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All the ideas for 'Croce and Collingwood', 'Infinity: Quest to Think the Unthinkable' and 'The Moral Problem'

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44 ideas

1. Philosophy / F. Analytic Philosophy / 4. Conceptual Analysis
23728 Analysis aims to express the full set of platitudes surrounding a given concept [Smith,M]
2. Reason / D. Definition / 1. Definitions
23744 Defining a set of things by paradigms doesn't pin them down enough [Smith,M]
4. Formal Logic / F. Set Theory ST / 2. Mechanics of Set Theory / b. Terminology of ST
10859 A set is 'well-ordered' if every subset has a first element [Clegg]
4. Formal Logic / F. Set Theory ST / 3. Types of Set / d. Infinite Sets
10857 Set theory made a closer study of infinity possible [Clegg]
10864 Any set can always generate a larger set - its powerset, of subsets [Clegg]
4. Formal Logic / F. Set Theory ST / 4. Axioms for Sets / b. Axiom of Extensionality I
10872 Extensionality: Two sets are equal if and only if they have the same elements [Clegg]
4. Formal Logic / F. Set Theory ST / 4. Axioms for Sets / c. Axiom of Pairing II
10875 Pairing: For any two sets there exists a set to which they both belong [Clegg]
4. Formal Logic / F. Set Theory ST / 4. Axioms for Sets / d. Axiom of Unions III
10876 Unions: There is a set of all the elements which belong to at least one set in a collection [Clegg]
4. Formal Logic / F. Set Theory ST / 4. Axioms for Sets / f. Axiom of Infinity V
10878 Infinity: There exists a set of the empty set and the successor of each element [Clegg]
4. Formal Logic / F. Set Theory ST / 4. Axioms for Sets / g. Axiom of Powers VI
10877 Powers: All the subsets of a given set form their own new powerset [Clegg]
4. Formal Logic / F. Set Theory ST / 4. Axioms for Sets / j. Axiom of Choice IX
10879 Choice: For every set a mechanism will choose one member of any non-empty subset [Clegg]
4. Formal Logic / F. Set Theory ST / 4. Axioms for Sets / k. Axiom of Existence
10871 Axiom of Existence: there exists at least one set [Clegg]
4. Formal Logic / F. Set Theory ST / 4. Axioms for Sets / l. Axiom of Specification
10874 Specification: a condition applied to a set will always produce a new set [Clegg]
6. Mathematics / A. Nature of Mathematics / 1. Mathematics
10880 Mathematics can be 'pure' (unapplied), 'real' (physically grounded); or 'applied' (just applicable) [Clegg]
6. Mathematics / A. Nature of Mathematics / 3. Nature of Numbers / e. Ordinal numbers
10861 Beyond infinity cardinals and ordinals can come apart [Clegg]
10860 An ordinal number is defined by the set that comes before it [Clegg]
6. Mathematics / A. Nature of Mathematics / 3. Nature of Numbers / g. Real numbers
10854 Transcendental numbers can't be fitted to finite equations [Clegg]
6. Mathematics / A. Nature of Mathematics / 3. Nature of Numbers / k. Imaginary numbers
10858 By adding an axis of imaginary numbers, we get the useful 'number plane' instead of number line [Clegg]
6. Mathematics / A. Nature of Mathematics / 3. Nature of Numbers / l. Zero
10853 Either lack of zero made early mathematics geometrical, or the geometrical approach made zero meaningless [Clegg]
6. Mathematics / A. Nature of Mathematics / 5. The Infinite / a. The Infinite
10866 Cantor's account of infinities has the shaky foundation of irrational numbers [Clegg]
6. Mathematics / A. Nature of Mathematics / 5. The Infinite / g. Continuum Hypothesis
10869 The Continuum Hypothesis is independent of the axioms of set theory [Clegg]
10862 The 'continuum hypothesis' says aleph-one is the cardinality of the reals [Clegg]
18. Thought / A. Modes of Thought / 5. Rationality / a. Rationality
23743 Capturing all the common sense facts about rationality is almost impossible [Smith,M]
20. Action / C. Motives for Action / 1. Acting on Desires
23739 Goals need desires, and so only desires can motivate us [Smith,M]
23724 A pure desire could be criticised if it were based on a false belief [Smith,M]
23736 A person can have a desire without feeling it [Smith,M]
23723 In the Humean account, desires are not true/false, or subject to any rational criticism [Smith,M]
23735 Subjects may be fallible about the desires which explain their actions [Smith,M]
23738 Humeans (unlike their opponents) say that desires and judgements can separate [Smith,M]
23742 If first- and second-order desires conflict, harmony does not require the second-order to win [Smith,M]
23746 Objective reasons to act might be the systematic desires of a fully rational person [Smith,M]
20. Action / C. Motives for Action / 3. Acting on Reason / a. Practical reason
23733 Motivating reasons are psychological, while normative reasons are external [Smith,M]
23740 Humeans take maximising desire satisfaction as the normative reasons for actions [Smith,M]
23745 We cannot expect even fully rational people to converge on having the same desires for action [Smith,M]
21. Aesthetics / A. Aesthetic Experience / 1. Aesthetics
20416 By 1790 aestheticians were mainly trying to explain individual artistic genius [Kemp]
21. Aesthetics / B. Nature of Art / 4. Art as Expression
20417 Expression can be either necessary for art, or sufficient for art (or even both) [Kemp]
20419 We don't already know what to express, and then seek means of expressing it [Kemp]
20418 The horror expressed in some works of art could equallly be expressed by other means [Kemp]
22. Metaethics / A. Ethics Foundations / 1. Nature of Ethics / h. Against ethics
23731 'Externalists' say moral judgements are not reasons, and maybe not even motives [Smith,M]
23732 A person could make a moral judgement without being in any way motivated by it [Smith,M]
22. Metaethics / A. Ethics Foundations / 2. Source of Ethics / b. Rational ethics
23729 Moral internalism says a judgement of rightness is thereby motivating [Smith,M]
23730 'Rationalism' says the rightness of an action is a reason to perform it [Smith,M]
22. Metaethics / A. Ethics Foundations / 2. Source of Ethics / h. Expressivism
23727 Expressivists count attitudes as 'moral' if they concern features of things, rather than their mere existence [Smith,M]
22. Metaethics / B. Value / 1. Nature of Value / a. Nature of value
23741 Is valuing something a matter of believing or a matter of desiring? [Smith,M]