Combining Texts

All the ideas for 'Mahaprajnaparamitashastra', 'Letters to Thomasius' and 'Recent Debates on the A Priori'

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4 ideas

6. Mathematics / A. Nature of Mathematics / 1. Mathematics

9226	If mathematical theories conflict, it may just be that they have different subject matter [Field,H]
	Full Idea: Unlike logic, in the case of mathematics there may be no genuine conflict between alternative theories: it is natural to think that different theories, if both consistent, are simply about different subjects.
	From: Hartry Field (Recent Debates on the A Priori [2005], 7)
	A reaction: For this reason Field places logic at the heart of questions about a priori knowledge, rather than mathematics. My intuitions make me doubt his proposal. Given the very simple basis of, say, arithmetic, I would expect all departments to connect.

9. Objects / D. Essence of Objects / 1. Essences of Objects

13432	The essence of a circle is the equality of its radii [Leibniz]
	Full Idea: The essence of a circle consists in the equality of all lines drawn from its centre to its circumference.
	From: Gottfried Leibniz (Letters to Thomasius [1669], 1669)
	A reaction: Compare Locke in Idea 13431 and Spinoza in Idea 13073 on the essence of geometrical figures. A key question is whether the essence is in the simplest definition, or in a complex and wide-ranging account, e.g. including conic sections for circles.

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').

27. Natural Reality / A. Classical Physics / 1. Mechanics / a. Explaining movement

12696	Bodies are recreated in motion, and don't exist in intervening instants [Leibniz]
	Full Idea: I have demonstrated that whatever moves is continuously created and that bodies are nothing at any time between the instants in motion.
	From: Gottfried Leibniz (Letters to Thomasius [1669], 1669.04), quoted by Daniel Garber - Leibniz:Body,Substance,Monad 1
	A reaction: Leibniz is a little over-confident about what he has 'demonstrated', but I think (from this remark) that he would not have been displeased with quantum theory, and the notion of a 'quantum leap' and a 'Planck time'. A 'conatus' is a 'smallest motion'.