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All the ideas for 'On Being (frags)', 'Thinking About Mathematics' and 'Principia Ethica'

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29 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]
21. Aesthetics / A. Aesthetic Experience / 4. Beauty
21233 The beautiful is whatever it is intrinsically good to admire [Moore,GE]
22. Metaethics / A. Ethics Foundations / 1. Nature of Ethics / b. Defining ethics
8039 Moore tries to show that 'good' is indefinable, but doesn't understand what a definition is [MacIntyre on Moore,GE]
22. Metaethics / A. Ethics Foundations / 2. Source of Ethics / a. Idealistic ethics
22151 The Open Question argument leads to anti-realism and the fact-value distinction [Boulter on Moore,GE]
11056 The naturalistic fallacy claims that natural qualties can define 'good' [Moore,GE]
8033 Moore cannot show why something being good gives us a reason for action [MacIntyre on Moore,GE]
8032 Can learning to recognise a good friend help us to recognise a good watch? [MacIntyre on Moore,GE]
22. Metaethics / A. Ethics Foundations / 2. Source of Ethics / c. Ethical intuitionism
11050 Moore's combination of antinaturalism with strong supervenience on the natural is incoherent [Hanna on Moore,GE]
23726 Despite Moore's caution, non-naturalists incline towards intuitionism [Moore,GE, by Smith,M]
22. Metaethics / B. Value / 1. Nature of Value / c. Objective value
18676 We should ask what we would judge to be good if it existed in absolute isolation [Moore,GE]
22. Metaethics / C. The Good / 1. Goodness / a. Form of the Good
11057 It is always an open question whether anything that is natural is good [Moore,GE]
22. Metaethics / C. The Good / 1. Goodness / b. Types of good
5925 The three main values are good, right and beauty [Moore,GE, by Ross]
22. Metaethics / C. The Good / 1. Goodness / c. Right and good
5902 For Moore, 'right' is what produces good [Moore,GE, by Ross]
5903 'Right' means 'cause of good result' (hence 'useful'), so the end does justify the means [Moore,GE]
23. Ethics / E. Utilitarianism / 1. Utilitarianism
5907 Relationships imply duties to people, not merely the obligation to benefit them [Ross on Moore,GE]