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All the ideas for 'Structures and Structuralism in Phil of Maths', 'Internalism Exposed' and 'Maxims and Reflections'

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30 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 / 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]
12. Knowledge Sources / D. Empiricism / 5. Empiricism Critique
7544 Many people imagine that to experience is to understand [Goethe]
13. Knowledge Criteria / A. Justification Problems / 3. Internal or External / a. Pro-internalism
6871 We can't only believe things if we are currently conscious of their justification - there are too many [Goldman]
6872 Internalism must cover Forgotten Evidence, which is no longer retrievable from memory [Goldman]
6874 Internal justification needs both mental stability and time to compute coherence [Goldman]
13. Knowledge Criteria / B. Internal Justification / 5. Coherentism / c. Coherentism critique
6873 Coherent justification seems to require retrieving all our beliefs simultaneously [Goldman]
13. Knowledge Criteria / C. External Justification / 3. Reliabilism / a. Reliable knowledge
6875 Reliability involves truth, and truth is external [Goldman]
13. Knowledge Criteria / E. Relativism / 3. Subjectivism
7541 Man never understands how anthropomorphic he is [Goethe]
16. Persons / C. Self-Awareness / 2. Knowing the Self
7543 We gain self-knowledge through action, not thought - especially when doing our duty [Goethe]
21. Aesthetics / A. Aesthetic Experience / 5. Natural Beauty
7540 Beauty is a manifestation of secret natural laws [Goethe]
22. Metaethics / C. The Good / 2. Happiness / d. Routes to happiness
7538 The happiest people link the beginning and end of life [Goethe]
24. Political Theory / B. Nature of a State / 1. Purpose of a State
7542 The best form of government teaches us to govern ourselves [Goethe]
25. Social Practice / C. Rights / 1. Basis of Rights
7539 To get duties from people without rights, you must pay them well [Goethe]