Page "Propositional calculus" Paragraph 27

* Material conditional also joins two simpler propositions, and we write, which is read " if then ".

The proposition to the left of the arrow is called the antecedent and the proposition to the right is called the consequent.

( There is no such designation for conjunction or disjunction, since they are commutative operations.

) It expresses that is true whenever is true.

Thus it is true in every case above except case 2, because this is the only case when is true but is not.

Using the example, if then expresses that if it is raining outside then there is a cold-front over Kansas.

The material conditional is often confused with physical causation.

The material conditional, however, only relates two propositions by their truth-values — which is not the relation of cause and effect.

It is contentious in the literature whether the material implication represents logical causation.