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All the ideas for 'Structures and Structuralism in Phil of Maths', 'works' and 'talk'

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39 ideas

3. Truth / F. Semantic Truth / 2. Semantic Truth
10170 While true-in-a-model seems relative, true-in-all-models seems not to be [Reck/Price]
4. Formal Logic / F. Set Theory ST / 4. Axioms for Sets / a. Axioms for sets
10166 ZFC set theory has only 'pure' sets, without 'urelements' [Reck/Price]
5. Theory of Logic / E. Structures of Logic / 5. Functions in Logic
15105 F(x) walked into a bar. The barman said.. [Sommers,W]
5. Theory of Logic / G. Quantification / 5. Second-Order Quantification
10175 Three types of variable in second-order logic, for objects, functions, and predicates/sets [Reck/Price]
6. Mathematics / A. Nature of Mathematics / 3. Nature of Numbers / g. Real numbers
10165 'Analysis' is the theory of the real numbers [Reck/Price]
6. Mathematics / B. Foundations for Mathematics / 4. Axioms for Number / a. Axioms for numbers
10174 Mereological arithmetic needs infinite objects, and function definitions [Reck/Price]
6. Mathematics / B. Foundations for Mathematics / 4. Axioms for Number / e. Peano arithmetic 2nd-order
10164 Peano Arithmetic can have three second-order axioms, plus '1' and 'successor' [Reck/Price]
6. Mathematics / B. Foundations for Mathematics / 6. Mathematics as Set Theory / a. Mathematics is set theory
10172 Set-theory gives a unified and an explicit basis for mathematics [Reck/Price]
6. Mathematics / B. Foundations for Mathematics / 7. Mathematical Structuralism / a. Structuralism
10167 Structuralism emerged from abstract algebra, axioms, and set theory and its structures [Reck/Price]
6. Mathematics / B. Foundations for Mathematics / 7. Mathematical Structuralism / b. Varieties of structuralism
10169 Relativist Structuralism just stipulates one successful model as its arithmetic [Reck/Price]
10179 There are 'particular' structures, and 'universal' structures (what the former have in common) [Reck/Price]
10181 Pattern Structuralism studies what isomorphic arithmetic models have in common [Reck/Price]
10182 There are Formalist, Relativist, Universalist and Pattern structuralism [Reck/Price]
6. Mathematics / B. Foundations for Mathematics / 7. Mathematical Structuralism / c. Nominalist structuralism
10168 Formalist Structuralism says the ontology is vacuous, or formal, or inference relations [Reck/Price]
10178 Maybe we should talk of an infinity of 'possible' objects, to avoid arithmetic being vacuous [Reck/Price]
6. Mathematics / B. Foundations for Mathematics / 7. Mathematical Structuralism / d. Platonist structuralism
10176 Universalist Structuralism is based on generalised if-then claims, not one particular model [Reck/Price]
10177 Universalist Structuralism eliminates the base element, as a variable, which is then quantified out [Reck/Price]
6. Mathematics / B. Foundations for Mathematics / 7. Mathematical Structuralism / e. Structuralism critique
10171 The existence of an infinite set is assumed by Relativist Structuralism [Reck/Price]
7. Existence / A. Nature of Existence / 3. Being / d. Non-being
12408 Sartre to Waitress: Coffee with no cream, please... [Sommers,W]
7. Existence / D. Theories of Reality / 4. Anti-realism
12397 Said Plato: 'The things that we feel... [Sommers,W]
8. Modes of Existence / E. Nominalism / 6. Mereological Nominalism
10173 A nominalist might avoid abstract objects by just appealing to mereological sums [Reck/Price]
11. Knowledge Aims / B. Certain Knowledge / 5. Cogito Critique
12407 Barman to Descartes: Would you like another drink?... [Sommers,W]
12399 There was a young student called Fred... [Sommers,W]
11. Knowledge Aims / C. Knowing Reality / 2. Phenomenalism
20963 A philosopher and his wife are out for a drive... [Sommers,W]
11. Knowledge Aims / C. Knowing Reality / 3. Idealism / c. Empirical idealism
12404 Dear Sir, Your astonishment's odd.... [Sommers,W]
12403 There once was a man who said: 'God... [Sommers,W]
12402 ..But if he's a student of Berkeley... [Sommers,W]
12409 The philosopher Berkeley once said.. [Sommers,W]
12. Knowledge Sources / B. Perception / 1. Perception
14694 "My dog's got synaesthesia." How does he smell? ..... [Sommers,W]
13. Knowledge Criteria / D. Scepticism / 1. Scepticism
12401 A toper who spies in the distance... [Sommers,W]
16. Persons / F. Free Will / 6. Determinism / a. Determinism
12410 There once was a man who said 'Damn!... [Sommers,W]
17. Mind and Body / B. Behaviourism / 4. Behaviourism Critique
9392 How do behaviourists greet each other? [Sommers,W]
22. Metaethics / A. Ethics Foundations / 2. Source of Ethics / c. Ethical intuitionism
7258 The forefather of modern intuitionism is Richard Price [Price,R, by Dancy,J]
24. Political Theory / C. Ruling a State / 2. Leaders / d. Elites
12405 'If you're aristocratic,' said Nietzsche... [Sommers,W]
24. Political Theory / D. Ideologies / 2. Anarchism
9391 Why do anarchists drink herbal tea? [Sommers,W]
26. Natural Theory / C. Causation / 9. General Causation / a. Constant conjunction
12400 Cries the maid: 'You must marry me Hume!'... [Sommers,W]
16527 Causation - we all thought we knew it/ Till Hume came along and saw through it/…. [Sommers,W]
27. Natural Reality / D. Time / 1. Nature of Time / c. Idealist time
17592 The barman called 'Time!', and Augustine said..... [Sommers,W]
27. Natural Reality / D. Time / 2. Passage of Time / c. Tenses and time
15208 The past, present and future walked into a bar.... [Sommers,W]