Combining Texts

All the ideas for 'Mahaprajnaparamitashastra', 'Causality and Explanation' and 'Elements of Intuitionism'

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4 ideas

6. Mathematics / A. Nature of Mathematics / 5. The Infinite / c. Potential infinite

15938	Platonists ruin infinity, which is precisely a growing structure which is never completed [Dummett]
	Full Idea: The platonist destroys the whole essence of infinity, which lies in the conception of a structure which is always in growth, precisely because the process of construction is never completed.
	From: Michael Dummett (Elements of Intuitionism [1977], p.57), quoted by Thomas J. McKay - Plural Predication
	A reaction: I don't warm to intuitionism, but I warm to this conception of infinity. Completed infinities are convenient reifications for mathematicians.

6. Mathematics / C. Sources of Mathematics / 10. Constructivism / a. Constructivism

15939	For intuitionists it is constructed proofs (which take time) which make statements true [Dummett]
	Full Idea: For an intuitionist a mathematical statement is rendered true or false by a proof or disproof, that is, by a construction, and constructions are effected in time.
	From: Michael Dummett (Elements of Intuitionism [1977], p.336), quoted by Shaughan Lavine - Understanding the Infinite VI.2
	A reaction: Lavine is quoting this to draw attention to the difficulties of thinking of it as all taking place 'in time', especially when dealing with infinities.

14. Science / D. Explanation / 2. Types of Explanation / i. Explanations by mechanism

16557	Salmon's mechanisms are processes and interactions, involving marks, or conserved quantities [Salmon, by Machamer/Darden/Craver]
	Full Idea: For Salmon mechanisms are composed of processes and interactions. The interactions are identified in terms of transmitted marks and statistical relations, or (more recently) exchanges of conserved quantities.
	From: report of Wesley Salmon (Causality and Explanation [1998], 3.1) by Machamer,P/Darden,L/Craver,C - Thinking About Mechanisms 3.1
	A reaction: They say that Salmon has too little to say about the activities that constitute a mechanism. A 'mark' doesn't sound too promising, but I quite like the exchange of conserved quantities, which gets into the guts of what is going on.

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').