Argument: a group of sentences put together in such a way that some of them (the premises) are given as the reasons for accepting another one of them (the conclusion).
Categorical Argument: an argument composed of categorical sentences. A categorical syllogism has two premises while a sorites has more than two premises.
Categorical Sentence: a sentence composed of a quantifier, a subject term, a copula, and a predicate term.
Category: a class or set of things.
Complementary Term: (See Term.)
Conclusion: (See Argument.)
Conversion: The switching of the subject and predicate terms in a sentence.
Copula: The "are" or "are not" connecting the subject and predicate terms in a categorical sentence.
Domain of Discourse: The realm to which the logic is being applied.
Equivalent Sentences: Categorical sentences are equivalent if they have the same terms or complements of the same terms and always have the same truth value. They are presented in the Tutorial as different ways of expressing the same proposition.
Exception: (See Numerically Expanded Logic.)
Existential Presupposition: The assumption that the category to which a term refers contains members. If it is assumed for term A's category it can be entered as a premise as "Some A are A"; or in the numerically expanded logic the assumption that A has at least 20 members can be premised as "At least none but 20 A are A."
Extreme Term: (See Term.)
Middle Term: (See Term.)
Nonstandard Form: (See Standard Form.)
Numerically Expanded Logic: Extensions of the traditional logic to cover numerically flexible quantifiers. In the logic represented by ReasonLines, "all" and "none" are extended to include "all but x" and "none but x," where the exception, x, is a nonnegative, whole number.
Particular: Pertaining to categorical sentences whose quantifier is "some"; also used in the numerically expanded logic for sentences whose quantifier is "At least none but x" and "At most all but x."
Predicate: (See Term.)
Proposition: A categorical proposition is that which is asserted by any group of four equivalent categorical sentences; that is, one and the same proposition is that which each equivalent statement expresses.
Quality: The affirmative or negative feature of a sentence.
Quantifier: The part of a categorical statement that precedes the subject term.
Quantity: The universal or particular feature of a sentence or proposition.
Schematic: an arrow between terms depicting a statement (or double-ended arrow depicting two equivalent statements), or an arrangement of arrows connecting two terms and their complements depicting a proposition, or a succession of proposition schematics depicting a categorical argument.
Sorites: (See Categorical Argument.)
Standard Form: An argument is in standard form if it does not use a term and also that term's complement in its sentences. If it does, it is in nonstandard form.
Syllogism: (See Categorical Argument.)
Tautology: A statement framed in such a way that it cannot be false.
Term: That part of a categorical sentence that refers to a class or category of things. In a sentence the subject term precedes the copula while the predicate term follows the copula. In an argument, a middle term occurs twice in the premise(s) but not in the conclusion while an extreme term occurs once in a premise and once in the conclusion. Together a term and its complement, like A and nonA, refer to everything in the domain of discourse.
Universal: Pertaining to categorical sentences whose quantifier is "All" or "No"; also used in the numerically expanded logic for sentences whose quantifier is "At least all but x" or "At most none but x."
Valid: An argument form is valid if its premises entail its conclusion. And this is the case if it is impossible to replace its variables, A, B, C, etc., with words that make its premises true at the same time it makes its conclusion false. But if such a replacement is possible, then the form is invalid.