Category:Paradoxes of Strict Implication

This category contains pages concerning Paradoxes of Strict Implication:

The strict implication operator has the following counter-intuitive properties:

Necessary Proposition is Strictly Implied by Every Proposition

If a proposition is necessarily true, then every proposition strictly implies it.

Let $P$ be a proposition of modal logic.

Let $P$ be necessarily true.

Then:

$\forall Q: Q \implies P$

where $Q$ is an arbitrary proposition in the universe of discourse.

Impossible Proposition Strictly Implies Every Proposition

If proposition is not possibly true, then it strictly implies every proposition.

Let $P$ be a proposition of modal logic.

Let $P$ be not possibly true.

Then:

$\forall Q: P \implies Q$

where $Q$ is an arbitrary proposition in the universe of discourse.