Combining Texts

All the ideas for 'Thinking About Mathematics', 'Liberal Individualism and Liberal Neutrality' and 'Maxims and Reflections'

expand these ideas     |    start again     |     specify just one area for these texts

23 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]
12. Knowledge Sources / D. Empiricism / 5. Empiricism Critique
7544 Many people imagine that to experience is to understand [Goethe]
13. Knowledge Criteria / E. Relativism / 3. Subjectivism
7541 Man never understands how anthropomorphic he is [Goethe]
16. Persons / C. Self-Awareness / 2. Knowing the Self
7543 We gain self-knowledge through action, not thought - especially when doing our duty [Goethe]
21. Aesthetics / A. Aesthetic Experience / 5. Natural Beauty
7540 Beauty is a manifestation of secret natural laws [Goethe]
22. Metaethics / C. The Good / 2. Happiness / d. Routes to happiness
7538 The happiest people link the beginning and end of life [Goethe]
24. Political Theory / B. Nature of a State / 1. Purpose of a State
7542 The best form of government teaches us to govern ourselves [Goethe]
24. Political Theory / D. Ideologies / 6. Liberalism / e. Liberal community
22818 Liberals are not too individualistic, because people recognise and value social relations [Kymlicka]
25. Social Practice / C. Rights / 1. Basis of Rights
7539 To get duties from people without rights, you must pay them well [Goethe]