### by
on

# The Standard of Equality of Numbers

A contribution to the case against Logicism.

The following notes are not intended as a general review of the paper.
It is an analysis of the arguments presented in the paper which may bear upon either the claim that * Mathematics is reducible to logic* or that *Mathematics is Analytic*.

There are, I believe, two main themes in this paper:

- First, the refutation of attempts to
*prove* the existence of infinite collections.
- Second, an exposition of the merits of Frege's derivation of arithmetic from a principle dubbed "Hume's Thesis".

The importance of the first theme lies in its relevance to the claims of logicism.
I don't really understand why Boolos attaches as much importance to the role of "Hume's" thesis as he does.

The gross structure of the paper is as follows:

- A discussion of Dedekind's proof that "there are infinite systems"
- A refutation of the reducibility of arithmetic to second order logic.
- Hume's Principle.

©
created 1994/10/19 modified 1998/01/18