just as a necessary consequence of truth is true. A proof entails what it proves. Falsehood is itself something, and when a thing’s necessary consequence is absent, one knows that the thing itself is absent. Thus, a thing’s falsity is inferred from the falsity of its necessary consequence, while it is established by establishing that which entails it. If the necessary consequence is false, that which entails it is likewise false, for that which entails falsehood is the necessary consequence. If the necessary consequence is false, that which entails it is false, because the absence of the necessary consequence entails absence. It was not said that the necessary consequence of falsehood is false.

Created things illustrate this: they necessarily entail the existence of the Creator, but their nonexistence does not entail the Creator’s nonexistence.

A proof always entails what it proves: the implication must hold in the forward direction, but need not hold in reverse. A definition, by contrast, must hold in both directions.

As for causes, a complete cause must entail its effect, unlike a cause that merely tends to produce an effect. Whether the implication holds in reverse requires distinctions explained at length elsewhere.

This classification also clarifies what the early Muslim generations and leading scholars meant by condemning speculative theology and its practitioners. Their condemnation encompasses those who reason from unsound proofs or argue in support of false doctrines.