Combining Texts

All the ideas for 'Mahaprajnaparamitashastra', 'New Foundations for Mathematical Logic' and 'The Semantic Tradition from Kant to Carnap'

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7 ideas

4. Formal Logic / F. Set Theory ST / 4. Axioms for Sets / a. Axioms for sets
9879 NF has no models, but just blocks the comprehension axiom, to avoid contradictions [Quine, by Dummett]
     Full Idea: Quine's New Foundations system of set theory, devised with no model in mind, but on the basis of a hunch that a purely formal restriction on the comprehension axiom would block all contradictions.
     From: report of Willard Quine (New Foundations for Mathematical Logic [1937]) by Michael Dummett - Frege philosophy of mathematics Ch.18
     A reaction: The point is that Quine (who had an ontological preference for 'desert landscapes') attempted to do without an ontological commitment to objects (and their subsequent models), with a purely formal system. Quine's NF is not now highly regarded.
4. Formal Logic / F. Set Theory ST / 4. Axioms for Sets / j. Axiom of Choice IX
18270 Choice suggests that intensions are not needed to ensure classes [Coffa]
     Full Idea: The axiom of choice was an assumption that implicitly questioned the necessity of intensions to guarantee the presence of classes.
     From: J. Alberto Coffa (The Semantic Tradition from Kant to Carnap [1991], 7 'Log')
     A reaction: The point is that Choice just picks out members for no particular reason. So classes, it seems, don't need a reason to exist.
12. Knowledge Sources / A. A Priori Knowledge / 8. A Priori as Analytic
18263 The semantic tradition aimed to explain the a priori semantically, not by Kantian intuition [Coffa]
     Full Idea: The semantic tradition's problem was the a priori; its enemy, Kantian pure intuition; its purpose, to develop a conception of the a priori in which pure intuition played no role; its strategy, to base that theory on a development of semantics.
     From: J. Alberto Coffa (The Semantic Tradition from Kant to Carnap [1991], 2 Intro)
     A reaction: It seems to me that intuition, in the modern sense, has been unnecessarily demonised. I would define it as 'rational insights which cannot be fully articulated'. Sherlock Holmes embodies it.
12. Knowledge Sources / A. A Priori Knowledge / 11. Denying the A Priori
18272 Platonism defines the a priori in a way that makes it unknowable [Coffa]
     Full Idea: The trouble with Platonism had always been its inability to define a priori knowledge in a way that made it possible for human beings to have it.
     From: J. Alberto Coffa (The Semantic Tradition from Kant to Carnap [1991], 7 'What')
     A reaction: This is the famous argument of Benacerraf 1973.
15. Nature of Minds / C. Capacities of Minds / 5. Generalisation by mind
18266 Mathematics generalises by using variables [Coffa]
     Full Idea: The instrument of generality in mathematics is the variable.
     From: J. Alberto Coffa (The Semantic Tradition from Kant to Carnap [1991], 4 'The conc')
     A reaction: I like the idea that there are variables in ordinary speech, pronouns being the most obvious example. 'Cats' is a variable involving quantification over a domain of lovable fluffy mammals.
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 / D. Time / 1. Nature of Time / a. Absolute time
18279 Relativity is as absolutist about space-time as Newton was about space [Coffa]
     Full Idea: If the theory of relativity might be thought to support an idealist construal of space and time, it is no less absolutistic about space-time than Newton's theory was about space.
     From: J. Alberto Coffa (The Semantic Tradition from Kant to Carnap [1991])
     A reaction: [He cites Minkowski, Weyl and Cartan for this conclusion] Coffa is clearly a bit cross about philosophers who draw naive idealist and relativist conclusions from relativity.