FOM: Remark on characterization of FOM

Moshe' Machover moshe.machover at
Wed Jan 14 08:46:35 EST 1998

Robert Tragesser proposes the following characterization of FOM

> Seeking a fruitful, central characterization of mathematics
> by answering Sol Feferman's exceedingly important questions:
>        What is distinctive about the verification structure
>  of mathematics?
>        What is distinctive about mathematical conceptions?

The trouble with this, as well as with some of the characterizations
proposed by others, is that they fail to distinguish between FOM and PhOM.
Both share, to a large extent, the same subject matter. Surely, as I
remarked in a previous posting, what distiguishes FOM from PhOM is that the
former approaches this subject matter *in mathematical fashion*. Thus FOM
is a branch of mathematics; in fact, it is perhaps characterizable as the
reflexive branch of mathematics.

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