Combining Texts

All the ideas for 'Mahaprajnaparamitashastra', 'Paradoxes: Form and Predication' and 'Rechnungsmethoden (dissertation)'

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4 ideas

5. Theory of Logic / G. Quantification / 6. Plural Quantification

14235	Saying 'they can become a set' is a tautology, because reference to 'they' implies a collection [Cargile]
	Full Idea: If the rule is asserted 'Given any well-determined objects, they can be collected into a set by an application of the 'set of' operation', then on the usual account of 'they' this is a tautology. Collection comes automatically with this form of reference.
	From: James Cargile (Paradoxes: Form and Predication [1979], p.115), quoted by Oliver,A/Smiley,T - What are Sets and What are they For? Intro
	A reaction: Is this a problem? Given they are well-determined (presumably implying countable) there just is a set of them. That's what set theory is, I thought. Of course, the iterative view talks of 'constructing' the sets, but the construction looks unstoppable.

6. Mathematics / A. Nature of Mathematics / 3. Nature of Numbers / c. Priority of numbers

18256	Quantity is inconceivable without the idea of addition [Frege]
	Full Idea: There is so intimate a connection between the concepts of addition and of quantity that one cannot begin to grasp the latter without the former.
	From: Gottlob Frege (Rechnungsmethoden (dissertation) [1874], p.2), quoted by Michael Dummett - Frege philosophy of mathematics 22 'Quantit'
	A reaction: Frege offers good reasons for making cardinals prior to ordinals, though plenty of people disagree.

6. Mathematics / C. Sources of Mathematics / 2. Intuition of Mathematics

9831	Geometry appeals to intuition as the source of its axioms [Frege]
	Full Idea: The elements of all geometrical constructions are intuitions, and geometry appeals to intuition as the source of its axioms.
	From: Gottlob Frege (Rechnungsmethoden (dissertation) [1874], Ch.6), quoted by Michael Dummett - Frege philosophy of mathematics
	A reaction: Very early Frege, but he stuck to this view, while firmly rejecting intuition as a source of arithmetic. Frege would have known well that Euclid's assumption about parallels had been challenged.

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').