Combining Texts

All the ideas for 'Mahaprajnaparamitashastra', 'works' and 'Frege on Apriority (with ps)'

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5 ideas

6. Mathematics / A. Nature of Mathematics / 2. Geometry
16901 The equivalent algebra model of geometry loses some essential spatial meaning [Burge]
     Full Idea: Geometrical concepts appear to depend in some way on a spatial ability. Although one can translate geometrical propositions into algebraic ones and produce equivalent models, the meaning of the propositions seems to me to be thereby lost.
     From: Tyler Burge (Frege on Apriority (with ps) [2000], 4)
     A reaction: I think this is a widely held view nowadays. Giaquinto has a book on it. A successful model of something can't replace it. Set theory can't replace arithmetic.
6. Mathematics / B. Foundations for Mathematics / 4. Axioms for Number / d. Peano arithmetic
16902 Peano arithmetic requires grasping 0 as a primitive number [Burge]
     Full Idea: In the Peano axiomatisation, arithmetic seems primitively to involve the thought that 0 is a number.
     From: Tyler Burge (Frege on Apriority (with ps) [2000], 5)
     A reaction: Burge is pointing this out as a problem for Frege, for whom only the logic is primitive.
9. Objects / C. Structure of Objects / 8. Parts of Objects / a. Parts of objects
8249 Class membership is not transitive, unlike being part of a part of the whole [Lesniewski, by George/Van Evra]
     Full Idea: Lesniewski distinguished the part-whole relationship from class membership. Membership is not transitive: if s is an element of t, and t of u, then s is not an element of u, whereas a part of a part is a part of the whole.
     From: report of Stanislaw Lesniewski (works [1916]) by George / Van Evra - The Rise of Modern Logic 7
     A reaction: If I am a member of a sports club, and my club is a member of the league, I am not thereby a member of the league (so clubs are classes, not wholes). This distinction is clearly fairly crucial in ontology.
12. Knowledge Sources / A. A Priori Knowledge / 1. Nature of the A Priori
16892 Is apriority predicated mainly of truths and proofs, or of human cognition? [Burge]
     Full Idea: Whereas Leibniz and Frege predicate apriority primarily of truths (or more fundamentally, proofs of truths), Kant predicates apriority primarily of cognition and the employment of representations.
     From: Tyler Burge (Frege on Apriority (with ps) [2000], 1)
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').