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All the ideas for 'Thinking About Mathematics', 'Letters to Leibniz 1' and 'Law,Liberty and Morality'

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26 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]
22. Metaethics / C. The Good / 1. Goodness / g. Consequentialism
23529 Conduct is not isolated from its effect on the moral code [Hart,HLA]
24. Political Theory / D. Ideologies / 5. Democracy / e. Democratic minorities
23530 The great danger of democracy is that the oppression of the minority becomes unobjectionable [Hart,HLA]
24. Political Theory / D. Ideologies / 6. Liberalism / a. Liberalism basics
23522 In an organised society all actions have some effect on other people [Hart,HLA]
25. Social Practice / A. Freedoms / 5. Freedom of lifestyle
23528 The value of liberty allows freedom of action, even if that distresses other people [Hart,HLA]
25. Social Practice / D. Justice / 2. The Law / a. Legal system
23523 The principle of legality requires crimes to be precisely defined in advance of any action [Hart,HLA]
23524 Some private moral issues are no concern of the law [Hart,HLA]
23521 Do morals influence law? Is morality an aspect of law? Can law be morally criticised? [Hart,HLA]
23525 Is the enforcement of morality morally justifiable? [Hart,HLA]
23526 Modern law still suppresses practices seen as immoral, and yet harmless [Hart,HLA]
25. Social Practice / D. Justice / 3. Punishment / b. Retribution for crime
23527 Moral wickedness of an offence is always relevant to the degree of punishment [Hart,HLA]
26. Natural Theory / D. Laws of Nature / 8. Scientific Essentialism / c. Essence and laws
17009 I won't object if someone shows that gravity consistently arises from the action of matter [Newton]