[FOM] What is a proof?

[A. Mani]

On Friday 23 Jan 2009 17:50:20 Ron Rood wrote:
> I find it hard to say whether Hilbert believed that axioms are
> known and in what sense. I do recall a paper from Bernays where he
> says that Hilbert held that knowledge is something that applies to a
> system of propositions and is not, or not primarily, a "propositional
> attitude". I am not sure whether Hilbert accepted the view that a
> proof in mathematics is a logical deduction.
>

Yes he did believe apparently. But his calculus was not a very refined one 
(esp before 1920). One reference is Zach's paper BSL 1999 (vol 5, No 3). It 
says a lot more about Bernay's contribution.

 "All these difficulties aside, the main point is still notable. Here, in 
1905, one of Hilbert's aims in the foundations of mathematics is made almost
explicit, namely the aim to provide decision procedures for logic on the one
hand, and particular systems of mathematics and science, e.g., arithmetic,
on the other."
  
Best

A. Mani


-- 
A. Mani
Member, Cal. Math. Soc