[hist-analytic] The Two Color Problem, Putnam, and the Synthetic A Priori

Roger Bishop Jones rbj at rbjones.com
Wed Nov 4 17:48:30 EST 2009


On Wednesday 04 November 2009 19:48:45 Bruce Aune wrote:
> I am surprised by Roger's objection.  There is nothing wrong with my
> definition of "x the determinate color of x at t = A." Roger says I
> first have to give a definition for "x has A at t," but this doesn't
> need defining; it just means that the individual x has the property A
> at a time t.

I agree that it need not be defined.

> Roger's other
> objection--that prior to giving the definition I gave we need to know
> (P) that whenever x has A at t and B at t, A = B--overlooks the fact
> that P does not follow from my definition, which is merely a
> terminological convenience.

I did not allege that P follows from your "definition".
I claim that it is a necessary condition for the property you cite to be a 
definition of a function.

It is easy to derive a contradiction if arbitrary formulae are admitted as 
definitions. (define f x = y iff y is a number, then prove 0=1).

> (P) is really a consequence of the principle DD.

It does not seem to me to be obvious that this is the case.

Can you prove it?

Roger




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