On "possibility" and "impossibility", also FTL.

[starslayer]

Euclidean space

Minor nitpick: it's Minkowski space, not Euclidean; Euclidean space has no time dimension.

[Darth Wong]

The general argument goes:

"If it's not impossible, then it's possible. Since you can't prove that it's impossible, then it must be possible."

As a general logic issue, this statement relies on a black/white true/false dichotomy that is possible in mathematics but is meaningless in reality. In reality, everything is a matter of probabilities (as QM shows us, this is literally true).

In other words, in mathematics and other man-made pure logic systems, it is possible to separate matters into "true/false" and use this kind of syllogism correctly. But in reality, it doesn't work because we do not have true/false; we have only varying degrees of likelihood and accuracy.

In other words, it is overwhelmingly likely that if I drop a quarter from my hand, it will fall to the floor according to the laws of gravity. But I technically cannot say it is absolutely true, because there is no such thing in reality. When we say something is "true" in the context of the real universe, we only mean that it is overwhelmingly likely to be correct. It's a short form, sort of like the way we don't preface every single statement in science class with "this is just a theory".

Keeping that in mind, it is absurd to say that just because you can't prove something is absolutely impossible, then it must be possible. In cases of situations which seem to violate great swathes of science, the statement is only valid if you agree that "possible" means "an infinitesimal probability, akin to the probability of your penis spontaneously morphing into a green winged lizard".