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All the ideas for 'Structures and Structuralism in Phil of Maths', 'Notes on John Wilkins' and 'Introduction of 'Essence of Christianity''

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27 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]
9. Objects / D. Essence of Objects / 14. Knowledge of Essences
12694 Essence is the distinct thinkability of anything [Leibniz]
18. Thought / A. Modes of Thought / 5. Rationality / a. Rationality
19451 When absorbed in deep reflection, is your reason in control, or is it you? [Feuerbach]
22. Metaethics / C. The Good / 1. Goodness / b. Types of good
19450 Reason, love and will are the highest perfections and essence of man - the purpose of his life [Feuerbach]
27. Natural Reality / G. Biology / 5. Species
19448 Consciousness is said to distinguish man from animals - consciousness of his own species [Feuerbach]
28. God / A. Divine Nature / 6. Divine Morality / b. Euthyphro question
19454 A God needs justice, kindness and wisdom, but those concepts don't depend on the concept of God [Feuerbach]
28. God / C. Attitudes to God / 4. God Reflects Humanity
19452 The nature of God is an expression of human nature [Feuerbach]
28. God / C. Attitudes to God / 5. Atheism
19453 If love, goodness and personality are human, the God who is their source is anthropomorphic [Feuerbach]
29. Religion / D. Religious Issues / 1. Religious Commitment / a. Religious Belief
19449 Religion is the consciousness of the infinite [Feuerbach]
19455 Today's atheism will tomorrow become a religion [Feuerbach]