Sentence examples for the conditional was from inspiring English sources

The truth-functional theory of the conditional was integral to Frege's new logic (1879).

(The conditional is a condition.

The conditional is clearly false.

Thus, the conditional is vacuously true.

The part is dependent on the whole, the conditional is dependent on the unconditional.

But on Hook's account, the conditional is false only if the consequent is false.

The antecedent of the conditional is indeed treated as an assumption.

Knowledge of the conditional is conditional knowledge (that is, conditional upon learning the antecedent and applying the inference rule modus ponens: If P then Q, P, therefore Q).

The conditional is not primitive however; it is defined in terms of two unary modal operators.

Consequently, for a sentence σ in the language of arithmetic, σ is true in arithmetic iff the conditional is valid.

This is easy: in such a model, the antecedent is false, and inspection of the above Strong Kleene table shows that when the antecedent of a conditional is false, the conditional is true, as would be the case classically.