[FOM] Information required regarding attribution to Kreisel

William Tait williamtait at mac.com
Sat Dec 31 11:42:53 EST 2011

On Dec 30, 2011, at 12:28 PM, Richard Heck wrote in reply to my (corrected

>> 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 to 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.
> I suppose one could go on about this for some time, but the inversion to which Bill refers---taking objectivity as fundamental, and characterizing the notion of object in terms of it---is probably the cornerstone of Crispin Wright's book /Frege's Conception of Numbers as Objects/. But the idea is already present in /Frege: Philosophy of Language/, esp. ch. 14, and I would suppose it must have featured in Dummett's lectures before that for some time. (I haven't asked Crispin, but I rather suspect he would acknowledge the roots of the idea in Dummett.) In any event, Dummett's appreciation of the point, and its basis in Frege, is already evident in such papers as "Nominalism", from 1956. But I doubt even that is the origin. Dummett may well have gotten the idea from Geach, who emphasizes it in many of his writings on Frege, e.g., "Frege's Grundlagen", from 1951.
> Rickett's take on this no doubt has unique features.  But, for my money, where he diverges from the tradition just described, he diverges from the truth, as well.

We are really off on a new thread, not having much to do with Haim Gaifman's original request---my fault---and I agree with Richard that FOM may not be the best place to continue it.  But please allow me my last words (promise!) on it:

Perhaps we can at least agree that reference to Frege would have carried more authority than reference to Kreisel (on this point). That was my main point and it is why I think that it is ironic that Dummett, a distinguished Frege scholar, chose to quote (or maybe not quote) Kreisel rather than Frege.

I think Richard is wrong about Dummett's understanding of the context principle. I of course didn't mean that he didn't discuss it; I only said that he didn't fully understand it. Richard refers to Chapter 14 of Dummett's book on Frege's philosophy of language. That chapter has the title "Abstract Objects", but the context principle is about meaning and reference to objects _in general_, and I think that is something that, at that time, Dummett didn't understand. Evidence for that is in his lecture "Platonism", delivered in 1967 and published in _Truth and Other Enigma_, where he writes

"When we scrutinize the doctrines of the arch-Platonist Frege,
the substance of the existential affirmation finally appears to
dissolve. For him mathematical objects are as genuine objects
as the sun and moon: but when we ask what these objects
are, we are told that they are the references of mathematical
terms, and ‘only in the context of a sentence does a name have
a reference.’ In other words, if an expression functions as a
singular term in sentences for which we have provided a clear
sense, i.e. for which we have legitimately stipulated determinate
truth conditions, then that expression is a term (proper name)
and accordingly has a reference: and to know those truth conditions
is to know what its reference is, since ‘we much not ask
after the reference of a name in isolation.’ So, then, to assert
that there are, e.g., natural numbers turns out to be to assert
no more than that we have correctly supplied the sentences of
number theory with determinate truth conditions; and now the
bold thesis that there are abstract objects as good as concrete
ones appears to evaporate to a tame assertion that few would
want to dispute."

I don't count this as understanding the context principle.  Perhaps Wright's book does better: I don't remember. I quoted Rickett's paper in part because the title "From objectivity to objecthood" says it all; but, without endorsing everything in the paper, I strongly disagree with Richard's evaluation of it and see it as the next step, after Dummett's pioneering work, in Frege scholarship. I will repeat, too, that Dummett came to a better understanding of Frege on this point in his book on Frege's philosophy of mathematics. 

An aside: when Dummett wrote about 'abstract objects', he meant to include things like numbers, sets and functions, which have not been abstracted from anything and so are concrete. Maybe we should turn the tide and call them 'ideal objects' instead.

Bill Tait

More information about the FOM mailing list