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
selfsupporting statement  a statement which has an immediately apparent truth value (determination of truth or falsity does not require additional information); selfsupporting statements are selfreports, true or false by definition, or true or false by logical structure
selfreport  statement concerning ones own desires, beliefs, or feelings
tautology  statement which is true by logical structure
selfcontradiction  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 (selfreport)
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.
