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In Aristotle's term logic there are two logical qualities: affirmation (kataphasis) and denial (apophasis). The logical quality of a proposition is whether it is affirmative (the predicate is affirmed of the subject) or negative (the predicate is denied of the subject). Thus "every man is a mortal" is affirmative, since "mortal" is affirmed of ...
Obversion changes the quality (that is the affirmativity or negativity) of the statement and the predicate term. [10] 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.
The affirmative, in an English example such as "the police chief here is a woman", declares a simple fact, in this case, it is a fact regarding the police chief and asserts that she is a woman. [5] In contrast, the negative, in an English example such as "the police chief here is not a man", is stated as an assumption for people to believe. [5]
In traditional logic, the process of negating the predicate of a categorical proposition and changing its quality (affirmative to negative, or vice versa) without altering its truth value. obversion The operation of forming the obverse of a categorical proposition, resulting in an equivalent statement with a negated predicate and opposite quality.
Subalternation is a relation between the particular statement and the universal statement of the same quality (affirmative or negative) such that the particular is implied by the universal, while superalternation is a relation between them such that the falsity of the universal (equivalently the negation of the universal) is implied by the ...
a: All A is B. (affirmative) e: No A is B. (negative) i: Some A is B. (affirmative) o: Some A is not B. (negative) The rule states that a syllogism in which both premises are of form a or i (affirmative) cannot reach a conclusion of form e or o (negative). Exactly one of the premises must be negative to construct a valid syllogism with a ...
Expressed in symbolic terms, . In intuitionistic logic, a proposition implies its double negation, but not conversely. This marks one important difference between classical and intuitionistic negation. Algebraically, classical negation is called an involution of period two.
The key to understanding the former examples and knowing whether a double negative is intensive or negative is finding a verb between the two negatives. If a verb is present between the two, the latter negative becomes an intensifier which does not negate the former.