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Full Idea
All pairs of contraries entail a pair of contradictories, since one member of such a pair always entails the negation of the other. P&Q and not-P are contraries, but the first entails P, which is contradictory of not-P.
Gist of Idea
Contrary pairs entail contradictions; one member entails negation of the other
Source
Peter Lipton (Inference to the Best Explanation (2nd) [2004], 09 'Is the best')
Book Ref
Lipton,Peter: 'Inference to the Best Explanation (2nd ed)' [Routledge 2004], p.156
| 192 | Only one thing can be contrary to something [Plato] |
| 1697 | The contrary of good is bad, but the contrary of bad is either good or another evil [Aristotle] |
| 1698 | Both sides of contraries need not exist (as health without sickness, white without black) [Aristotle] |
| 24052 | From one thing alone we can infer its contrary [Aristotle] |
| 4333 | Contraries are by definition as far distant as possible from one another [Aristotle] |
| 1708 | In "Callias is just/not just/unjust", which of these are contraries? [Aristotle] |
| 608 | There is no middle ground in contradiction, but there is in contrariety [Aristotle] |
| 1684 | Two falsehoods can be contrary to one another [Aristotle] |
| 16854 | Contrary pairs entail contradictions; one member entails negation of the other [Lipton] |