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All the ideas for 'Thinking About Mathematics', 'People and Their Bodies' and 'The Nature of Mental States'

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24 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]
9. Objects / E. Objects over Time / 5. Temporal Parts
16209 How can point-duration slices of people have beliefs or desires? [Thomson]
12. Knowledge Sources / C. Rationalism / 1. Rationalism
8725 Rationalism tries to apply mathematical methodology to all of knowledge [Shapiro]
17. Mind and Body / B. Behaviourism / 2. Potential Behaviour
2590 Dispositions need mental terms to define them [Putnam]
17. Mind and Body / B. Behaviourism / 4. Behaviourism Critique
2591 Total paralysis would mean that there were mental states but no behaviour at all [Putnam]
17. Mind and Body / C. Functionalism / 1. Functionalism
2588 Is pain a functional state of a complete organism? [Putnam]
2589 Functionalism is compatible with dualism, as pure mind could perform the functions [Putnam]
2592 Functional states correlate with AND explain pain behaviour [Putnam]
17. Mind and Body / D. Property Dualism / 3. Property Dualism
2587 Temperature is mean molecular kinetic energy, but they are two different concepts [Putnam]
17. Mind and Body / E. Mind as Physical / 7. Anti-Physicalism / b. Multiple realisability
6376 Neuroscience does not support multiple realisability, and tends to support identity [Polger on Putnam]
2330 If humans and molluscs both feel pain, it can't be a single biological state [Putnam, by Kim]