Information AboutBoole's Syllogistic |
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In Boolean logic, the universal statements "all S is P" and "no S is P" (contraries in the traditional Aristotelian schema) are compossible provided that the set of "S" is the empty set. "All S is P" is construed to mean that "there is nothing that is both S and not-P"; "no S is P", that "there is nothing that is both S and P". For example, since there is nothing that is a round square, it is true both that nothing is a round square and purple, and that nothing is a round square and ''not''-purple. Therefore, both universal statements, that "all round squares are purple" and "no round squares are purple" are true. Similarly, the sub-contrary relationship is dissolved between the existential statements "some S is P" and "some S is not P". The former is interpreted as "there is some S such that S is P" and the latter, "there is some S such that S is not P", both of which are clearly false where S is nonexistent. Thus, the sub-altern relationship between universal and existential also does not hold, since for a nonexistent S, "All S is P" is true but does not entail "Some S is P", which is false. Of the Aristotelian Square Of Opposition , only the contradictory relationships remain intact. SEE ALSO |
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