| affirmative claim | A claim that includes one class or part of one class within another: A- and I-claims.
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| categorical claim | Any standard-form categorical claim or any claim that means the same as some standard-form categorical claim. See standard-form categorical claim.
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| categorical logic | A system of logic based on the relations of inclusion and exclusion among classes ("categories"). This branch of logic specifies the logical relationships among claims that can be expressed in the forms "All Xs are Ys," "No Xs are Ys," "Some Xs are Ys," and "Some Xs are not Ys." Developed by Aristotle in the fourth century B.C.E., categorical logic is also known as Aristotelian or traditional logic.
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| categorical syllogism | A two-premise deductive argument in which every claim is categorical and each of three terms appears in two of the claims--for example, all soldiers are martinets and no martinets are diplomats, so no soldiers are diplomats.
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| complementary term | A term is complementary to another term if and only if it refers to everything that the first term does not refer to.
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| contradictory claims | Two claims that are exact opposites--that is, they could not both be true at the same time and could not both be false at the same time.
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| contrapositive | The claim that results from switching the places of the subject and predicate terms in a claim and replacing both terms with complementary terms.
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| contrary claims | Two claims that could not both be true at the same time but could both be false at the same time.
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| converse | The converse of a categorical claim is the claim that results from switching the places of the subject and predicate terms.
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| equivalent claims | Two claims are equivalent if and only if they would be true in all and exactly the same circumstances.
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| negative claim | A claim that excludes one class or part of one class from another: E- and O-claims.
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| obverse | The obverse of a categorical claim is that claim that is directly across from it in the square of opposition, with the predicate term changed to its complementary term.
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| predicate term | The noun or noun phrase that refers to the second class mentioned in a standard-form categorical claim.
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| square of opposition | A table of the logical relationships between two categorical claims that have the same subject and predicate terms.
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| standard-form categorical claim | Any claim that results from putting words or phrases that name classes in the blanks of one of the following structures: "All ____ are _____"; "No _____ are _____"; "Some _____ are _____"; and "Some _____ are not _____."
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| subcontrary claims | Two claims that can both be true at the same time but cannot both be false at the same time.
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| subject term | The noun or noun phrase that refers to the first class mentioned in a standard-form categorical claim.
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| syllogism | A deductive argument with two premises.
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| term | A word or an expression that refers to or denotes something.
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| Venn diagram | A graphic means of representing a categorical claim or categorical syllogism by assigning classes to overlapping circles. Invented by English mathematician John Venn (1834-1923).
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