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15102 | S4 says there must be some necessary truths (the actual ones, of which there is at least one) [Cameron] |
Full Idea: S4 says there must be some necessary truths, because the actual necessary truths must be necessary. (It says if there are some actual necessary truths then that is so - but the S4 axiom is an actual necessary truth, if true). | |
From: Ross P. Cameron (On the Source of Necessity [2010], 2) |
18170 | The Axiom of Reducibility is self-effacing: if true, it isn't needed [Quine] |
Full Idea: The Axiom of Reducibility is self-effacing: if it is true, the ramification it is meant to cope with was pointless to begin with. | |
From: Willard Quine (Introduction to Russell's Theory of Types [1967], p.152), quoted by Penelope Maddy - Naturalism in Mathematics I.1 | |
A reaction: Maddy says the rejection of Reducibility collapsed the ramified theory of types into the simple theory. |