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Single Idea 9405

[filed under theme 4. Formal Logic / A. Syllogistic Logic / 1. Aristotelian Logic ]

Full Idea

Square of Opposition: horizontals - 'contraries' can't both be true, and 'subcontraries' can't both be false; verticals - 'subalternatives' have downwards-only implication; diagonals - 'contradictories' have opposite truth values.

Gist of Idea

Square of Opposition: not both true, or not both false; one-way implication; opposite truth-values

Source

Aristotle (On Interpretation [c.330 BCE], Ch.12-13)

Book Ref

Aristotle: 'Categories and De Interpretatione', ed/tr. Ackrill,J.R. [OUP 1963], p.62

A Reaction

This is still used in modern discussion (e.g. by Stalnaker against Kripke), and there is a modal version of it (Fitting and Mendelsohn p.7). Corners read: 'All F are G', 'No F are G', 'Some F are G' and 'Some F are not G'.

Related Idea

Idea 15879 The Square of Opposition has two contradictory pairs, one contrary pair, and one sub-contrary pair [Harré]

The 19 ideas from 'On Interpretation'

22272 Aristotle's later logic had to treat 'Socrates' as 'everything that is Socrates' [Potter on Aristotle]
2337 For Aristotle meaning and reference are linked to concepts [Aristotle, by Putnam]
13763 Spoken sounds vary between people, but are signs of affections of soul, which are the same for all [Aristotle]
1701 A prayer is a sentence which is neither true nor false [Aristotle]
1702 Things may be necessary once they occur, but not be unconditionally necessary [Aristotle]
1703 It is necessary that either a sea-fight occurs tomorrow or it doesn't, though neither option is in itself necessary [Aristotle]
21593 In talking of future sea-fights, Aristotle rejects bivalence [Aristotle, by Williamson]
1704 Statements are true according to how things actually are [Aristotle]
1705 It doesn't have to be the case that in opposed views one is true and the other false [Aristotle]
1706 Non-existent things aren't made to exist by thought, because their non-existence is part of the thought [Aristotle]
1707 Maybe necessity and non-necessity are the first principles of ontology [Aristotle]
1708 In "Callias is just/not just/unjust", which of these are contraries? [Aristotle]
9405 Square of Opposition: not both true, or not both false; one-way implication; opposite truth-values [Aristotle]
9728 Modal Square 1: □P and ¬◊¬P are 'contraries' of □¬P and ¬◊P [Aristotle, by Fitting/Mendelsohn]
9729 Modal Square 2: ¬□¬P and ◊P are 'subcontraries' of ¬□P and ◊¬P [Aristotle, by Fitting/Mendelsohn]
9730 Modal Square 3: □P and ¬◊¬P are 'contradictories' of ¬□P and ◊¬P [Aristotle, by Fitting/Mendelsohn]
9731 Modal Square 4: □¬P and ¬◊P are 'contradictories' of ¬□¬P and ◊P [Aristotle, by Fitting/Mendelsohn]
9732 Modal Square 5: □P and ¬◊¬P are 'subalternatives' of ¬□¬P and ◊P [Aristotle, by Fitting/Mendelsohn]
9733 Modal Square 6: □¬P and ¬◊P are 'subalternatives' of ¬□P and ◊¬P [Aristotle, by Fitting/Mendelsohn]