Combining Texts

All the ideas for 'Mahaprajnaparamitashastra', 'Introduction to 'Absolute Generality'' and 'Summa'

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9 ideas

4. Formal Logic / F. Set Theory ST / 1. Set Theory

13451	The two best understood conceptions of set are the Iterative and the Limitation of Size [Rayo/Uzquiano]
	Full Idea: The two best understood conceptions of set are the Iterative Conception and the Limitation of Size Conception.
	From: Rayo,A/Uzquiasno,G (Introduction to 'Absolute Generality' [2006], 1.2.2)

4. Formal Logic / F. Set Theory ST / 4. Axioms for Sets / m. Axiom of Separation

13452	Some set theories give up Separation in exchange for a universal set [Rayo/Uzquiano]
	Full Idea: There are set theories that countenance exceptions to the Principle of Separation in exchange for a universal set.
	From: Rayo,A/Uzquiasno,G (Introduction to 'Absolute Generality' [2006], 1.2.2)

5. Theory of Logic / G. Quantification / 2. Domain of Quantification

13449	We could have unrestricted quantification without having an all-inclusive domain [Rayo/Uzquiano]
	Full Idea: The possibility of unrestricted quantification does not immediately presuppose the existence of an all-inclusive domain. One could deny an all-inclusive domain but grant that some quantifications are sometimes unrestricted.
	From: Rayo,A/Uzquiasno,G (Introduction to 'Absolute Generality' [2006], 1.1)
	A reaction: Thus you can quantify over anything you like, but only from what is available. Eat what you like (in this restaurant).

13450	Absolute generality is impossible, if there are indefinitely extensible concepts like sets and ordinals [Rayo/Uzquiano]
	Full Idea: There are doubts about whether absolute generality is possible, if there are certain concepts which are indefinitely extensible, lacking definite extensions, and yielding an ever more inclusive hierarchy. Sets and ordinals are paradigm cases.
	From: Rayo,A/Uzquiasno,G (Introduction to 'Absolute Generality' [2006], 1.2.1)

5. Theory of Logic / G. Quantification / 5. Second-Order Quantification

13453	Perhaps second-order quantifications cover concepts of objects, rather than plain objects [Rayo/Uzquiano]
	Full Idea: If one thought of second-order quantification as quantification over first-level Fregean concepts [note: one under which only objects fall], talk of domains might be regimented as talk of first-level concepts, which are not objects.
	From: Rayo,A/Uzquiasno,G (Introduction to 'Absolute Generality' [2006], 1.2.2)
	A reaction: That is (I take it), don't quantify over objects, but quantify over concepts, but only those under which known objects fall. One might thus achieve naïve comprehension without paradoxes. Sound like fun.

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.

19. Language / F. Communication / 5. Pragmatics / a. Contextual meaning

13448	The domain of an assertion is restricted by context, either semantically or pragmatically [Rayo/Uzquiano]
	Full Idea: We generally take an assertion's domain of discourse to be implicitly restricted by context. [Note: the standard approach is that this restriction is a semantic phenomenon, but Kent Bach (2000) argues that it is a pragmatic phenomenon]
	From: Rayo,A/Uzquiasno,G (Introduction to 'Absolute Generality' [2006], 1.1)
	A reaction: I think Kent Bach is very very right about this. Follow any conversation, and ask what the domain is at any moment. The reference of a word like 'they' can drift across things, with no semantics to guide us, but only clues from context and common sense.

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').