Glossary

Argument   A piece of reasoning in which one statement (the conclusion) is supported by other statements (the premises).

Axiom   A statement that is assumed to be true without proof.

Conclusion   A statement in an argument that is supported by premises.

Deductive argument   An argument in which the conclusion is presented as following with necessity from the premises.

Fallacy   An error in reasoning.

Fuzzy logic   A type of logic that rejects the classical two values T and F and replaces them with unit intervals.

Inductive argument   An argument in which the conclusion is presented as following with a high probability from the premises.

Intuition   What seems to be the case; noninferential belief; what we would say in a given situation.

Logic   The study of the methods and principles for distinguishing good reasoning from bad.

Paradox    A set of mutually inconsistent propositions, each of which seems true; an argument with seemingly true premises, seemingly good reasoning, and an obviously false or contradictory conclusion; an unacceptable conclusion derived from seemingly true premises and apparently valid reasoning.

Premise   A statement offered in support of a conclusion.

Soundness   A deductive argument is sound when its premises are true and the argument is valid.

Syllogism    A two-premise deductive argument that employs three main terms major, minor, and middle. The major term is the predicate term of the conclusion. The minor term is the subject term of the conclusion. The middle term occurs in each premise but not the conclusion. For example, consider the following deductive argument:

1. All men are mortal.

2. Socrates is a man.

3. Socrates is mortal.

Mortal is the major term, man is the middle term, and Socrates is the minor term. Every syllogism has a major premise that contains the major term and a minor premise that contains the minor term. In this case, (1) is the major premise and (2) is the minor premise.

Subjective probability    The degree to which one believes something.

Validity   A deductive argument is valid when it is impossible for its premises to be true and its conclusion false; in a valid deductive argument, the premises fully support the conclusion.