[FOM] Richard Epstein's view

[Timothy Y. Chow]

Arnon Avron wrote:

>Even people like Epstein should accept as meaningful and absolute 
>propositions of the sort: "The formal sentence A is/isn't a theorem of 
>the formal system T". I do not see how a view of mathematics (or science 
>in general)  that denies this can be coherent, and in what possible sense 
>can the truth of such a proposition be "only true or false in 
>application".

Here is a possible sense in which the truth of such a proposition might be 
regarded as "only true or false in application."  One might maintain that 
the concept of a "formal sentence" is an abstraction of physically 
concrete marks, and that syntactic rules are an abstraction of physical 
processes for manipulating physically concrete marks.  What is 
straightforwardly true is that (for example) a suitably trained human 
being with normal vision and motor skills will generate certain chalk 
marks on a chalkboard under certain conditions, or that (for example) a 
suitably programmed electronic computer with properly functioning hardware 
will generate certain patterns of pixels on an electronic display under 
certain conditions.  The theoremhood of A is true only insofar as these 
concrete instantiations of its theoremhood are true.

Tim