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4 ideas
15941 | For intuitionists excluded middle is an outdated historical convention [Brouwer] |
Full Idea: From the intuitionist standpoint the dogma of the universal validity of the principle of excluded third in mathematics can only be considered as a phenomenon of history of civilization, like the rationality of pi or rotation of the sky about the earth. | |
From: Luitzen E.J. Brouwer (works [1930]), quoted by Shaughan Lavine - Understanding the Infinite VI.2 | |
A reaction: [Brouwer 1952:510-11] |
17587 | The 'Law' of Excluded Middle needs all propositions to be definitely true or definitely false [Inwagen] |
Full Idea: I think the validity of the 'Law' of Excluded Middle depends on the assumption that every proposition is definitely true or definitely false. | |
From: Peter van Inwagen (Material Beings [1990], 18) | |
A reaction: I think this is confused. He cites vagueness as the problem, but that is a problem for Bivalence. If excluded middle is read as 'true or not-true', that leaves the meaning of 'not-true' open, and never mentions the bivalent 'false'. |
17558 | Variables are just like pronouns; syntactic explanations get muddled over dummy letters [Inwagen] |
Full Idea: Explanations in terms of syntax do not satisfactorily distinguish true variables from dummy or schematic letters. Identifying variables with pronouns, however, provides a genuine explanation of what variables are. | |
From: Peter van Inwagen (Material Beings [1990], 02) | |
A reaction: I like this because it shows that our ordinary thought and speech use variables all the time ('I've forgotten something - what was it?'). He says syntax is fine for maths, but not for ordinary understanding. |
17583 | There are no heaps [Inwagen] |
Full Idea: Fortunately ....there are no heaps. | |
From: Peter van Inwagen (Material Beings [1990], 18) | |
A reaction: This is the nihilist view of (inorganic) physical objects. If a wild view solves all sorts of problems, one should take it serious. It is why I take reductive physicalism about the mind seriously. (Well, it's true, actually) |