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2 ideas
18832 | Mathematical statements and entities that result from an infinite process must lack a truth-value [Dummett] |
Full Idea: On an intuitionistic view, neither the truth-value of a statement nor any other mathematical entity can be given as the final result of an infinite process, since an infinite process is precisely one that does not have a final result. | |
From: Michael Dummett (Elements of Intuitionism (2nd ed) [2000], p.41), quoted by Ian Rumfitt - The Boundary Stones of Thought 7.3 | |
A reaction: This is rather a persuasive reason to sympathise with intuitionism. Mathematical tricks about 'limits' have lured us into believing in completed infinities, but actually that idea is incoherent. |
7035 | God does not create the world, and then add the classes [Heil] |
Full Idea: It is hard to see classes as an 'addition of being'; God does not create the world, and then add the classes. | |
From: John Heil (From an Ontological Point of View [2003], 13.4 n6) | |
A reaction: This seems right. We may be tempted into believing in the reality of classes when considering maths, but it seems utterly implausible when considering trees or cows. |