Combining Texts

All the ideas for 'Folk Psychology', 'Structures and Structuralism in Phil of Maths' and 'Fourfold Root of Princ of Sufficient Reason'

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29 ideas

2. Reason / B. Laws of Thought / 2. Sufficient Reason
21918 Sufficient Reason can't be proved, because all proof presupposes it [Schopenhauer, by Lewis,PB]
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]
7. Existence / E. Categories / 1. Categories
21920 No need for a priori categories, since sufficient reason shows the interrelations [Schopenhauer, by Lewis,PB]
8. Modes of Existence / E. Nominalism / 6. Mereological Nominalism
10173 A nominalist might avoid abstract objects by just appealing to mereological sums [Reck/Price]
10. Modality / A. Necessity / 3. Types of Necessity
21362 Necessity is physical, logical, mathematical or moral [Schopenhauer, by Janaway]
11. Knowledge Aims / C. Knowing Reality / 3. Idealism / a. Idealism
21361 For Schopenhauer, material things would not exist without the mind [Schopenhauer, by Janaway]
11. Knowledge Aims / C. Knowing Reality / 3. Idealism / b. Transcendental idealism
21919 Object for a subject and representation are the same thing [Schopenhauer]
14. Science / D. Explanation / 2. Types of Explanation / a. Types of explanation
21917 The four explanations: objects by causes, concepts by ground, maths by spacetime, ethics by motive [Schopenhauer, by Lewis,PB]
18. Thought / A. Modes of Thought / 4. Folk Psychology
7518 If folk psychology gives a network of causal laws, that fits neatly with functionalism [Churchland,PM]
7520 Folk psychology never makes any progress, and is marginalised by modern science [Churchland,PM]
7519 Many mental phenomena are totally unexplained by folk psychology [Churchland,PM]
18. Thought / D. Concepts / 2. Origin of Concepts / b. Empirical concepts
21921 Concepts are abstracted from perceptions [Schopenhauer, by Lewis,PB]
20. Action / C. Motives for Action / 3. Acting on Reason / c. Reasons as causes
21363 Motivation is causality seen from within [Schopenhauer]