Tracking Reason: Proof, Consequence, and TruthWhen 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. |
Contents
General Introduction | 3 |
Part I Truth | 7 |
Part II Mathematical Proof | 115 |
Part III Semantics and the Notion of Consequence | 189 |
General Conclusion | 229 |
| 231 | |
| 239 | |
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algorithmic systems anaphorically anaphorically unrestricted apply assumptions AU-quantifiers axioms Azzouni biconditional blind endorsements blind truth-endorsements BTDist can’t chapter characterization claim concepts construal contexts course deflationism device doesn’t domain empirical English epistemic example exist explicit express fact false first-order logic formal grammatical grasp I’ve implication impredicative inconsistent indicated inference introspection intuitive involved isn’t Kripke L1-language liar liar paradoxes logical principles mathe mathematical practice mathematicians mature mathematics meaning metaphysical model theory modus ponens natural languages notion of consequence notion of truth ontic ontic commitments ordinary language ordinary mathematical proof ordinary notion paradoxes philosophers properties propositions quantifiers reason recognize regimentation require role rules semantic ascent sense sentences of L0 sentential set theory sort specific statements subject matter syntactic T-biconditionals tacit Tarski’s Tarskian approach theorem theory of truth things true truth conditions truth deflationist truth idiom truth predicate truth values truthmakers uttered vernacular what’s