[FOM] Formalization Thesis

[Ron Rood]

It strikes me as if the discussion on FT primarily concentrates on 
faithful reconstructions of mathematical theorems into sentences of 
some formal system. However, mathematical knowledge is based on axioms, 
definitions and proofs. I would asume that these need to be addressed 
in some formulation of FT as well.

1. How should we understand the concept of a faithful reconstruction of 
a mathematical proof? This question seems to presuppose that we know 
quite well what a mathematical proof is. But do we?

2. How should we understand the concept of a faithful reconstruction as 
applied to axioms? Note that in modern mathematics, axioms typically 
serve to provide an implicit definition of a collection of models. 
Should these models somehow be incorporated in our formulation of FT? 
If so, how?

3. Other types of definitions used in mathematics are, for example, 
stipulative definitions and constructive definitions (I mean, 
definitions defining an object by describing a construction of that 
object). Should a formulation of FT somehow take these various types of 
definitions into account? How?


Ron