Ch 4: Entailment

Affirming the consequent

A deductively invalid logical form where P is inferred from the premises If P then Q and Q.

Antecedent

The clause in a conditional that expresses the condition, immediately following "if."

Conditional

A statement composed of two sentential clauses joined by "if...then...".

Consequent

The clause in a conditional that expresses what follows if the antecedent is true, usually coming right after "then."

Counterexample

An example that shows a universal claim is false, demonstrating a logical form's invalidity.

Deductively valid argument

An argument where the premises entail the conclusion; if the premises are true, the conclusion must be true.

Deductively valid logical form

A logical form where every argument with that form is deductively valid.

Denying the antecedent

A deductively invalid logical form where not Q is inferred from the premises If P then Q and not P.

Disjunction

A sentence that is true if either P or Q is true, and false only when both are false, formed by combining P and Q with "either...or...."

Disjunctive syllogism

A deductively valid logical form where Q is inferred from the premises Either P or Q and not P.

Flipping the argument

Assuming the conclusion is false and checking if all premises could still be true; if so, premises do not entail the conclusion.

Hypothetical syllogism

A deductively valid logical form where If P then R is inferred from If P then Q and If Q then R.

Logical form

A structure shared by different arguments, illustrated by replacing certain words or sentences with variables.

Modus ponens

A deductively valid logical form where Q is inferred from the premises If P then Q and P.

Modus tollens

A deductively valid logical form where not P is inferred from the premises If P then Q and not Q.

Negation

The negation of a sentence is true when the original sentence is false and false when the original sentence is true, often formed by inserting "not."