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Ideas for 'fragments/reports', 'The Epic of Gilgamesh' and 'Philosophy of Mathematics'

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2 ideas

5. Theory of Logic / D. Assumptions for Logic / 2. Excluded Middle
Every proposition is either true or false [Chrysippus, by Cicero]
     Full Idea: We hold fast to the position, defended by Chrysippus, that every proposition is either true or false.
     From: report of Chrysippus (fragments/reports [c.240 BCE]) by M. Tullius Cicero - On Fate ('De fato') 38
     A reaction: I am intrigued to know exactly how you defend this claim. It may depend what you mean by a proposition. A badly expressed proposition may have indeterminate truth, quite apart from the vague, the undecidable etc.
The law of excluded middle might be seen as a principle of omniscience [Shapiro]
     Full Idea: The law of excluded middle might be seen as a principle of omniscience.
     From: Stewart Shapiro (Philosophy of Mathematics [1997], 6.3)
     A reaction: [E.Bishop 1967 is cited] Put that way, you can see why a lot of people (such as intuitionists in mathematics) might begin to doubt it.