Chapter 9 Glossary
This alphabetical glossary contains short definitions for all the important terms and concepts from the chapter. You will also find hyperlinks to Websites relevant to the study of these terms and concepts. You should employ good critical thinking when evaluating the merit of any information you find on the World Wide Web, including what you find by following these links.
A-claim: A categorical claim of the form "All S are P." (Mnemonic: "All" begins with "A.")
Affirmative claim: A claim that includes one class within the other; and A- or I-claim.
Categorical claim: The study of relations among categories or groups of things. Categorical logic treats categorical claims.
Categorical syllogism: A syllogism in which both premises and the conclusion are categorical claims, and in which three terms appear. Each term appears exactly twice, once in each of exactly two claims.
Complementary term: A term naming everything not in the class named by another term. If "T" is the term, "non-T" is the complementary term.
Contradictory claims: Two corresponding claims that fall into one of these pairs: Either one is an A-claim and the other and O-claim, or one is an E-claim and the other an I-claim. Contradictory claims have opposite truth values, so that if one is true the other is false.
Contrapositive: A claim formed by switching the subject and predicate terms of a categorical claim, and replacing both by their complementary terms. A- and O-claims are equivalent to their contrapositives.
Contrary claims: Two corresponding claims, of which one is an A-claim and the other an E-claim. Contrary claims are never both true.
Converse: A claim formed by switching subject and predicate terms of a categorical claim. E- and I-claims are equivalent to their converses.
Corresponding claims: Two or more standard-form categorical claims possessing the same subject term and the same predicate term.
Distributed term: In a categorical claim, a term of which the claim asserts something true of all members of the class named.
E-claim: A categorical claim of the form "No S are P." (Mnemonic: "E" means that a set is being called "empty.")
I-claim: A categorical claim of the form "Some S are P." "Some" here may mean as few as one, or as many as all. Thus in categorical logic, "Some ants are biters" does not contradict the claim "All ants are biters"; and it is fully compatible with the claim "Most ants are biters." (Mnemonic: The "I" refers to a claim that speaks of at least one "individual.")
Major term: In a categorical syllogism, the predicate term of the conclusion; symbolized by P.
Middle term: In a categorical syllogism, the term appearing in both premises but not in the conclusion.
Minor term: In a categorical syllogism, the subject term of the conclusion; symbolized by S.
Negative claim: A claim that excludes one class from the other; and E- or O-claim. Negative claims in standard form either begin with a "no" or contain a "not."
O-claim: A categorical claim of the form "Some S are not P." Note the meaning of "some" discussed under "I-claim." (Mnemonic: The claim "Some S are not P" contains more Os than any other.)
Obverse: A claim formed by changing a categorical claim from affirmative to negative (or vice versa), and replacing the predicate term with its complementary term. All claims are equivalent to their obverses.
Predicate term: The second term in a standard-form claim. Note that the predicate term often cannot be identified until the categorical claim has been written in standard form.
Square of opposition: A diagram that shows the logical relations among all corresponding categorical claims. there are three such relations: contrary, subcontrary, and contradictory.
Standard-form categorical claim: A categorical claim written so as to belong clearly to one of the four groups: A-, E-, I-, and O-claims. The subject and predicate terms must either be nouns or noun phrases.
Subcontrary claims: Two corresponding claims, of which one is an I-claim and the other an O-claim. Subcontrary claims are never both false.
Subject term: The first term in a standard-form claim. Note that the subject term often cannot be identified until the categorical claim has been written in standard form.
Syllogism: A deductive argument with two premises.
Term: A noun or noun phrase functioning as either the subject term or the predicate term of a categorical claim.
Venn diagram: A diagram for illustrating categorical claims, or for testing the validity of categorical syllogisms.
General Categorical Logic Web links:
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