axiom?").

  It's not an answer at all to the question why it is trivially true.
It is merely the observation that since you put in question trivial
theorems of ordinary mathematics, your regarding Con(PA) as not being
a faithful translation of "PA is consistent" becomes a side issue.

> Except (again!) the faithfulness of the translation was the issue of
> the thread. And the intensional equivalence of two sentences should
> not turn on whether something else is true or not.

  Naturally it turns on whether we take other things to be true. You
yourself referred to an "environment".

Relevant Pages

  • Re: Name the thesis: "Formal sentences capture informal ones"
    ... > something which includes the truth of the successor axiom, ... > of causality instead of grounds ("why has ordinary mathematics come to ... It's not an answer at all to the question why it is trivially true. ...
    (sci.logic)
  • Re: X = Z
    ... travel a path and return to its beginning, a goal of mathematics is ... that have otherwise generally canonical meaning. ... Fashion has nothing to do with truth. ... appear on the subject of 'primes' above and below mine, ...
    (sci.math)
  • Re: Simple Question and the philosophy of infinity
    ... concepts in mathematics correspond to sensual experiences. ... It's quite possible that nature would operate in no way ... and is thus immune to evidence, it must be the case that evidence ... isn't about this Truth. ...
    (sci.electronics.basics)
  • Re: THIS STATEMENT HAS NO PROOF IN ANY SYSTEM = true or false?
    ... Its truth condition is stated as ... analysis of what saying "GC is true" means. ... in science and in mathematics. ... Of course, one can also talk of truth for *uninterpreted formulas*, using ...
    (sci.math)
  • Re: THIS STATEMENT HAS NO PROOF IN ANY SYSTEM = true or false?
    ... Its truth condition is stated as ... analysis of what saying "GC is true" means. ... in science and in mathematics. ... Of course, one can also talk of truth for *uninterpreted formulas*, using ...
    (sci.logic)