[FOM] Information required regarding attribution to Kreisel
hg17 at columbia.edu
Thu Dec 29 11:08:44 EST 2011
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.
The nearest it comes to something that might suggest the idea is
in a footnote (1, page 138):
"Incidentally, it should be noted that Wittgenstein
argues against a notion of a mathematical object (presumably:
substance), but, at least in places (p. 124,35
or p. 96, 71, lines 5 and 4 from below) not against the objectivity
I believe that the idea came to Dummett as he was reading the review,
and the quote is his own formulation. I could not find the dictum in
other review of Wittgenstein, nor in other works that I checked. Dummett's
attribution appears to be the only source for the folklore about the
source of the dictum.
I should add that I have a personal stake in this inquiry. Dummett's
1963 lecture appeared in print in his paper "Realism" published first in
his 1978 collection "Truth and other enigmas". Previous to that I
published in Erkenntnis in 1975 and 1976 two parts of a work entitled
"Ontology and Conceptual Frameworks" which was devoted to an
elaboration of a position based on the dictum. When I wrote the
first part I was unaware of Dummett's 1963 lecture. Putnam called my
attention to Dummett and, following the folklore,to Kreisel and I
mentioned them in the second part.
As far as I know my work was the first in which such a position
appeared in print,
though it might be implicit in Dummett's previous published work.
I can be mistaken, and will be thankful for further information.
I came to this question as I was writing a paper "On Ontology and
Realism in Mathematics", to appear in the Review of Symbolic Logic.
Further philosophical clarifications of the issue will be found
in the introductory section 1.
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