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Specifically, it has the first proposition universal and affirmative, but the second and third particular and negative, and the middle term the attribute in the two first. For example, Every virtue is attended with discretion. Some kinds of zeal are not attended with discretion. Therefore, some kinds of zeal are not virtues.
Examples of these are the universal affirmative 'every man is white', and the universal negative 'no man is white'. These cannot be true at the same time. However, these are not contradictories because both of them may be false. For example, it is false that every man is white, since some men are not white.
For example, by obversion, a universal affirmative statement become a universal negative statement with the predicate term that is the class complement of the predicate term of the original universal affirmative statement.
A universal affirmative proposition ("Every man is mortal") and the non-universal denial of that proposition in a way ("Some men are not mortal") are called contradictories. Of contradictories, one must be true, the other false. Contraries cannot both be true, although they can both be false, and hence their contradictories are both true.
The syllogism is an inference in which one proposition (the "conclusion") follows of necessity from two other propositions (the "premises"). A proposition may be universal or particular, and it may be affirmative or negative. Traditionally, the four kinds of propositions are: A-type: Universal and affirmative ("All philosophers are mortal")
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The immediately inferred proposition is termed the "obverse" of the original proposition, and is a valid form of inference for all types (A, E, I, O) of categorical propositions. In a universal affirmative and a universal negative proposition the subject term and the predicate term are both replaced by their negated counterparts:
The U.S. Supreme Court's landmark decision Thursday striking down affirmative action has intensified angst among many higher education leaders who say extending access to a diversity of students ...