Combining Texts

All the ideas for 'Structures and Structuralism in Phil of Maths', 'Model Theory for Modal Logic I' and 'The Elements of Law'

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28 ideas

1. Philosophy / C. History of Philosophy / 4. Later European Philosophy / b. Seventeenth century philosophy
7396 Hobbes created English-language philosophy [Hobbes, by Tuck]
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 / D. Modal Logic ML / 3. Modal Logic Systems / h. System S5
9560 S5 provides the correct logic for necessity in the broadly logical sense [Fine,K]
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 / B. Perception / 4. Sense Data / a. Sense-data theory
16638 The qualities of the world are mere appearances; reality is the motions which cause them [Hobbes]
12. Knowledge Sources / D. Empiricism / 1. Empiricism
7405 Experience can't prove universal truths [Hobbes]
16688 Evidence is conception, which is imagination, which proceeds from the senses [Hobbes]
20. Action / C. Motives for Action / 1. Acting on Desires
7408 It is an error that reason should control the passions, which give right guidance on their own [Hobbes, by Tuck]
22. Metaethics / A. Ethics Foundations / 1. Nature of Ethics / d. Ethical theory
7407 Good and evil are what please us; goodness and badness the powers causing them [Hobbes]
22. Metaethics / A. Ethics Foundations / 2. Source of Ethics / j. Ethics by convention
7410 Self-preservation is basic, and people judge differently about that, implying ethical relativism [Hobbes, by Tuck]
22. Metaethics / C. The Good / 1. Goodness / c. Right and good
7409 Hobbes shifted from talk of 'the good' to talk of 'rights' [Hobbes, by Tuck]
28. God / C. Attitudes to God / 4. God Reflects Humanity
7411 The attributes of God just show our inability to conceive his nature [Hobbes]