Combining Texts

All the ideas for 'Mahaprajnaparamitashastra', 'reports' and 'Structures and Structuralism in Phil of Maths'

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28 ideas

1. Philosophy / D. Nature of Philosophy / 2. Invocation to Philosophy
1765 Diogenes said avoidance of philosophy is the lack of a desire to live properly [Diogenes of Sin., by Diog. Laertius]
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 / 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]
8. Modes of Existence / E. Nominalism / 6. Mereological Nominalism
10173 A nominalist might avoid abstract objects by just appealing to mereological sums [Reck/Price]
13. Knowledge Criteria / D. Scepticism / 6. Scepticism Critique
1762 When someone denied motion, Diogenes got up and walked away [Diogenes of Sin., by Diog. Laertius]
20. Action / C. Motives for Action / 3. Acting on Reason / b. Intellectualism
7813 Cynicism was open to anyone, and needed neither education nor sophistication [Diogenes of Sin., by Grayling]
22. Metaethics / A. Ethics Foundations / 2. Source of Ethics / e. Human nature
1763 Diogenes said a plucked chicken fits Plato's definition of man [Diogenes of Sin., by Diog. Laertius]
22. Metaethics / A. Ethics Foundations / 2. Source of Ethics / j. Ethics by convention
5071 The Cynics rejected what is conventional as irrational, and aimed to live by nature [Taylor,R on Diogenes of Sin.]
22. Metaethics / C. The Good / 2. Happiness / d. Routes to happiness
7812 For peace of mind, you need self-government, indifference and independence [Diogenes of Sin.]
23. Ethics / C. Virtue Theory / 3. Virtues / a. Virtues
7903 The six perfections are giving, morality, patience, vigour, meditation, and wisdom [Nagarjuna]
24. Political Theory / B. Nature of a State / 4. Citizenship
1764 Diogenes said he was a citizen of the world [Diogenes of Sin., by Diog. Laertius]
24. Political Theory / D. Ideologies / 2. Anarchism
5968 Diogenes masturbated in public, wishing he could get rid of hunger so easily [Diogenes of Sin., by Plutarch]
25. Social Practice / A. Freedoms / 3. Free speech
1766 Diogenes said that the most excellent thing among men was freedom of speech [Diogenes of Sin., by Diog. Laertius]