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E&I, A&O The statements cannot both be true and cannot both be false. Opposite truth values All dogs are mammals and Some dogs are not mammals |
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A&E The statements cannot both be true, otherwise the truth value cannot be determined. All cars are green and No cars are green |
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E&O The statements cannot both be false, otherwise the truth value cannot be determined. Some business leaders are women and Some business leaders are not women |
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| Superimplication (Subaltern) |
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| In reference to the Square, truth goes down and falsity goes up, otherwise the resultant truth value cannot be determined. The superaltern implies the subaltern. More precisely, | | | | If the superaltern is true, then the subaltern is true. | | | | If the superaltern is false, then the subaltern is undetermined. | | | | If the subaltern is true, then the superaltern is undetermined. | | | | If the subaltern is false, then the superaltern is false. All cars are green and No cars are green |
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Universal Affirmative All S is P |
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Universal Negative No S is P |
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Particular Affirmative Some S is P |
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Particular Negative Some S is non-P |
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interchanging the subject and predicate terms of a categorical proposition (it is valid, or preserves the truth value) for the E and I propositions only) No snakes are mammals and No mammals are snakes |
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changing the quality and replacing the predicate term with its complementary class (valid, or preserves truth value for all propositions--the A, E, I, and O). All lizards are reptiles and No lizards are non-reptiles No spiders are insects and All spiders are non-insects |
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replacing the subject term by the complement of its predicate term and replace the predicate term by the complement of its subject term (valid, or preserves truth value only for the A and O propositions). All voters are citizens and All non-citizens are non-voters |
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| all knowledge is derived from experience; John Locke |
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| reality is only mind & spirit; Hegel |
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| reality is matter in motion; Karl Marx |
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derived from the idea of being, not by observation; St. Anslem |
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| appeals to observation/senses |
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| reality and god are the same |
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| separation of philosophical and theological |
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| no final truth, approach all things with doubt |
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an object with both form and matter |
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