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