[FOM] Formalization Thesis

[David Auerbach]

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