Glossary

ambiguity	Ambiguity is the condition of having more than one interpretation or meaning. There are two basic ways in which ambiguity can arise. The first is lexical ambiguity or equivocation, in which a word or phrase has more than one lexical definition and so can be understood in more than one way. Alternatively, two different words that look or sound the same may become confused and lead to fallacious inference. The second basic way ambiguity can arise is structural ambiguity or amphiboly, in which a string of words in a sentence has more than one legitimate grammatical interpretation and so can be understood in more than one way.
antecedent	A conditional statement asserts a relation between two statements of which it is made stating that if the antecedent (first) statement is true, then the consequent (second) statement is also true. For example, in the conditional statement “If it is raining, then you will get wet,” “it is raining” is the antecedent, and “you will get wet” is the consequent.
appeal to tradition	In the fallacy of the appeal to tradition, the fact that a social or cultural practice has been done a certain way in the past is taken to be reason for it to be done in the future.
argument	An argument in the broad sense is a social exchange between several reasoners who advance claims and then support them with reasons. In a narrow sense, argument is a set of statements in which it is claimed that the truth or likelihood of the premises support the conclusion.
argument pattern	Logical arguments usually occur in characteristic patterns. These patterns represent the formal relationships that the premises have with each other in light of which they support the conclusion. An argument pattern is a formal structure that many different arguments fit.
categorical logic	This is the traditional logic of terms, developed by Aristotle, covering a theory of the syllogism and a theory of immediate inference.
chained enthymeme	A chain argument (or chained enthymeme) is two or more arguments that are joined together by one or more implicit statements that form the conclusion of one argument and a premise in the next.
claim	The claim is the assertion of a sentence; the claim that it is true.
classification	Classification is a kind of division according to a rule: a group of individuals is divided into subgroups by a rule that sorts them by a set of common properties.
complement	The complement of a class is everything in the universe of discourse that is not a member of that class.
conclusion	A claim or statement made in an argument that its premises are intended to support. The aim of giving an argument is to rationally persuade an audience that a conclusion is true or likely if its premises are.
conditional statement	A conditional statement asserts a relation between two statements of which it is composed, stating that if the antecedent (first) statement is true, then the consequent (second) statement is also true. For example, the conditional statement “If it is raining, then you will get wet” is a conditional.
consequent	A conditional statement asserts a relation between two statements of which it is made, stating that if the antecedent (first) statement is true, then the consequent (second) statement is also true. For example, in the conditional statement “If it is raining, then you will get wet,” “it is raining” is the antecedent, and “you will get wet” is the consequent.
constructive dilemma (see argument patterns)	A valid argument pattern that takes the form If P, then Q If R, then S P or R ∴ Q or S
context	The context of a statement or argument is the set of background conditions that are implicitly assumed to hold. We often need to make some aspect of the context explicit to fully reconstruct the meaning of an argument.
contradiction	A contradiction statement that is false under every possible interpretation; its negation is a logical truth.
contraposition (in immediate inference)	In the traditional logic of terms, the contrapositive of a categorical statement is the new categorical that results from putting the complement of the original subject term in the predicate place and putting the complement of the original predicate term in the place subject place; in short, both terms are turned into their complement and their positions switched.
contrary (see subcontrary)	Two statements are contraries if both can be false but at most one can be true—for example, “Today is Friday” and “Today is Wednesday.”
conversion (in immediate inference)	In the traditional logic of terms, the converse of a categorical statement is made by interchanging the statements’ subject and predicate terms. This procedure is called conversion.
counter-example	A counter-example of an argument is a situation in which the premises are true and the conclusion is false. If an argument is valid, there is no possible counter-example, and the statement produced by conjoining the premises with the negation of the conclusion is a contradiction.
critical thinking	Thinking that is disciplined by being guided by principles of good method.
deductive (argument)	A deductive argument is one whose conclusion can be derived from its premises by procedures that preserve truth; in short, a deductive argument is one in which the truth of the conclusion follows from the truth of the premises.
definition	The definition of a term is a statement that specifies what the term means.
definition, argument from	An argument from definition is an argument in which the conclusion is presented as following simply by definition or by the meanings of the words used in the argument.
disjunctive syllogism (see argument patterns)	Disjunctive syllogism is a valid argument pattern taking the form: P or Q Not P ∴ Q
fallacy (see fallacy list in Chapter 5)	A fallacy is an argument that violates one or more of the conditions of a cogent argument.
generalization	Is a statement concerning a class of things stating that all or some number of members of that class have some feature.
