8 ideas
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. |
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. |
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. |
20795 | Some things are their own criterion, such as straightness, a set of scales, or light [Sext.Empiricus] |
Full Idea: Dogmatists say something can be its own criterion. The straight is the standard of itself, and a set of scales establishes the equality of other things and of itself, and light seems to reveal not just other things but also itself. | |
From: Sextus Empiricus (Against the Mathematicians [c.180], 442) | |
A reaction: Each of these may be a bit dubious, but deserves careful discussion. |
20794 | How can sceptics show there is no criterion? Weak without, contradiction with [Sext.Empiricus] |
Full Idea: The dogmatists ask how the sceptic can show there is no criterion. If without a criterion, he is untrustworthy; with a criterion he is turned upside down. He says there is no criterion, but accepts a criterion to establish this. | |
From: Sextus Empiricus (Against the Mathematicians [c.180], 440) | |
A reaction: This is also the classic difficulty for foundationalist views of knowledge. Is the foundation justified, or not? |
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. |
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'). |
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. |