Founding Mathematics on Semantic Conventions

<div>1. Introduction</div><div>1.1 Overview and Guide to Partial Reading</div><div><br></div><div>2. Classical Mathematics and Plenitudinous Combinatorialism</div><div>2.1 Large Cardinal Axioms and Theorems of Arithmetic</div><div>2.2 Transfinite Ordinals</div><div>2.3 Transfinite Cardinals</div>2.4 The Continuum Hypothesis<div><br></div><div>3 Intuitionism and Choice Sequences</div><div>3.1 General Introduction</div><div>3.2 Brouwer on Freely Proceeding Choice Sequences</div><div>3.3 Constitution of Free Choice Sequences</div><div>3.4 Evaluation of Brouwer’s Claim</div>3.5 Verificationism and Intuitionistic Logic<div><br></div><div>4. From Logicism to Predicativism</div><div>4.1 Frege</div><div>4.2 Russell</div><div>4.3 Weyl</div><div>4.4 Weyl’s Failure to Include All Real Numbers</div><div><br></div><div>5. Conventional Truth</div><div>5.1 The Obvious Solution to the Liar Paradox</div><div>5.2 Conventional Truth Conditions</div><div>5.3 The Dogma</div><div>5.4 Possible Language Conventions</div><div>5.5 T-schemas and Expressive Strength</div><div>5.6 Dialectical Situation</div>5.7 The View from Nowhere<div>5.8 Comparison with Chihara’s Position</div><div>5.9 Revenge</div><div><br></div><div>6. Semantic Conventionalism for Mathematics</div><div>6.1 Needs Assessment</div><div>6.2 Simple Arithmetic as a Conventional Language</div><div>6.3 Quine’s Anti-Conventionalism</div><div>6.4 Rule-Following</div><div>6.5 Choice of Logic</div><div><br></div><div>7. A Convention for a Type-free Language</div><div>7.1 The Kripke Convention and Its Shortcomings</div><div>7.2 Reformulating the Kripke Convention</div><div>7.3 Adding a Conditional with Supervaluational Semantics</div><div>7.4 Denoting Terms for Applied Mathematics</div><div>7.5 Meta-Theorems</div><div><br></div><div>8. Basic Mathematics</div><div>8.1 Logic</div><div>8.2 Natural Numbers</div><div>8.3 Integers</div><div>8.4 Rational Numbers</div><div>8.5 Classicality So Far</div><div>8.6 Classes</div><div>8.7 An Example of Applied Mathematics</div><div><br></div><div>9. Real Analysis</div><div>9.1 Functions</div><div>9.2 Real Numbers</div><div>9.3 Exponentiation</div><div>9.4 Completeness</div><div>9.5 Suprema, Infima, and Roots</div><div>9.6 Continuity</div><div>9.7 Operations on Function</div><div>9.8 Differentiation</div><div>9.9 Integration</div><div>9.10 Unbounded Intervals and Piecewise Continuity</div><div>9.11 Completifications of Functions Generalized</div><div>9.12 Another Example of Applied Mathematics</div><div>9.13 Diagonalization</div><div><br></div><div>10. Possibility</div><div>10.1 All Possible Real Numbers</div><div>10.2 Modal Metaphysics</div><div>10.3 Conclusion</div><div><br></div><div>References</div><div>Index of symbols</div><div>General index</div>