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All the ideas for 'Thinking About Mathematics', 'Inventing Logical Necessity' and 'The Elements of Law'

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26 ideas

1. Philosophy / C. History of Philosophy / 4. Later European Philosophy / b. Seventeenth century philosophy
7396 Hobbes created English-language philosophy [Hobbes, by Tuck]
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]
10. Modality / A. Necessity / 6. Logical Necessity
12189 Logical necessity involves a decision about usage, and is non-realist and non-cognitive [Wright,C, by McFetridge]
12. Knowledge Sources / B. Perception / 4. Sense Data / a. Sense-data theory
16638 The qualities of the world are mere appearances; reality is the motions which cause them [Hobbes]
12. Knowledge Sources / C. Rationalism / 1. Rationalism
8725 Rationalism tries to apply mathematical methodology to all of knowledge [Shapiro]
12. Knowledge Sources / D. Empiricism / 1. Empiricism
16688 Evidence is conception, which is imagination, which proceeds from the senses [Hobbes]
7405 Experience can't prove universal truths [Hobbes]
19. Language / A. Nature of Meaning / 7. Meaning Holism / b. Language holism
7320 Holism cannot give a coherent account of scientific methodology [Wright,C, by Miller,A]
20. Action / C. Motives for Action / 1. Acting on Desires
7408 It is an error that reason should control the passions, which give right guidance on their own [Hobbes, by Tuck]
22. Metaethics / A. Ethics Foundations / 1. Nature of Ethics / d. Ethical theory
7407 Good and evil are what please us; goodness and badness the powers causing them [Hobbes]
22. Metaethics / A. Ethics Foundations / 2. Source of Ethics / j. Ethics by convention
7410 Self-preservation is basic, and people judge differently about that, implying ethical relativism [Hobbes, by Tuck]
22. Metaethics / C. The Good / 1. Goodness / c. Right and good
7409 Hobbes shifted from talk of 'the good' to talk of 'rights' [Hobbes, by Tuck]
28. God / C. Attitudes to God / 4. God Reflects Humanity
7411 The attributes of God just show our inability to conceive his nature [Hobbes]