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All the ideas for 'Thinking About Mathematics', 'The Philosophy of Leibniz' and 'Action, Reasons and Causes'

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25 ideas

1. Philosophy / F. Analytic Philosophy / 5. Linguistic Analysis
7529 All philosophy should begin with an analysis of propositions [Russell]
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 / B. Change in Existence / 4. Events / b. Events as primitive
7949 Varied descriptions of an event will explain varied behaviour relating to it [Davidson, by Macdonald,C]
12. Knowledge Sources / C. Rationalism / 1. Rationalism
8725 Rationalism tries to apply mathematical methodology to all of knowledge [Shapiro]
20. Action / A. Definition of Action / 2. Duration of an Action
20020 If one action leads directly to another, they are all one action [Davidson, by Wilson/Schpall]
20. Action / B. Preliminaries of Action / 1. Intention to Act / a. Nature of intentions
20072 We explain an intention by giving an account of acting with an intention [Davidson, by Stout,R]
20. Action / C. Motives for Action / 2. Acting on Beliefs / a. Acting on beliefs
20045 Acting for a reason is a combination of a pro attitude, and a belief that the action is appropriate [Davidson]
20. Action / C. Motives for Action / 3. Acting on Reason / c. Reasons as causes
23734 The best explanation of reasons as purposes for actions is that they are causal [Davidson, by Smith,M]
23737 Reasons can give purposes to actions, without actually causing them [Smith,M on Davidson]
20075 Early Davidson says intentional action is caused by reasons [Davidson, by Stout,R]
6664 Reasons must be causes when agents act 'for' reasons [Davidson, by Lowe]
3395 Davidson claims that what causes an action is the reason for doing it [Davidson, by Kim]