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The subject of one premise, must be the predicate of the other, and so it is necessary to eliminate from the logic any terms which cannot function both as subject and predicate, namely singular terms. However, in a popular 17th-century version of the syllogism, Port-Royal Logic, singular terms were treated as universals: [12] All men are mortals
In the picture, the blue pattern term matches the black subject term at position 1, with the matching substitution { x ↦ a, y ↦ a+1, z ↦ a+2 } indicated by blue variables immediately left to their black substitutes. Intuitively, the pattern, except for its variables, must be contained in the subject; if a variable occurs multiple ...
The premise in a syllogism that includes the minor term, which is the subject of the conclusion. minor term The term that appears as the subject in the conclusion of a syllogism. modal actualism The philosophical position that only actual, existing objects are possible, denying the existence of merely possible objects. modal agnosticism
In logic, a categorical proposition, or categorical statement, is a proposition that asserts or denies that all or some of the members of one category (the subject term) are included in another (the predicate term). [1]
In Aristotelian logic, the subject can be universal, particular, indefinite, or singular. For example, the term "all humans" is a universal subject in the proposition "all humans are mortal". A similar proposition could be formed by replacing it with the particular term "some humans", the indefinite term "a human", or the singular term "Socrates".
More modern logicians allow some variation. Each of the premises has one term in common with the conclusion: in a major premise, this is the major term (i.e., the predicate of the conclusion); in a minor premise, this is the minor term (i.e., the subject of the conclusion). For example:
In traditional logic, obversion is a "type of immediate inference in which from a given proposition another proposition is inferred whose subject is the same as the original subject, whose predicate is the contradictory of the original predicate, and whose quality is affirmative if the original proposition's quality was negative and vice versa". [1]
The term "logical form" itself was introduced by Bertrand Russell in 1914, in the context of his program to formalize natural language and reasoning, which he called philosophical logic. Russell wrote: "Some kind of knowledge of logical forms, though with most people it is not explicit, is involved in all understanding of discourse.