Combining Texts

All the ideas for 'fragments/reports', 'The Foundations of Mathematics' and 'Notes on Logic'

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3 ideas

5. Theory of Logic / D. Assumptions for Logic / 2. Excluded Middle
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]
7. Existence / D. Theories of Reality / 8. Facts / d. Negative facts
22312 Facts can be both positive and negative [Wittgenstein, by Potter]
     Full Idea: In 1913 Wittgenstein was explicit that there are both positive and negative facts.
     From: report of Ludwig Wittgenstein (Notes on Logic [1913], B7) by Michael Potter - The Rise of Analytic Philosophy 1879-1930 47 'Mole'
     A reaction: This is a prelude to the Tractatus, in which negative facts are denied in T1.11 (and in a 1919 letter), but then affirmed in T2.06.
10. Modality / A. Necessity / 8. Transcendental Necessity
490 Everything happens by reason and necessity [Leucippus]
     Full Idea: Nothing happens at random; everything happens out of reason and by necessity.
     From: Leucippus (fragments/reports [c.435 BCE], B002), quoted by (who?) - where?