FOM: Maths Barbie

[William Tait]

On Monday, March 4, 2002, at 10:42 AM, Neil Tennant wrote:

> On Sat, 2 Mar 2002, Dean Buckner wrote:
>
>> So [Heck] concludes "The notion of one-one correspondence is very
>> sophisticated".  He is implying (i think) that (i) children develop
>> numerical concepts in stages or layers (ii) the order of development 
>> shows
>> which concepts are "logically prior".  So it looks like Hume's 
>> principle is
>> not logically prior to some basic mathematical concepts, and it is 
>> therefore
>> a mistake to base foundational theories upon it.
>
> Are neo-Fregeans forgetting the words of their master?:
>
>> "[w]hat comes first in the logical and objective order
>> is not what comes first in the psychological and
>> historical order" ?
>
> This GOTTLOB FREGE, in his essay "On the law of inertia", originally
> published as "Ueber das Traegheitsgesetz" in 1891 in Zeitschrift fuer
> Philosophie und philosophische Kritik. You can find it in the Frege 
> volume
> known as the Kleine Schriften. The English translation of this essay is 
> by
> Hans Kaal, and is in the "Englished" volume of the KS edited by Brian
> McGuiness.

I made this complaint to Richard Heck when he spoke about this at Notre 
Dame last spring---but I quoted (or paraphrased) Aristotle Post. Analy. 
71b34 instead ``Things are prior...in two ways; for it is not the same 
to be prior by nature and prior in relation to us...'' It is, to me, not 
surprising that Frege failed to cite Aristotle; but it is a little 
surprising that Richard made no adjustment in his write-up of his talk. 
For, even if Aristotle or Frege had not written it, it is nevertheless 
true.

Bill Tait