[FOM] Information required regarding attribution to Kreisel

William Tait williamtait at mac.com
Fri Dec 30 01:03:31 EST 2011

On Dec 29, 2011, at 10:08 AM, Haim Gaifman wrote:

> I shall be grateful to anyone who can find in Kreisel's works
> the dictum expressed by the following quote that was attributed to
> him  in a 1963 lecture by Dummett:
> "The point is not the existence of mathematical objects, 
> but the objectivity of mathematical truth".
> Dummett refers to Kreisel's review of Wittgenstein. But Kreisel's
> review of "Remarks on the foundations of mathematics" (in the British
> Journal of the Philosophy of Science, 1958) contains no such quote. 
> .........
> Dummett's1963 lecture appeared in print in his paper "Realism" published first in
> his 1978 collection "Truth and other enigmas".

I thought that Kreisel did write the above somewhere, but I can't remember where and so may have a false memory. (What else is new?)  My first thought was  that it is in his paper "Mathematical Logic" in a volume edited by Saaty, but I've looked at the paper and can't find the quoted passage (or anything like it). If I am right, it would be in a paper from the late 1960's or early 1970's. 

Incidentally, Dummett does attribute the above quote to Kreisel in

title =   {The philosophical basis of intuitionistic logic},
   crossref = {LogicColloquium'73},
   pages =   {215--247},

But I don't find the attribution in "Realism".  

There is an irony about Dummett's attribution to Kreisel: the content of the quote could well be regarded as a consequence of Frege's discussion in the introduction and section 60 of his _Foundations of Arithmetic_; I am referring to what is called his 'context principle'. But Dummett, who set the standard of Frege scholarship in the 1960's, didn't really understand this part of Frege at that time. It was Tom Rickett's, with his 1986 paper

  title =   {From objectivity and objecthood: Frege’s 
metaphysics of judgement},
  crossref = {haaparanta-hintikka},
   pages =   {65--96},

who established what seems to be the correct reading of Frege in this respect. (In his book on Frege's philosophy of mathematics  and in

 title =  {The context principle: centre of Frege's philosophy},
    crossref = {max-stelzner}, 
    pages = {3-19},

in the early 1990's, Dummett also seems to have come around to this reading of Frege.)

Bill Tait

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