Combining Texts

All the ideas for 'Thinking About Mathematics', 'Henry V' and 'The Central Questions of Philosophy'

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29 ideas

2. Reason / E. Argument / 3. Analogy
5331 You can't infer that because you have a hidden birth-mark, everybody else does [Ayer]
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]
7. Existence / D. Theories of Reality / 11. Ontological Commitment / b. Commitment of quantifiers
2611 It is currently held that quantifying over something implies belief in its existence [Ayer]
9. Objects / D. Essence of Objects / 3. Individual Essences
16520 We see properties necessary for a kind (in the definition), but not for an individual [Ayer]
12. Knowledge Sources / C. Rationalism / 1. Rationalism
8725 Rationalism tries to apply mathematical methodology to all of knowledge [Shapiro]
15. Nature of Minds / A. Nature of Mind / 4. Other Minds / c. Knowing other minds
2613 The theory of other minds has no rival [Ayer]
5328 Originally I combined a mentalistic view of introspection with a behaviouristic view of other minds [Ayer]
5330 Physicalism undercuts the other mind problem, by equating experience with 'public' brain events [Ayer]
16. Persons / B. Nature of the Self / 5. Self as Associations
5325 Is something an 'experience' because it relates to other experiences, or because it relates to a subject? [Ayer]
5326 Qualia must be united by a subject, because they lead to concepts and judgements [Ayer]
16. Persons / B. Nature of the Self / 7. Self and Body / a. Self needs body
5324 Bodily identity and memory work together to establish personal identity [Ayer]
16. Persons / C. Self-Awareness / 2. Knowing the Self
5322 Self-consciousness is not basic, because experiences are not instrinsically marked with ownership [Ayer]
16. Persons / D. Continuity of the Self / 2. Mental Continuity / c. Inadequacy of mental continuity
5327 Temporal gaps in the consciousness of a spirit could not be bridged by memories [Ayer]
17. Mind and Body / E. Mind as Physical / 1. Physical Mind
5329 Why shouldn't we say brain depends on mind? Better explanation! [Ayer]
19. Language / D. Propositions / 6. Propositions Critique
2610 Talk of propositions is just shorthand for talking about equivalent sentences [Ayer]
25. Social Practice / E. Policies / 1. War / b. Justice in war
23565 Our obedience to the king erases any crimes we commit for him [Shakespeare]