Combining Texts

All the ideas for 'Introduction to the Philosophy of History', 'Introduction to the Philosophy of Mathematics' and 'Guidebook to Wittgenstein's Tractatus'

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36 ideas

1. Philosophy / C. History of Philosophy / 4. Later European Philosophy / d. Nineteenth century philosophy
20109 Hegel inserted society and history between the God-world, man-nature, man-being binary pairs [Hegel, by Safranski]
1. Philosophy / H. Continental Philosophy / 3. Hermeneutics
23449 Interpreting a text is representing it as making sense [Morris,M]
4. Formal Logic / E. Nonclassical Logics / 2. Intuitionist Logic
17926 Rejecting double negation elimination undermines reductio proofs [Colyvan]
17925 Showing a disproof is impossible is not a proof, so don't eliminate double negation [Colyvan]
5. Theory of Logic / D. Assumptions for Logic / 1. Bivalence
23484 Bipolarity adds to Bivalence the capacity for both truth values [Morris,M]
5. Theory of Logic / D. Assumptions for Logic / 2. Excluded Middle
17924 Excluded middle says P or not-P; bivalence says P is either true or false [Colyvan]
5. Theory of Logic / G. Quantification / 1. Quantification
23494 Conjunctive and disjunctive quantifiers are too specific, and are confined to the finite [Morris,M]
5. Theory of Logic / J. Model Theory in Logic / 3. Löwenheim-Skolem Theorems
17929 Löwenheim proved his result for a first-order sentence, and Skolem generalised it [Colyvan]
5. Theory of Logic / K. Features of Logics / 1. Axiomatisation
17930 Axioms are 'categorical' if all of their models are isomorphic [Colyvan]
6. Mathematics / A. Nature of Mathematics / 3. Nature of Numbers / e. Ordinal numbers
17928 Ordinal numbers represent order relations [Colyvan]
6. Mathematics / A. Nature of Mathematics / 4. Using Numbers / c. Counting procedure
23451 Counting needs to distinguish things, and also needs the concept of a successor in a series [Morris,M]
23460 To count, we must distinguish things, and have a series with successors in it [Morris,M]
23452 Discriminating things for counting implies concepts of identity and distinctness [Morris,M]
6. Mathematics / A. Nature of Mathematics / 5. The Infinite / a. The Infinite
17923 Intuitionists only accept a few safe infinities [Colyvan]
6. Mathematics / A. Nature of Mathematics / 5. The Infinite / j. Infinite divisibility
17941 Infinitesimals were sometimes zero, and sometimes close to zero [Colyvan]
6. Mathematics / B. Foundations for Mathematics / 1. Foundations for Mathematics
17922 Reducing real numbers to rationals suggested arithmetic as the foundation of maths [Colyvan]
6. Mathematics / B. Foundations for Mathematics / 4. Axioms for Number / f. Mathematical induction
17936 Transfinite induction moves from all cases, up to the limit ordinal [Colyvan]
6. Mathematics / B. Foundations for Mathematics / 6. Mathematics as Set Theory / a. Mathematics is set theory
17940 Most mathematical proofs are using set theory, but without saying so [Colyvan]
6. Mathematics / B. Foundations for Mathematics / 7. Mathematical Structuralism / a. Structuralism
17931 Structuralism say only 'up to isomorphism' matters because that is all there is to it [Colyvan]
6. Mathematics / B. Foundations for Mathematics / 7. Mathematical Structuralism / e. Structuralism critique
17932 If 'in re' structures relies on the world, does the world contain rich enough structures? [Colyvan]
14. Science / C. Induction / 6. Bayes's Theorem
17943 Probability supports Bayesianism better as degrees of belief than as ratios of frequencies [Colyvan]
14. Science / D. Explanation / 2. Types of Explanation / e. Lawlike explanations
17939 Mathematics can reveal structural similarities in diverse systems [Colyvan]
14. Science / D. Explanation / 2. Types of Explanation / f. Necessity in explanations
17938 Mathematics can show why some surprising events have to occur [Colyvan]
14. Science / D. Explanation / 2. Types of Explanation / m. Explanation by proof
17934 Proof by cases (by 'exhaustion') is said to be unexplanatory [Colyvan]
17933 Reductio proofs do not seem to be very explanatory [Colyvan]
17935 If inductive proofs hold because of the structure of natural numbers, they may explain theorems [Colyvan]
17942 Can a proof that no one understands (of the four-colour theorem) really be a proof? [Colyvan]
15. Nature of Minds / C. Capacities of Minds / 5. Generalisation by mind
17937 Mathematical generalisation is by extending a system, or by abstracting away from it [Colyvan]
19. Language / D. Propositions / 1. Propositions
23491 There must exist a general form of propositions, which are predictabe. It is: such and such is the case [Morris,M]
22. Metaethics / C. The Good / 2. Happiness / a. Nature of happiness
23274 World history has no room for happiness [Hegel]
24. Political Theory / A. Basis of a State / 1. A People / b. The natural life
23275 The state of nature is one of untamed brutality [Hegel]
24. Political Theory / A. Basis of a State / 1. A People / c. A unified people
23276 The soul of the people is an organisation of its members which produces an essential unity [Hegel]
24. Political Theory / D. Ideologies / 6. Liberalism / g. Liberalism critique
23272 The human race matters, and individuals have little importance [Hegel]
24. Political Theory / D. Ideologies / 14. Nationalism
23273 In a good state the goal of the citizens and of the whole state are united [Hegel]
25. Social Practice / A. Freedoms / 5. Freedom of lifestyle
23271 The goal of the world is Spirit's consciousness and enactment of freedom [Hegel]
25. Social Practice / E. Policies / 5. Education / d. Study of history
23270 We should all agree that there is reason in history [Hegel]