Chapter 4: Entailment Terms

Affirming the consequent

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

Antecedent

In a conditional, the clause that expresses the condition—that is, the clause immediately following if. (precdingg int ime or order, previous, preexisting)

Conditional

A statement composed of two sentential clauses joined by if…then…. (Sometimes then is omitted, as in: If Bob starts dancing, I will leave.)

Consequent

In a conditional, the clause that expresses what is said to follow if the antecedent is true. The consequent usually comes right after then.

Counterexample

an example that shows that a universal claim is false: for example, if Betty is happy, then Betty is a counterexample to the claim Everyone is unhappy—assuming the speaker is really talking about everyone! As we know, for a logical form to be deductively valid, every instance must be deductively valid. So a logical form can sometimes be shown to be deductively invalid by providing a counterexample to this universal claim—namely, an instance of it that is not deductively valid. Such a counterexample will be particularly vivid if the premises are actually true and the conclusion false.

Deductively valid argument

What makes an argument deductively valid is that its premises entail its conclusion: if the premises were true, the conclusion would have to be true.

Deductively valid logical form

What makes a logical form deductively valid is that 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

The disjunction of two sentences P and Q is a sentence that is true as long as either P is true or Q is true, and false only when both P and Q are false. It can be formed by combining P and Q with either…or….

Disjunctive syllogism

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

Flipping the argument

Assuming that the conclusion is false, and asking whether all of the premises could still be true. If so, the premises do not entail the conclusion.

Hypothetical syllogism

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 that can be shared by different arguments; it can be illustrated by replacing certain words or sentences with variables until the arguments are the same.

Modus ponens

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

Modus tollens

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 into the sentence that is being negated.