[FOM] Formalization Thesis
David Auerbach
auerbach at unity.ncsu.edu
Sat Dec 29 10:46:31 EST 2007
On Dec 28, at 1:40 AM, Vaughan Pratt wrote:
> No, but an assessment of the degree of faithfulness of each example
> might help, especially if the examples covered a representative
> range of
> degrees of faithfulness.
It would then be useful to look at the highest degrees of
faithfulness, say,
0''+0''=0'''' (where that designates the relevant sentence of PA)
or, stepping it a notch,
(x) - 0=x' (where that designates the relevant sentence of PA).
It would also be useful to decide on the relata. Are we after a 3-
place relation of proposition, expression, interpreted theory? Or
proposition, expression, interpreted language? (The way I put it above
assumes the former, else I should have written 'the relevant sentence
in the language of arithmetic'). I think it will turn out, in any
case, that 'interpreted' here needs to be something stronger than the
usual model theoretic (or even model theoretically-inspired) notion
simple because an extensional version won't do. The obvious formal
version of 'the even prime plus 2 equals 4' doesn't say what
0''+0''=0'''' does. Not that Carnap didn't know all this...
David Auerbach
Department of Philosophy & Religion
Box 8103
NCSU
Raleigh, NC 27695-8103
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