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

From: Aatu Koskensilta (aatu.koskensilta_at_xortec.fi)
Date: 01/29/05 

Date: Sat, 29 Jan 2005 22:46:55 +0200

tchow@lsa.umich.edu wrote:

> Or maybe, "Informal mathematical statements are adequately
> expressed by formal sentences"? Help me out here.

There are usually numerous different ways of formalizing a given
informal mathematical statement which are not logically equivalent. So
we must have a qualifying clause saying something like "relative to the
relevant background theory". But what is the relevant background theory?
Something like this springs to mind:

  T is the relevant background theory if all obvious formalizations of
  the informal mathematical statement are equivalent according to T

But this is still a far cry from the Church-Turing thesis when it comes
to usability or level of trust one should place on the thesis. For
example, we should have some notion of what exactly are the obvious
formalizations of a given mathematical statement before the above
determines any theory at all. I for one have no idea how such a notion
could be mathematically defined. 

-- 
Aatu Koskensilta (aatu.koskensilta@xortec.fi)
"Wovon man nicht sprechen kann, daruber muss man schweigen"
  - Ludwig Wittgenstein, Tractatus Logico-Philosophicus