The Conceptual Roots of Mathematics is a comprehensive study of the foundation of mathematics. J.R. Lucas, one of the most distinguished Oxford scholars, covers a vast amount of ground in the philosophy of mathematics, showing us that it is actually at the heart of the study of epistemology and metaphysics.

chapter 1|32 pages

Plato’s Philosophies of Mathematics

chapter 2|35 pages


chapter 3|22 pages


chapter 4|24 pages

Numbers: The Cardinal Approach

chapter 5|12 pages

Numbers: The Ordinal Approach

chapter 6|31 pages

Numbers: The Abstract Approach

chapter 7|42 pages

The Infinite

chapter 8|25 pages

The Implications of Gödel’s Theorem

chapter 9|47 pages

Transitive Relations

chapter 10|20 pages


chapter 11|20 pages

Magnitude and Measure

chapter 12|29 pages

Down With Set Theory

chapter 13|23 pages

Chastened Logicism?

chapter 14|36 pages

Mathematical Knowledge

chapter 15|34 pages

Realism Revisited