Notes on the Foundations of Mathematics

Note 1

Peircers,

I will have to be off and on the internet for the next month or so,
and won't be able to keep up with the formal activities on the list.
But I have been thinking a lot about the current state of discussion,
along with the several bouts of past discussions on topics related to
Peirce's "Kaina Stoicheia" -- I tend to call it that so as not to get
it confused with the four volumes of 'The New Elements of Mathematics'.

The editors of 'The Essential Peirce' say that "New Elements" was written
"as a preface to an intended book on the foundations of mathematics", but
that much already requires our careful reflection in view of the way that
Peirce makes normative science, logic included, depend on the strife-born
twins of phenomenology and mathematics.  Now, "foundations of mathematics"
is a loose enough term that what the editors say may well be true, in one
sense or another, but that sense is likely to be radically other than the
meaning of thinkers who would reduce mathematics to deductive logic alone.

At any rate, that is a topic for another discussion.

What I'm noticing in my reflections on past and present discussions of
these topics is the evident lack of a common language when it comes to
the foundation of mathematics, in whatever sense we might have in mind.
So I thought it might serve to collect a few notes on the subject from
here and there among the canons and allied commentaries on foundations.

I am going to start with excerpts from the now-classic textbook by
Raymond L. Wilder, 'Introduction to the Foundations of Mathematics'.
This book was my first formal introduction to the subject, used in
the course that Frank Harary taught at U of M back in the 1970s.

Regards,

Jon

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