Logic Vocabulary Definitions

(Knowing the definitions of these terms is critical - both to understanding the concepts and to passing logic tests!)

logic - the science and art of reason

statement - a sentence which is true or false (has a truth value)

inductive logic - draws conclusions based on observations or experiences; conclusions are never certain, only strong or weak

deductive logic - deals with arguments that are valid or invalid; conclusions are certain, given the premises are true

Law of Excluded Middle - excludes the possibility of truth value between true and false

Law of Identity - if a statement is true, then it is true

Law of Noncontradiction - a statement cannot be both true and false

self-supporting statement - a statement which has an immediately apparent truth value (determination of truth or falsity does not require additional information); self-supporting statements are self-reports, true or false by definition, or true or false by logical structure

self-report - statement concerning ones own desires, beliefs, or feelings

tautology - statement which is true by logical structure

self-contradiction - statement which is false by logical structure

supported statements - statements which require proof to determine truth or falsity

consistency - statements are consistent when they can be true at the same time

implication - occurs when the truth of the first statement implies the truth of the second

logical equivalence - occurs when the truth of the first statement implies the truth of the second and the second implies the first

independence - the truth or falsity of one statement does not affect the truth or falsity of the other

real disagreement - true inconsistency

apparent disagreement - result of a difference of opinion or perception (self-report)

verbal disagreement - result of different definitions being understood

categorical statement - affirms or denies something about a given subject

contradiction - both statements cannot be true or false

contrariety - both statements may be false, but both cannot be true

subcontrariety - both statements may be true, but both cannot be false

A statement - all S are P

E statement - no S are P

I statement - some S are P

O statement - some S are not P

subimplication - the truth of a particular statement is inferred from the truth of the universal

superimplication - the implication of falsity of a particular to the falsity of the universal

argument - a set of statements, one of which appears to be implied or supported by the others

premise - a statement which supports or implies the conclusion

validity - the conclusion is necessarily true if the premises are true

minor term - the subject term of the conclusion

major term - the predicate term of the conclusion

middle term - term in both premises, but not in the conclusion

syllogism - an argument with two premises and three terms

schema - the representation of a syllogism arranged in standard order by abbreviations for the terms.

mood of a syllogism - refers to the combination of A, E, I, and O statements in a syllogism

figure of a syllogism - identifies the placement of the middle term

counterexample - a syllogism made up of the same form as original argument, but with obviously true premises and false conclusion to prove the form invalid

distributed term - a term which refers to all members of its class

Fallacy of the Undistributed Middle - committed when a syllogism does not have a distributed middle term in at least one premise

Fallacy of an Illicit Major/Minor - committed when the major or minor term of a syllogism is distributed in its conclusion but not in its premise

Fallacy of a Negative Premise and an Affirmative Conclusion - committed when a syllogism contains a negative premise and an affirmative conclusion

Fallacy of Two Affirmative Premises and a Negative Conclusion - committed when a syllogism contains two affirmative premises and a negative conclusion

Fallacy of Two Negative Premises - committed when a syllogism contained two negative premises

immediate inference - a statement which can be inferred directly from another statement

converse - switches subject and predicate of a statement

obverse - changes the quality and changes the predicate to its complement

contrapositive - switches subject and predicate and switches each to their complements

singular statement - statement referring to a single person or thing, usually translated as universal

indefinite statements - statements referring to a few people or things, usually translated as particular

hypothetical statements - statements using if. . .then language

parameters - limits or boundaries in a statement, such as whoever, whatever, whenever, however, always, never

enthememes - arguments in which a statement is left assumed

antecedent - categorical statement following if

consequent - categorical statement following then

pure hypothetical syllogism - syllogism whose arguments use only hypotheticals

mixed hypothetical syllogism - syllogism combining hypothetical and categorical statements

modus ponens - if P then Q. P, therefore Q

modus tollens - if P then Q. ~Q therefore ~P

asserting the consequent - if P then Q. Q therefore P

denying the antecedent - if P then Q. ~P therefore ~Q

Source: Wilson & Nance.  Introductory Logic 3rd Ed. Canon Press, 2002.