Combining Texts

Ideas for 'On Interpretation', 'On Propositions: What they are, and Meaning' and 'A Powerful Particulars View of Causation'

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6 ideas

4. Formal Logic / D. Modal Logic ML / 1. Modal Logic
9728 Modal Square 1: □P and ¬◊¬P are 'contraries' of □¬P and ¬◊P [Aristotle, by Fitting/Mendelsohn]
     Full Idea: Modal Square of Opposition 1: 'It is necessary that P' and 'It is not possible that not P' are the contraries (not both true) of 'It is necessary that not P' and 'It is not possible that P'.
     From: report of Aristotle (On Interpretation [c.330 BCE], Ch.12a) by M Fitting/R Mendelsohn - First-Order Modal Logic 1.4
9729 Modal Square 2: ¬□¬P and ◊P are 'subcontraries' of ¬□P and ◊¬P [Aristotle, by Fitting/Mendelsohn]
     Full Idea: Modal Square of Opposition 2: 'It is not necessary that not P' and 'It is possible that P' are the subcontraries (not both false) of 'It is not necessary that P' and 'It is possible that not P'.
     From: report of Aristotle (On Interpretation [c.330 BCE], Ch.12b) by M Fitting/R Mendelsohn - First-Order Modal Logic 1.4
9730 Modal Square 3: □P and ¬◊¬P are 'contradictories' of ¬□P and ◊¬P [Aristotle, by Fitting/Mendelsohn]
     Full Idea: Modal Square of Opposition 3: 'It is necessary that P' and 'It is not possible that not P' are the contradictories (different truth values) of 'It is not necessary that P' and 'It is possible that not P'.
     From: report of Aristotle (On Interpretation [c.330 BCE], Ch.12c) by M Fitting/R Mendelsohn - First-Order Modal Logic 1.4
9731 Modal Square 4: □¬P and ¬◊P are 'contradictories' of ¬□¬P and ◊P [Aristotle, by Fitting/Mendelsohn]
     Full Idea: Modal Square of Opposition 4: 'It is necessary that not P' and 'It is not possible that P' are the contradictories (different truth values) of 'It is not necessary that not P' and 'It is possible that P'.
     From: report of Aristotle (On Interpretation [c.330 BCE], Ch.12d) by M Fitting/R Mendelsohn - First-Order Modal Logic 1.4
9732 Modal Square 5: □P and ¬◊¬P are 'subalternatives' of ¬□¬P and ◊P [Aristotle, by Fitting/Mendelsohn]
     Full Idea: Modal Square of Opposition 5: 'It is necessary that P' and 'It is not possible that not P' are the subalternatives (first implies second) of 'It is not necessary that not P' and 'It is possible that P'.
     From: report of Aristotle (On Interpretation [c.330 BCE], Ch.12e) by M Fitting/R Mendelsohn - First-Order Modal Logic 1.4
9733 Modal Square 6: □¬P and ¬◊P are 'subalternatives' of ¬□P and ◊¬P [Aristotle, by Fitting/Mendelsohn]
     Full Idea: Modal Square of Opposition 6: 'It is necessary that not P' and 'It is not possible that P' are the subalternatives (first implies second) of 'It is not necessary that P' and 'It is possible that not P'.
     From: report of Aristotle (On Interpretation [c.330 BCE], Ch.12f) by M Fitting/R Mendelsohn - First-Order Modal Logic 1.4