Combining Texts

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

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6 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 / B. Unity of Objects / 2. Substance / c. Types of substance

16616	Substances 'substand' (beneath accidents), or 'subsist' (independently) [Eustachius]
	Full Idea: It is proper to substance both to stretch out or exist beneath accidents, which is to substand, and to exist per se and not in another, which is to subsist.
	From: Eustachius a Sancto Paulo (Summa [1609], I.1.3b.1.2), quoted by Robert Pasnau - Metaphysical Themes 1274-1671 06.2
	A reaction: This reflects Aristotle wavering between 'ousia' being the whole of a thing, or the substrate of a thing. In current discussion, 'substance' still wavers between a thing which 'is' a substance, and substance being the essence.

9. Objects / C. Structure of Objects / 2. Hylomorphism / a. Hylomorphism

16585	Prime matter is free of all forms, but has the potential for all forms [Eustachius]
	Full Idea: Everyone says that prime matter, considered in itself, is free of all forms and at the same time is open to all forms - or, that matter is in potentiality to all forms.
	From: Eustachius a Sancto Paulo (Summa [1609], III.1.1.2.3), quoted by Robert Pasnau - Metaphysical Themes 1274-1671 03.1
	A reaction: This is the notorious doctrine developed to support the hylomorphic picture derived from Aristotle. No one could quite figure out what prime matter was, so it faded away.

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').