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

From: Mitch Harris (harrisq_at_tcs.inf.tu-dresden.de)
Date: 01/31/05 

Date: Mon, 31 Jan 2005 11:14:18 +0100

Torkel Franzen wrote:
> tchow@lsa.umich.edu writes:
>
>>The Church-Turing thesis is familiar to many people, largely because it
>>has been widely discussed both in textbooks and in popular science writing.
>>Having a name helps, too.
>>
>>There is an analogous thesis that is relevant to logic and the foundations
>>of mathematics:
>>
>> (*) Formal sentences (in PA or ZFC for example) adequately express
>> their informal counterparts.
>
> (*) is rather too imprecise to be given a catchy name.

Yes, but I think that's the kind of discussion Tim is looking for, to
help make it more precise, if possible. I think the statement has
difficulties not with precision (or possible precision) but about
self-reference. If it is to be made more precise, then the concept
"informal sentence" must be made more precise.

> What is the
> informal counterpart of a formal sentence in PA or ZFC?

It sounds to me like Tim's direction is from the informal to the
formal, though at some point your question needs to be addressed, too.

As someone else mentioned, is the informal counterpart of a formal
sentence just its expression in natural language? 

-- 
Mitch Harris
(remove q to reply)

Relevant Pages

  • Re: Name the thesis: "Formal sentences capture informal ones"
    ... >>has been widely discussed both in textbooks and in popular science writing. ... >>There is an analogous thesis that is relevant to logic and the foundations ... is the informal counterpart of a formal ...
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  • Re: Name the thesis: "Formal sentences capture informal ones"
    ... > has been widely discussed both in textbooks and in popular science writing. ... > There is an analogous thesis that is relevant to logic and the foundations ... informal counterpart of a formal sentence in PA or ZFC? ...
    (comp.theory)
  • Re: Name the thesis: "Formal sentences capture informal ones"
    ... > has been widely discussed both in textbooks and in popular science writing. ... > There is an analogous thesis that is relevant to logic and the foundations ... informal counterpart of a formal sentence in PA or ZFC? ...
    (sci.logic)
  • Re: Name the thesis: "Formal sentences capture informal ones"
    ... > There is an analogous thesis that is relevant to logic and the foundations ... What is the informal counterpart of a randomly chosen formal ... in the language of arithmetic or in the language of set ... Every informal mathematical statement can be given a faithful ...
    (comp.theory)
  • Re: Name the thesis: "Formal sentences capture informal ones"
    ... > There is an analogous thesis that is relevant to logic and the foundations ... What is the informal counterpart of a randomly chosen formal ... in the language of arithmetic or in the language of set ... Every informal mathematical statement can be given a faithful ...
    (sci.logic)