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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]
| 639 | Socrates developed definitions as the basis of syllogisms, and also inductive arguments [Socrates, by Aristotle] |
| 22272 | Aristotle's later logic had to treat 'Socrates' as 'everything that is Socrates' [Potter on Aristotle] |
| 9405 | Square of Opposition: not both true, or not both false; one-way implication; opposite truth-values [Aristotle] |
| 22271 | Aristotle was the first to use schematic letters in logic [Aristotle, by Potter] |
| 11060 | Aristotelian syllogisms are three-part, subject-predicate, existentially committed, with laws of thought [Aristotle, by Hanna] |
| 18909 | Aristotelian sentences are made up by one of four 'formative' connectors [Aristotle, by Engelbretsen] |
| 8080 | Aristotelian identified 256 possible syllogisms, saying that 19 are valid [Aristotle, by Devlin] |
| 13912 | Aristotle replaced Plato's noun-verb form with unions of pairs of terms by one of four 'copulae' [Aristotle, by Engelbretsen/Sayward] |
| 8071 | Aristotle listed nineteen valid syllogisms (though a few of them were wrong) [Aristotle, by Devlin] |
| 18953 | Modern notation frees us from Aristotle's restriction of only using two class-names in premises [Putnam] |
| 13643 | Aristotelian logic is complete [Shapiro] |
| 23505 | Aristotelian logic cannot express 'Everyone loves someone' [White,RM] |
| 13913 | The four 'perfect syllogisms' are called Barbara, Celarent, Darii and Ferio [Engelbretsen/Sayward] |
| 13914 | Syllogistic logic has one rule: what is affirmed/denied of wholes is affirmed/denied of their parts [Engelbretsen/Sayward] |
| 18913 | Traditional term logic struggled to express relations [Engelbretsen] |