[HM] Logicism, Intuitionism, Formalism

Samuel S. Kutler (s-kutler@sjca.edu)
Tue, 12 Jan 1999 10:37:32 -0500 (EST)

Friends:

Long ago I took a course in

The Foundations of Mathematics.

The assigned text was by Raymond L Wilder with a title the same as my
course, published by Wiley in 1952. I own the 2nd edition: 1956. Part II
of Wilder's text is called

DEVELOPMENT OF VARIOUS VIEWPOINTS ON FOUNDATIONS,

and, among other chapters, it contains chapters

IX. The Frege-Russell Thesis: Mathematics as Extension of Logic

X. Intuitionism

XI. Formalism

However, I haven't found that the mathematicians that I meet feel called
upon to decide which thesis to accept. Do most mathematicians--even those
who are concerned with foundations--find themselves alligned with one of
these schools? Have developments since the mid-fifties make it likely that
one of these views will prevail, or are these even the right categories?

Best wishes,

Sam Kutler