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All the ideas for 'Thinking About Mathematics', 'works' and 'Prisoner's Dilemma'

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23 ideas

5. Theory of Logic / D. Assumptions for Logic / 2. Excluded Middle
8729 Intuitionists deny excluded middle, because it is committed to transcendent truth or objects [Shapiro]
6. Mathematics / A. Nature of Mathematics / 3. Nature of Numbers / b. Types of number
8763 The number 3 is presumably identical as a natural, an integer, a rational, a real, and complex [Shapiro]
6. Mathematics / A. Nature of Mathematics / 3. Nature of Numbers / h. Reals from Cauchy
18249 Cauchy gave a formal definition of a converging sequence. [Shapiro]
6. Mathematics / B. Foundations for Mathematics / 1. Foundations for Mathematics
8764 Categories are the best foundation for mathematics [Shapiro]
6. Mathematics / B. Foundations for Mathematics / 5. Definitions of Number / f. Zermelo numbers
8762 Two definitions of 3 in terms of sets disagree over whether 1 is a member of 3 [Shapiro]
6. Mathematics / B. Foundations for Mathematics / 7. Mathematical Structuralism / a. Structuralism
8760 Numbers do not exist independently; the essence of a number is its relations to other numbers [Shapiro]
8761 A 'system' is related objects; a 'pattern' or 'structure' abstracts the pure relations from them [Shapiro]
6. Mathematics / C. Sources of Mathematics / 6. Logicism / d. Logicism critique
8744 Logicism seems to be a non-starter if (as is widely held) logic has no ontology of its own [Shapiro]
6. Mathematics / C. Sources of Mathematics / 7. Formalism
8749 Term Formalism says mathematics is just about symbols - but real numbers have no names [Shapiro]
8750 Game Formalism is just a matter of rules, like chess - but then why is it useful in science? [Shapiro]
8752 Deductivism says mathematics is logical consequences of uninterpreted axioms [Shapiro]
6. Mathematics / C. Sources of Mathematics / 10. Constructivism / b. Intuitionism
8753 Critics resent the way intuitionism cripples mathematics, but it allows new important distinctions [Shapiro]
6. Mathematics / C. Sources of Mathematics / 10. Constructivism / c. Conceptualism
8731 Conceptualist are just realists or idealist or nominalists, depending on their view of concepts [Shapiro]
6. Mathematics / C. Sources of Mathematics / 10. Constructivism / d. Predicativism
8730 'Impredicative' definitions refer to the thing being described [Shapiro]
12. Knowledge Sources / C. Rationalism / 1. Rationalism
8725 Rationalism tries to apply mathematical methodology to all of knowledge [Shapiro]
23. Ethics / B. Contract Ethics / 1. Contractarianism
22717 Self-interest can fairly divide a cake; first person cuts, second person chooses [Poundstone]
23. Ethics / B. Contract Ethics / 6. Game Theory
22718 Formal game theory is about maximising or minimising numbers in tables [Poundstone]
22719 The minimax theorem says a perfect game of opposed people always has a rational solution [Poundstone]
23. Ethics / B. Contract Ethics / 7. Prisoner's Dilemma
22721 The tragedy in prisoner's dilemma is when two 'nice' players misread each other [Poundstone]
22720 Two prisoners get the best result by being loyal, not by selfish betrayal [Poundstone]
23. Ethics / B. Contract Ethics / 8. Contract Strategies
22722 TIT FOR TAT says cooperate at first, then do what the other player does [Poundstone]
22723 Do unto others as you would have them do unto you - or else! [Poundstone]
26. Natural Theory / D. Laws of Nature / 9. Counterfactual Claims
4398 An event causes another just if the second event would not have happened without the first [Lewis, by Psillos]