Video Lectures
A curated collection of 16 video lectures on logic, the philosophy of mathematics, and the foundations of scientific reasoning — featuring Ray Monk, Michael Dummett, A. J. Ayer, Bryan Magee, Graham Priest, Ernest Nagel, W. V. Quine, and more.
1. Intro to the Philosophy of Mathematics (Ray Monk)
Ray Monk introduces the central questions of the philosophy of mathematics — the nature of mathematical truth, the existence of mathematical objects, and the relationship between mathematics and the physical world.
2. Logic: The Structure of Reason
An exploration of the foundations of logic — from syllogistic reasoning to modern formal systems. How does logical structure underpin scientific and mathematical reasoning?
3. What Is Probability? Difficulties Understanding Probability
A deep dive into the conceptual puzzles of probability — frequentist vs. Bayesian interpretations, the problem of induction, and how probability relates to scientific confirmation.
4. What Are Numbers? Philosophy of Mathematics
What kind of entities are numbers? Do they exist independently of human minds (Platonism), or are they human constructions (nominalism)? This lecture explores the ontological status of mathematical objects.
5. The History of Logic: The Logic of Aristotle
An examination of Aristotle's syllogistic logic — the first formal system of deductive reasoning and its lasting influence on the philosophy of science and methodology.
6. Philosophy of Mathematics & Frege — Michael Dummett (1994)
Michael Dummett discusses Frege's logicist program — the attempt to reduce mathematics to logic — and its philosophical implications for our understanding of truth, meaning, and objectivity.
7. A History of the Infinite
From Zeno's paradoxes to Cantor's transfinite numbers — how the concept of infinity has challenged and shaped philosophy, mathematics, and science across millennia.
8. Frege, Russell, & Modern Logic — A. J. Ayer & Bryan Magee (1987)
A. J. Ayer and Bryan Magee discuss the revolution in logic initiated by Frege and Russell, the foundations of analytic philosophy, and its impact on the philosophy of science.
9. Zeno, Infinite Divisibility, & Indivisibility
Zeno's paradoxes of motion and infinite divisibility — fundamental challenges to our understanding of space, time, and continuity that remain relevant to the philosophy of physics.
10. Revising Logic — Graham Priest
Graham Priest argues for the revision of classical logic — exploring paraconsistent logic, dialetheism, and the philosophical consequences of accepting true contradictions.
11. Ernest Nagel on Computers, Logic, & Mind (1962)
Ernest Nagel — one of the 20th century's foremost philosophers of science — discusses the relationship between formal logic, computation, and the nature of mind.
12. An Infinite Past — Richard Sorabji (2003)
Richard Sorabji examines the philosophical arguments for and against an infinite past — from Aristotle and the Kalam cosmological argument to modern cosmology.
13. W. V. Quine on Necessary Truth (1963)
Quine challenges the analytic-synthetic distinction and the notion of necessary truth — a foundational critique that reshaped 20th-century philosophy of science and epistemology.
14. Central Problem in the Philosophy of Mathematics
Bryan Magee identifies the central problem: How can mathematics, which appears to be a purely abstract discipline, be so extraordinarily useful in describing the physical world?
15. How Does It Fit the World?
The puzzle of mathematical applicability — why does abstract mathematics 'fit' physical reality? Eugene Wigner called this the 'unreasonable effectiveness of mathematics.'
16. Philosophy of Science — Supplementary Lecture
An additional lecture on key topics in the philosophy of science — scientific methodology, theory choice, and the demarcation between science and non-science.
About This Collection
These lectures span the philosophy of mathematics and logic — disciplines intimately connected to the philosophy of science. Understanding the nature of mathematical truth, logical reasoning, and probability is essential for grasping debates about scientific method, confirmation theory, and the structure of scientific theories.
Videos sourced from the Logic & Philosophy of Mathematics playlist. All content is publicly available on YouTube.