Combining Texts

All the ideas for 'Thinking About Mathematics', 'Contrib to Critique of Hegel's Phil of Right' and 'Intro to 'Creating the Kingdom of Ends''

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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]
16. Persons / A. Concept of a Person / 4. Persons as Agents
9757 A person viewed as an agent makes no sense without its own future [Korsgaard]
9758 To make sense of personal identity, focus on agency rather than experience [Korsgaard]
20. Action / A. Definition of Action / 1. Action Theory
9759 Theory of action focuses on explanation and prediction; practical action on justification and choice [Korsgaard]
22. Metaethics / B. Value / 2. Values / i. Self-interest
9760 Self-concern may be a source of pain, or a lack of self-respect, or a failure of responsibility [Korsgaard]
23. Ethics / A. Egoism / 1. Ethical Egoism
9761 Personal concern for one's own self widens out into concern for the impersonal [Korsgaard]
24. Political Theory / C. Ruling a State / 4. Changing the State / c. Revolution
21991 The middle class gain freedom through property, but workers can only free all of humanity [Marx, by Singer]
21990 Theory is as much a part of a revolution as material force is [Marx]
29. Religion / D. Religious Issues / 1. Religious Commitment / a. Religious Belief
7128 Religion is the opium of the people, and real happiness requires its abolition [Marx]