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2 ideas
| 18844 | You would cripple mathematics if you denied Excluded Middle [Hilbert] |
| Full Idea: Taking the principle of Excluded Middle away from the mathematician would be the same, say, as prohibiting the astronomer from using the telescope or the boxer from using his fists. | |
| From: David Hilbert (The Foundations of Mathematics [1927], p.476), quoted by Ian Rumfitt - The Boundary Stones of Thought 9.4 | |
| A reaction: [p.476 in Van Heijenoort] |
| 6023 | 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. |