The parentheses following each definition refers to a section in which a fuller discussion may be found.
affirmative quality is a form that does not distribute its predicate. (Study 1)
affirming the consequent is a fallacy, resulting when one asserts the consequent of an implication in order to infer the antecedent as conclusion. (Study 1)
argument is a series of connected reasons in support of a position or a conclusion. (Intro)
axiom is a first principle or premise. (Study 3)
conclusion is the proposition deduced from a previous proposition or set of propositions. (Intro)
contradiction refers to the opposition between two propositions which cannot both be false together and cannot both be true together. ( Study 2)
contraposition consists in contradicting both subject and predicate terms, then interchanging them; valid for A and O, but not for I; E by limitation. (Study 2)
contraries are two propositions which cannot be both true together, but could be both false. (Study 2)
conversion is the interchange of the subject and predicate of a proposition; valid for E, I but not for O, A per accidens, or by limitation. (Study 2)
copula is the present tense of the verb to be; connects the subject and predicate. (Study 1)
denying the antecedent is a fallacy: when one denies the antecedent of an implication in order to infer the denial of the consequent as conclusion. (Study 4)
dilemma An argument form that is valid when criteria of valid or true implications of premises and a complete disjunction of the other premise are met; symbolized: (a < b) (c < d) (a + c) < (b + d). (Study 4)
disjunctive hypothetical syllogism Symbolically: Either a or b, not-a; therefore, b. (Study 4)
distribution A distributed term in a proposition is one modified by All, or No. (Study 1)
enthymeme is an argument in which one or more of the propositions is suppressed or taken for granted. (Study 3)
fallacy is a mistake in reasoning. (Study 4)
figure in a syllogism is the relative position of the middle term in the premises; there are 4 positions or 4 figures.( Study 1; Study 3)
form is the subject and predicate arrangement in a proposition; there are four forms: All a is b; No a is b; Some a is b; and Some a is not b. (Study 3)
frame is the form of a syllogism, determined by the positions of the terms in the premises and conclusion; the mood and figure of a syllogism. (Study 3)
immediate inference is an argument of one premise and a conclusion. (Study 2)
inference is the forming of a conclusion from premises by logical methods. (Intro)
law of contradiction states that the same attribute cannot at the same time belong and not belong to the same subject and in the same respect: symbolized: Not both a and not-a; or (aa')'. (Intro; Study 5)
law of excluded middle states that everything must either be or not be; symbolized: a or not-a; or (a + a'). (Intro; Study 5)
law of identity states: If any proposition is true, then it is true; symbolized: a < a. (Intro; Study 5)
logic is the science of necessary inference. (Intro)
logical connective is the part that joins simple propositions to form compound propositions; "and," "or," "not," and "implies" symbolized. (Study 5)
major premise is the premise that contains the major term. (Study 3)
major term is the predicate of the conclusion of a syllogism or an inference. (Study 3)
mediate inference See "syllogism." (Study 3)
middle term is the term which one finds in each of the premises of a syllogism, but not in the conclusion. (Study 3)
minor premise is the premise that contains the minor term. (Study 3)
minor term is the subject of the conclusion of a syllogism or an inference.( Study 3)
modus ponens means "a way of constructing;" symbolically: "If p, then q; p; therefore, q." (Study 2; Study 5)
modus tollens means "a way of destroying;" symbolically: "If p, then q; not-q; therefore,not-p. (Study 4)
mood refers to the forms of a syllogism designated by A, E, I, or O; the major premise designation comes first, followed by the designation for the minor, then the designation for the conclusion. (Study 3)
negation The law that states that every proposition is either true or false. (Study 5)
negative quality is a form that distributes its predicate. (Study 1)
nonstandard categorical proposition is a categorical other than A, E, I, and O. (Study 1)
obversion is the replacement of one form by another in which the quality of the first is changed and the predicate replaced by its contradictory or complement; by this the term No is defined by the term All. (Study 2)
particular quantity is a form that does not distribute its subject. (Study 1)
per accidens means conversion of A form to I form. (Study 3)
premise is the proposition of an argument from which a conclusion is drawn; reason intended to support a conclusion. (Intro)
proposition is a form of words in which the predicate is either affirmed or denied of the subject; the meaning expressed by a declarative sentence. (Intro)
reductio ad absurdum Also reductio ad impossible. Deducing by valid inference a conclusion you know to be false. (Study 3)
reflexive is a relationship between one of its objects and the object itself. (Study 2)
sorites is a chain of propositions: the predicate of each is the subject of the next, the conclusion consisting of the first subject and last predicate. (Study 3)
square of opposition refers to a scheme for displaying the four relationships of contrariety, subcontrariety, subalternation, and contradiction among the forms A, E, I, and O. (Study 2)
subalterns is the opposition between two propositions both alike in quality; the propositions may both be true together or both false together. (Study 2)
subcontraries are two propositions (I and O) which cannot both be false together, but could both be true. (Study 2)
syllogism is an argument of three propositions, two premises and a conclusion, with the conclusion's subject term in one of the premises, the predicate of the conclusion in the other premise, and a third term only in both premises. (Study 3)
symmetrical is a relationship which if it holds between two objects, a and b, also holds between b and a. (Study 2)
theorem is a proposition deduced from an axiom. (Study 3)
transitive is a relationship which if it holds for a and b, and also for b and c, holds as well between a and c. (Study 2)
transitive hypothetical syllogism (See "transitive.") (Study 4)
truth table A scheme for analyzing forms and relations among them. (Study 5)
universal quantity is a form that distributes it subject. (Study 1)
valid A property of arguments in which the conclusion necessarily follows from the premises; an argument is valid if the form of the conclusion is true every time the forms of the premises are true. (Intro; Study 3)
valid inference An inference is valid whenever the form of the conclusion is true every time the forms of the premises are.( Intro; Study 2)