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All the ideas for 'poems', 'Naturalism in Mathematics' and 'Semantic Necessity'

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33 ideas

4. Formal Logic / F. Set Theory ST / 2. Mechanics of Set Theory / b. Terminology of ST
18194 'Forcing' can produce new models of ZFC from old models [Maddy]
4. Formal Logic / F. Set Theory ST / 4. Axioms for Sets / a. Axioms for sets
18195 A Large Cardinal Axiom would assert ever-increasing stages in the hierarchy [Maddy]
4. Formal Logic / F. Set Theory ST / 4. Axioms for Sets / f. Axiom of Infinity V
18191 Axiom of Infinity: completed infinite collections can be treated mathematically [Maddy]
4. Formal Logic / F. Set Theory ST / 4. Axioms for Sets / i. Axiom of Foundation VIII
18193 The Axiom of Foundation says every set exists at a level in the set hierarchy [Maddy]
4. Formal Logic / F. Set Theory ST / 4. Axioms for Sets / p. Axiom of Reducibility
18169 Axiom of Reducibility: propositional functions are extensionally predicative [Maddy]
5. Theory of Logic / E. Structures of Logic / 1. Logical Form
18168 'Propositional functions' are propositions with a variable as subject or predicate [Maddy]
5. Theory of Logic / E. Structures of Logic / 8. Theories in Logic
14620 Theories in logic are sentences closed under consequence, but in truth discussions theories have axioms [Fine,K]
6. Mathematics / A. Nature of Mathematics / 5. The Infinite / d. Actual infinite
18171 Cantor and Dedekind brought completed infinities into mathematics [Maddy]
18190 Completed infinities resulted from giving foundations to calculus [Maddy]
6. Mathematics / A. Nature of Mathematics / 5. The Infinite / i. Cardinal infinity
18175 For any cardinal there is always a larger one (so there is no set of all sets) [Maddy]
18196 An 'inaccessible' cardinal cannot be reached by union sets or power sets [Maddy]
18172 Infinity has degrees, and large cardinals are the heart of set theory [Maddy]
6. Mathematics / A. Nature of Mathematics / 5. The Infinite / l. Limits
18187 Theorems about limits could only be proved once the real numbers were understood [Maddy]
6. Mathematics / B. Foundations for Mathematics / 5. Definitions of Number / c. Fregean numbers
18182 The extension of concepts is not important to me [Maddy]
18177 In the ZFC hierarchy it is impossible to form Frege's set of all three-element sets [Maddy]
6. Mathematics / B. Foundations for Mathematics / 5. Definitions of Number / e. Caesar problem
18164 Frege solves the Caesar problem by explicitly defining each number [Maddy]
6. Mathematics / B. Foundations for Mathematics / 6. Mathematics as Set Theory / a. Mathematics is set theory
18163 Mathematics rests on the logic of proofs, and on the set theoretic axioms [Maddy]
18185 Unified set theory gives a final court of appeal for mathematics [Maddy]
18183 Set theory brings mathematics into one arena, where interrelations become clearer [Maddy]
18186 Identifying geometric points with real numbers revealed the power of set theory [Maddy]
18184 Making set theory foundational to mathematics leads to very fruitful axioms [Maddy]
18188 The line of rationals has gaps, but set theory provided an ordered continuum [Maddy]
6. Mathematics / C. Sources of Mathematics / 4. Mathematical Empiricism / b. Indispensability of mathematics
18207 Maybe applications of continuum mathematics are all idealisations [Maddy]
18204 Scientists posit as few entities as possible, but set theorist posit as many as possible [Maddy]
6. Mathematics / C. Sources of Mathematics / 6. Logicism / c. Neo-logicism
18167 We can get arithmetic directly from HP; Law V was used to get HP from the definition of number [Maddy]
7. Existence / D. Theories of Reality / 11. Ontological Commitment / e. Ontological commitment problems
18205 The theoretical indispensability of atoms did not at first convince scientists that they were real [Maddy]
10. Modality / C. Sources of Modality / 1. Sources of Necessity
14530 The role of semantic necessity in semantics is like metaphysical necessity in metaphysics [Fine,K, by Hale/Hoffmann,A]
15. Nature of Minds / C. Capacities of Minds / 6. Idealisation
18206 Science idealises the earth's surface, the oceans, continuities, and liquids [Maddy]
19. Language / C. Assigning Meanings / 2. Semantics
14618 Semantics is either an assignment of semantic values, or a theory of truth [Fine,K]
14621 Semantics is a body of semantic requirements, not semantic truths or assigned values [Fine,K]
19. Language / C. Assigning Meanings / 7. Extensional Semantics
14622 Referential semantics (unlike Fregeanism) allows objects themselves in to semantic requirements [Fine,K]
19. Language / E. Analyticity / 4. Analytic/Synthetic Critique
14619 The Quinean doubt: are semantics and facts separate, and do analytic sentences have no factual part? [Fine,K]
22. Metaethics / A. Ethics Foundations / 2. Source of Ethics / j. Ethics by convention
6017 Nomos is king [Pindar]