Tracking Reason Proof, Consequence, and Truth

When ordinary people - mathematicians among them - take something to follow (deductively) from something else, they are exposing the backbone of our self-ascribed ability to reason. Jody Azzouni investigates the connection between that ordinary notion of consequence and the formal analogues invented by logicians. One claim of the book is that, despite our apparent intuitive grasp of consequence, we do not introspect rules by which we reason, nor do we grasp the scope and range of the domain, as it were, of our reasoning. This point is illustrated with a close analysis of a paradigmatic case of ordinary reasoning: mathematical proof.

General Introduction. Part I. Truth. 1. Truth and Truth Conditions. 2. The Transcendence of Truth. 3. Anaphorically Unrestricted Quantifiers. 4. Regimentation and Paradox. 5. The Inconsistency of Natural Languages. Conclusion to Part I. Part II. Mathematical Proof. 6. The Uniqueness of Mathematics as a Social Practice. 7. The Derivation-Indicator View of Mathematical Practice. 8. How to Nominalize Formalism. Conclusion to Part II. Part III. Semantics an the Notion of Consequence. Introduction to Part II. 9. Semantics and the Notion of Consequence. Conclusion to Part III. General Conclusion. Bibliography. Index.