Combining Texts

All the ideas for 'Mahaprajnaparamitashastra', 'Phil of Mathematics: why nothing works' and 'Whitehead and the Rise of Modern Logic'

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4 ideas

5. Theory of Logic / A. Overview of Logic / 7. Second-Order Logic
Quine says higher-order items are intensional, and lack a clearly defined identity relation [Quine, by Shapiro]
     Full Idea: Quine (in 1941) attacked 'Principia Mathematica' because the items in the range of higher-order variables (attributes etc) are intensional and thus do not have a clearly defined identity relation.
     From: report of Willard Quine (Whitehead and the Rise of Modern Logic [1941]) by Stewart Shapiro - Foundations without Foundationalism 1.3
6. Mathematics / C. Sources of Mathematics / 1. Mathematical Platonism / b. Against mathematical platonism
How can you contemplate Platonic entities without causal transactions with them? [Putnam]
     Full Idea: Platonism has the attendant problem of how we can succeed in thinking about and referring to entities we can have no causal transactions with.
     From: Hilary Putnam (Phil of Mathematics: why nothing works [1979], Modalism)
6. Mathematics / C. Sources of Mathematics / 6. Logicism / b. Type theory
Russell confused use and mention, and reduced classes to properties, not to language [Quine, by Lackey]
     Full Idea: Quine (1941) said that Russell had confused use and mention, and thus thought he had reduced classes to linguistic entities, while in fact he reduced them only to Platonic properties.
     From: report of Willard Quine (Whitehead and the Rise of Modern Logic [1941]) by Douglas Lackey - Intros to Russell's 'Essays in Analysis' p.133
     A reaction: This is cited as the 'orthodox critical interpretation' of Russell and Whitehead. Confusion of use and mention was a favourite charge of Quine's.
23. Ethics / C. Virtue Theory / 3. Virtues / a. Virtues
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').