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All the ideas for 'Thinking About Mathematics', 'Community and Citizenship' and 'Thought and Talk'

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25 ideas

3. Truth / A. Truth Problems / 1. Truth
6396 A sentence is held true because of a combination of meaning and belief [Davidson]
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]
11. Knowledge Aims / A. Knowledge / 4. Belief / a. Beliefs
11145 Having a belief involves the possibility of being mistaken [Davidson]
11. Knowledge Aims / A. Knowledge / 4. Belief / e. Belief holism
6397 The concept of belief can only derive from relationship to a speech community [Davidson]
12. Knowledge Sources / C. Rationalism / 1. Rationalism
8725 Rationalism tries to apply mathematical methodology to all of knowledge [Shapiro]
18. Thought / A. Modes of Thought / 1. Thought
6392 Thought depends on speech [Davidson]
18. Thought / A. Modes of Thought / 8. Human Thought
6393 A creature doesn't think unless it interprets another's speech [Davidson]
18. Thought / D. Concepts / 5. Concepts and Language / a. Concepts and language
11144 Concepts are only possible in a language community [Davidson]
19. Language / A. Nature of Meaning / 6. Meaning as Use
6395 An understood sentence can be used for almost anything; it isn't language if it has only one use [Davidson]
19. Language / A. Nature of Meaning / 7. Meaning Holism / b. Language holism
6394 The pattern of sentences held true gives sentences their meaning [Davidson]
24. Political Theory / B. Nature of a State / 4. Citizenship
22817 Citizenship involves a group of mutually supporting rights, which create community and equality [Miller,D]
24. Political Theory / D. Ideologies / 14. Nationalism
22816 Socialists reject nationality as a false source of identity [Miller,D]