Feferman’s virtual book: Logic, Mathematics, and Conceptual Structuralism

In the 2018 collection of articles Feferman on Foundations (about which more in a follow-up post), we learn that shortly before his death Sol Feferman proposed to OUP a sequel to his terrific volume of papers In the Light of Logic. He wanted to collect together some more of his later papers of broader philosophical interest, under the suggested title Logic, Mathematics, and Conceptual Structuralism.

Sadly the proposal seems not to have been taken up. However, but apart from any introduction he might have written, the book does exist in a virtual state, as all the papers are on Feferman’s website. So here is his proposed Table of Contents, linked to the papers which are divided into five groups (hopefully I’ve linked to the right targets!) :

I. My Route

Philosophy of mathematics: 5 questions.

II. The Mathematical Mind

Mathematical intuition vs. mathematical monsters.And so on… Reasoning with infinite diagrams.Gödel’s incompleteness theorems, free will, and mathematical thought.

III. What is Classical Logicality?

Tarski’s conceptual analysis of semantical notions.Logic, logics, and logicism.Set-theoretical invariance criteria for logicality. Which quantifiers are logical? A combined semantical and inferential criterion

IV. Conceptual Structuralism

Logic, mathematics, and conceptual structuralism.Conceptions of the continuum.

V. New Axioms for Mathematics?

Does mathematics need new axioms?Is the Continuum Hypothesis a definite mathematical problem?

Some of these pieces are rightly very well known; others I haven’t come across before — so I’m now really looking forward to reading this virtual book.

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