What Is Philosophy?2. Logic3. Critical Thinking, 1: Intellectual Virtue4. Critical Thinking, 2: Fallacies5. Absolute TruthPart II: Epistemology6. Skepticism About the External World7. Global Skepticism vs. Foundationalism8. Defining “Knowledge”Part III: Metaphysics9. Arguments for Theism10. Arguments for Atheism11. Free Will12. Personal IdentityPart IV: Ethics13. Metaethics14. Ethical Theory, 1: Utilitarianism15. Ethical Theory, 2: Deontology16. Applied Ethics, 1: The Duty of Charity17. Applied Ethics, 2: Animal Ethics18. Concluding ThoughtsAppendix: A Guide to WritingGlossary

    He treats philosophical issues as they arise organically in mathematics, discussing such topics as platonism, realism, logicism, structuralism, formalism, infinity, and intuitionism in mathematical contexts. He organizes the book by mathematical themes--numbers, rigor, geometry, proof, computability, incompleteness, and set theory--that give rise again and again to philosophical considerations.

    Informed by his work on the computational universe of possible programs and on computational language design, Wolfram explains new and existing ideas about combinators with unique clarity and stunning visualizations, as well as provides insights on their historical connections and the curious story of Moses Sch�onfinkel, inventor of combinators. Though invented well before Turing machines, combinators have often been viewed as an inaccessibly abstract approach to computation. This book brings them to life as never before in a thought-provoking and broadly accessible exposition of interest across mathematics and computer science, as well as to those concerned with the foundations of formal and computational thinking, and with the history of ideas"--

    How is this remarkable result proved? This short book explains. It also discusses Gödel's Second Incompleteness Theorem. Based on lecture notes for a course given in Cambridge for many years, the aim is to make the Theorems available, clearly and accessibly, even to those with a quite limited formal background.