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3 ideas
10117 | Intuitonists in mathematics worried about unjustified assertion, as well as contradiction [Brouwer, by George/Velleman] |
Full Idea: The concern of mathematical intuitionists was that the use of certain forms of inference generates, not contradiction, but unjustified assertions. | |
From: report of Luitzen E.J. Brouwer (Intuitionism and Formalism [1912]) by A.George / D.J.Velleman - Philosophies of Mathematics Ch.6 | |
A reaction: This seems to be the real origin of the verificationist idea in the theory of meaning. It is a hugely revolutionary idea - that ideas are not only ruled out of court by contradiction, but that there are other criteria which should also be met. |
4897 | A proposition is a set of possible worlds for which its intension delivers truth [Perry] |
Full Idea: The proposition expressed by a sentence can be thought of as a set of possible worlds, the worlds for which its intension delivers truth. | |
From: John Perry (Knowledge, Possibility and Consciousness [2001], §8.1) | |
A reaction: It has always struck me as important to hang on to the concept of a 'proposition' (over and above sentences). This idea gives a metaphysics for the concept, and the 'language of thought' offers appropriate brain structures. A neat picture. |
4890 | A sharp analytic/synthetic line can rarely be drawn, but some concepts are central to thought [Perry] |
Full Idea: Although there is seldom a sharp analytic/synthetic distinction to be drawn in the case of our concepts, there are clearly things that are more and less central. | |
From: John Perry (Knowledge, Possibility and Consciousness [2001], §3.2) | |
A reaction: Most Americans seem enslaved to Quine on this one, so it is nice to see the obvious being stated for once. Human thought is an organic offshoot of the natural world. To think it is all arbitrary and changeable is human arrogance. |