hypothetical syllogism (see argument patterns)	Hypothetical syllogism is the valid argument pattern having the form: If P, then Q If Q, then R ∴ if P, then R
implicit (see premise)	An implicit statement is a statement that is assumed to be true in some context but is not explicitly stated.
indicative sentence	An indicative sentence is one that when uttered makes a truth claim—that is, either true or false.
inductive (inductive argument, inductive inference, inductive strength)	An inductive argument makes a general claim on the strength of a set of particular statements. Inductive arguments are not true by virtue of their form but because the generalization is made true by the way the world is. An inductive inference is the mental act of drawing an inductive conclusion from a set of particular premises. Inductive strength is the degree to which the premises support the likelihood of the conclusion.
inference	An inference is a mental act or piece of reasoning that culminates in a conclusion.
invalid (see valid)	An argument is invalid if has a counter-example. One can show that an argument is invalid by constructing a counter-example or by showing that its negation is valid.
justification	Justification is a relation that grounds. To say that a conclusion is justified is to say that the premises provide adequate grounds for asserting the conclusion.
logic	Logic is the systematic study of arguments.
modus ponens (see argument patterns)	Modus ponens is the valid argument pattern having the form: If P, then Q P ∴ Q
modus tollens (see argument patterns)	Modus tollens is the valid argument pattern having the form: If P, then Q Not Q ∴ not P
necessary	A statement that is necessary is never false.
necessary condition (see sufficient condition)	A necessary condition of a statement must be satisfied for the statement to be true.
necessary truth	A necessary truth is the same as a logical truth or tautology.
obversion (in immediate inference)	In the traditional logic of terms, the obverse categorical statement is the product of changing the quality of the statement and replacing the statement’s predicate term with its complement.
premise	A premise is a claim made in an argument to ground or support the conclusion.
proof	A proof is a procedure that demonstrates the truth of a conclusion; alternately a proof is the set of statements that are the product of such a demonstration.
quality	In the traditional logic of terms, the quality of a categorical statement is the character (affirmative or negative) of the relationship it affirms between its subject and predicate terms: it is an affirmative statement if it states that the class designated by its subject term is included, either as a whole or only in part, within the class designated by its predicate term, and it is a negative statement if it wholly or partially excludes members of the subject class from the predicate class.
reasoning	Reasoning is a mental process in which the mind is moved to endorse statements because they appear to be justified by other statements the person accepts.
refutation by counter-example	A procedure in logic whereby an argument is shown not to be valid by the construction of a genuine counter-example in which the premises are true and the conclusion false.
relevance	A word with a very general application, indicating the bearing that one thing has on something else.
soundness, sound	Soundness is the property of being sound; a sound argument is a valid argument that has true premises.
standard form	The standard form of an argument is a way of regimenting it to show the relation between premises and conclusion. We do this by stacking the premises first and separating the conclusion with a line. For example, the argument “You are tired and tired people should sleep so you should sleep” has the standard form: Premise 1: You are tired. Premise 2: Tired people should sleep. _______________ Conclusion: You should sleep.
statement	A sentence used to make a claim (which can be true or false).
subcontrary (see contrary)	Two statements are subcontraries if both can be true but at most one can be false true—for example, “some dogs are black” and “some dogs are not black.” The relation of being contraries depends on the subject terms having reference (in the case of the example, that there are dogs).
sufficient condition (see necessary condition)	A sufficient condition is one that, if satisfied, assures the statement’s truth.
syllogism	A syllogism is a very general argument pattern that involves two premises and a conclusion and three terms. In the traditional logic of terms, a syllogism is an argument composed of three categorical statements, two of which are premises and the third is the conclusion. The three statements jointly contain three non-logical referring terms, each appearing in two of the three statements. See Chapter 8.
truth	A statement is true if things are as the statement says they are. To assert that a sentence—for example, “it is raining”—is true, it suffices to assert the sentence (because “it is raining” is true if and only if it is raining).
truth value	Logic statements are evaluated as either true or false. These two possibilities are the possible truth values of the sentence.
universe of discourse	The universe of discourse in a situation is the set of all the things there are in the universe under discussion. This universe of discourse is typically either just reality or else a stipulated domain under discussion, such as “all the people in this room.”
validity, valid	An argument is valid if and only if there is no possible situation in which the premises are true and the conclusion is false. Validity is the property of a valid deductive argument.
Venn diagram	A method of representing the properties of sets useful in diagramming categorical statements and determining validity in categorical syllogisms, named for John Venn, its inventor.

About the Authors