Combining Texts

All the ideas for 'Structure and Nature', 'Morality and the emotions' and 'Thinking About Mathematics'

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

22 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
10242 I apply structuralism to concrete and abstract objects indiscriminately [Quine]
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 / D. Theories of Reality / 6. Physicalism
10243 My ontology is quarks etc., classes of such things, classes of such classes etc. [Quine]
12. Knowledge Sources / C. Rationalism / 1. Rationalism
8725 Rationalism tries to apply mathematical methodology to all of knowledge [Shapiro]
18. Thought / A. Modes of Thought / 3. Emotions / c. Role of emotions
24008 Reference to a person's emotions is often essential to understanding their actions [Williams,B]
18. Thought / A. Modes of Thought / 3. Emotions / g. Controlling emotions
24009 Moral education must involve learning about various types of feeling towards things [Williams,B]
22. Metaethics / A. Ethics Foundations / 2. Source of Ethics / h. Expressivism
24007 Emotivism saw morality as expressing emotions, and influencing others' emotions [Williams,B]
23. Ethics / C. Virtue Theory / 2. Elements of Virtue Theory / e. Character
24010 An admirable human being should have certain kinds of emotional responses [Williams,B]
23. Ethics / D. Deontological Ethics / 6. Motivation for Duty
24012 Kant's love of consistency is too rigid, and it even overrides normal fairness [Williams,B]