Combining Texts

All the ideas for 'Mahaprajnaparamitashastra', 'Grundlagen (Foundations of Theory of Manifolds)' and 'Elimination of Metaphysics by Analysis of Language'

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4 ideas

1. Philosophy / E. Nature of Metaphysics / 7. Against Metaphysics
16252 Metaphysics uses empty words, or just produces pseudo-statements [Carnap]
     Full Idea: Since metaphysics doesn't want to assert analytic propositions, nor fall within the domain of physical science, it is compelled to employ words for which no criteria of application are specified, ..or else combine meaningful words..into pseudo-statements.
     From: Rudolph Carnap (Elimination of Metaphysics by Analysis of Language [1959]), quoted by Tim Maudlin - The Metaphysics within Physics 2.4
     A reaction: A classic summary of the logical positivist rejection of metaphysics. I incline to treat metaphysics as within the domain of science, but at a level of generality so high that practising scientists become bewildered and give up.
4. Formal Logic / F. Set Theory ST / 1. Set Theory
15946 Cantor developed sets from a progression into infinity by addition, multiplication and exponentiation [Cantor, by Lavine]
     Full Idea: Cantor's development of set theory began with his discovery of the progression 0, 1, ....∞, ∞+1, ∞+2, ..∞x2, ∞x3, ...∞^2, ..∞^3, ...∞^∞, ...∞^∞^∞.....
     From: report of George Cantor (Grundlagen (Foundations of Theory of Manifolds) [1883]) by Shaughan Lavine - Understanding the Infinite VIII.2
6. Mathematics / A. Nature of Mathematics / 3. Nature of Numbers / e. Ordinal numbers
15911 Ordinals are generated by endless succession, followed by a limit ordinal [Cantor, by Lavine]
     Full Idea: Ordinal numbers are generated by two principles: each ordinal has an immediate successor, and each unending sequence has an ordinal number as its limit (that is, an ordinal that is next after such a sequence).
     From: report of George Cantor (Grundlagen (Foundations of Theory of Manifolds) [1883]) by Shaughan Lavine - Understanding the Infinite III.4
23. Ethics / C. Virtue Theory / 3. Virtues / a. Virtues
7903 The six perfections are giving, morality, patience, vigour, meditation, and wisdom [Nagarjuna]
     Full Idea: The six perfections are of giving, morality, patience, vigour, meditation, and wisdom.
     From: Nagarjuna (Mahaprajnaparamitashastra [c.120], 88)
     A reaction: What is 'morality', if giving is not part of it? I like patience and vigour being two of the virtues, which immediately implies an Aristotelian mean (which is always what is 'appropriate').