Ideas from 'The Semantic Tradition from Kant to Carnap' by J. Alberto Coffa [1991], by Theme Structure

[found in 'The Semantic Tradition from Kant to Carnap' by Coffa,J.Alberto [CUP 1993,0-521-44707-0]].

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4. Formal Logic / F. Set Theory ST / 4. Axioms for Sets / j. Axiom of Choice IX
Choice suggests that intensions are not needed to ensure classes
                        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
The semantic tradition aimed to explain the a priori semantically, not by Kantian intuition
                        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
Platonism defines the a priori in a way that makes it unknowable
                        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
Mathematics generalises by using variables
                        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.
27. Natural Reality / D. Time / 1. Nature of Time / a. Absolute time
Relativity is as absolutist about space-time as Newton was about space
                        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.