One of the mysteries of the English language finally explained.
Denoting propositions which can both be true, but cannot both be false (e.g. some X are Y and some X are not Y).
- ‘The particular statements: I and O are subcontrary: ‘Some S are P’ and ‘Some S are not P’ can be true, but both cannot be false.’
- ‘It follows that high or low probability are contrary to necessity of opposite polarity, and subcontrary to possibility of opposite polarity.’
- ‘In traditional logic the I and O statements are considered subcontrary to one another; in other words, they can both be true at the same time, but cannot both be false.’
- ‘Similarly, ‘some unicorns have horns’ and ‘some unicorns do not have horns’ are both regarded as false, and so they are not subcontrary.’’
- ‘Paradox seems to arise when conditional statements have subcontrary statements as antecedent and consequent.’
A subcontrary proposition.
- ‘Again, I and O propositions are subcontrary, but not contrary or contradictory.’
- ‘The case of subcontraries will be revealed to include an unjustified presupposition in the section concerning the modern square of opposition.’
- ‘Given that traditional logicians did think the subcontraries have ‘existential import’, how do we resolve the apparent contradiction?’
- ‘Particular statements are subcontraries. ‘Some man is just’ and ‘some man is not just’ cannot be false together’
Late 16th century: from late Latin subcontrarius, translation of Greek hupenantios.
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