Introduction to Mathematical Philosophy

This work offers a clear‑headed tour of the foundations of mathematics aimed at listeners with little or no background in formal logic. Rather than overwhelming the audience with symbolic notation, it explains the essential ideas behind concepts such as number, infinity, and continuity in plain language. The author stresses the method of logical analysis, showing how it reshapes traditional philosophical questions.

The chapters begin with the familiar natural numbers, then move through the definition of order, the nature of relations, and the construction of rational, real and complex numbers. Later sections explore infinite cardinalities, series, limits, the axiom of infinity, and the hierarchy of logical types that guard against paradox. By the end the listener will have a solid grasp of how modern mathematical logic informs both the practice of mathematics and the broader philosophical discourse.