Definitions Flashcards
Logic
The study of methods for evaluating whether the premises of an argument adequately support its conclusion.
argument
A set of statements where some of the statements, called the premises, are intended to support another, called the conclusion.
statement
a sentence that is either true or false.
deductive argument
an argument in which the premises are intended to guarantee the conclusion.
inductive argument
an argument in which the premises are intended to make the conclusion probable, without guaranteeing it.
valid argument
an argument in which it is necessary that, if the premises are true, then the conclusion is true
invalid argument
an argument in which it is not necessary that, if the premises are true, then the conclusion is true.
sound argument
a valid argument in which all of the premises are true.
unsound argument
an argument that either is invalid or has at least one false premise.
argument form
a pattern of reasoning.
substitution instance
an argument that results from uniformly replacing the variables in that form with statements (or terms)
valid argument form
an argument form in which every substitution instance is a valid argument.
formally valid argument
an argument that is valid in virtue of its form.
negation
the negation of a statement is its denial.
conditional statement
an if-then statement, often simply called a “conditional.”
antecedent
the if-clause of a conditional.
consequent
the then-clause of a conditional.
disjunction
an either-or statement.
disjuncts
the statements that make up a disjunction.
fallacy of denying the antecedent
an invalid argument form: If A, then B; not A; so, not B.
invalid argument form
one that has some invalid substitution instances
counterexample
a counterexample to an argument form is a substitution instance in which the premises are true and the conclusion is false.
good counterexample
a good counterexample to an argument form is a substitution instance in which the premises are well-known truths and the conclusion is a well-known falsehood.
fallacy of affirming the consequent
an invalid argument form: If A, then B; B; so, A.
categorical statement
a statement that relates two classes or categories, where a class is a set or collection of things.
term
a word or phrase that stands for a class of things.
conjunction
an “and” statement
excess verbiage
a word or statement that adds nothing to the argument.
discount
an acknowledgment of a fact or possibility that might be thought to render the argument invalid, weak, unsound, or uncogent.
repetition
a restatement of a premise or conclusion, perhaps with a slightly altered wording.
assurance
a statement, word, or phrase that indicates the author is confident of a premise or inference.
hedge
a statement, word, or phrase that indicates that the author is confident of a premise or inference.
enthymeme
an argument with an implicit premise or conclusion.
atomic statement
one that does not have any other statement as a component.
compound statement
one that has at least one atomic statement as a component.
main logical opoerator
a compound statement is the one that governs the largest component or components of a compound statement.
minor logical operator
an operator that governs smaller components.
well-formed formula
(WFF) is a grammatically correct symbolic expression.
conjuncts
the statements composing a conjunction.
logical equivalence
two statements are logically equivalent if and only if they agree in truth value on every assignment of truth values to their atomic components.
statement variable
a lowercase letter that serves as a placeholder for any statement - for example, p, q, r, s.
truth-functional
a compound statement is truth-functional if its truth value is completely determined by the truth value of the atomic statements that compose it.
material conditional
a conditional that is false only when its antecedent is true and its consequent is false; otherwise, it is true.
material biconditional
a conjunction of two material conditionals; it is true when its constituent statements have the same truth value and false when they differ in truth value.
tautology
a statement is a tautology if and only if it is true on every assignment of truth values to its atomic components.
contradiction
a statement is a contradiction if and only if it is false on every assignment of truth values to its atomic components.
contingent statement
a statement is contingent if and only if it is true on some assignments of truth values to its atomic components and false on others.
