PHIL222 - Truth Tables L4

Joint truth table

A method used to check if an argument is valid by assigning columns for each premise and the conclusion.

Valid argument

An argument is valid if there is no row in the truth table where all premises are true and the conclusion is false.

Invalid argument

An argument is invalid if there is at least one row in the truth table where all premises are true and the conclusion is false.

Counterexample

A scenario in which the premises of an argument are true while the conclusion is false, indicating the argument is invalid.

Sound argument

An argument is sound if it is valid and its premises are true in the actual row of its truth table.

Tautology

A proposition that comes out true in every row of its truth table.

Contradiction

A proposition that comes out false in every row of its truth table.

Satisfiable proposition

A proposition that is not a contradiction and can be true in at least one row of its truth table.

Contingent proposition

A proposition that is true in the actual row but not a tautology.

Logically equivalent

Two propositions that have the same truth value in every row of their joint truth table.

Jointly unsatisfiable

Two propositions that do not have the truth value T in any row of their joint truth table.

Contraries

Two propositions that are jointly unsatisfiable and have at least one row where both are false.

Set of propositions

A collection of propositions, written with braces and separated by commas, e.g. {P, Q, R}.

Unsatisfiable set of propositions

A set in which there is no row of the truth table where all propositions in the set are true.

Counterexample to an argument

An assignment of truth values to propositions that illustrates the argument's invalidity.

Foolproof test for validity

The capability of truth tables to determine whether arguments are valid.

Truth value

The assigned value of a proposition in a truth table, indicating whether it is true or false.