We will show that the statement “Everything is possible.” leads to contradiction and is therefore meaningless.

Lemma 1. “It is not the case that everything is possible.”

Proof by Contradiction.

Let Statement 1 be “Everything is possible.”

Let T be “Making U not possible.” where U is a thing. Undoubtedly T is also a thing in its own right. It follows by an universal instantiation of Statement 1 that T is possible. Because T is possible, it can be realised and after T is realised, U is not possible; however, the consequence that U is not possible would contradict Statement 1; it follows that T must be not possible in order for Statement 1 to hold true; however, if T is not possible, then it serves as a falsifying counterexample to Statement 1. On the other hand, if T is possible, then U is not possible, which also serves as a falsifying counterexample to Statement 1. Therefore, we have just shown that regardless of the truth value of T, regardless of whether T is possible or not, Statement 1 is always incorrect.

The conclusion is that not strictly everything is possible. Now that you have been told, do not shamelessly brag “Everything is possible.” to everybody you meet, especially to mathematicians who have too much leisure time. Conversely, if you meet a mathematician who brags “Everything is possible.”, wake them up and drag them back to The Right Way using this argument.