Law of excluded middle. The two statements are equivalent.
1. This isn't a two valued system, you can think it may be possible without believing it's possible.
2. Rhetorically these are very different statements, and I believe GP was referring to the rhetorical difference between them.
Stated another way, if something is "not impossible", then what is it?
> I would probably have titled it "I think FTL travel might not be impossible".
(Emphasis added)
Belief isn't binary, ergo no LEM.
LEM doesn't apply to all logical systems, it only applies to two-valued logic. In practice lots of logic is 3 valued or otherwise non-binary (such as partial equality or when we have a probability distribution over a set of outcomes). Some schools of mathematics (the constructivists and intuitionalists) actually reject the LEM.
I personally, as a PhD in having internet opinions, wouldn't go so far as to reject it, but relying on the LEM or proof by contradiction is a risk. You've shown `~X`, and you're betting that a proof of `X` does not exist. But it could be that `X and ~X` is the paradox that reveals your axioms are flawed. But I digress.
The criticism is that X isn't shown to be true, it's just not shown to be false. That would be sufficient if the only values were true and false, but that's not the case here. What the original commenter was saying was, even if you accept her argument in full, it moves the needle to "maybe".
> I would probably have titled it "I think FTL travel might not be impossible".
Again, what does “not impossible” mean? The only meaning, logically, is “not impossible = possible.”
The fact that you’ve used the word “not” implies a two state system. LEM applies.
The original title made sense. Your proposed change to the title is either: equivalent to the original title or logically inconsistent.
- known possible
- not known to be possible or impossible
- known impossible
"Is possible" suggests case 1, if "is known" is implied (we are talking about science here, so that should be the case). "Is not known to be impossible" covers 2&3.
Can we flip the question around? Under what scenario would you accept the middle condition of, "we do not know whether X is or is not possible" to exist?
For instance, we don't know whether God exists or not (just a contrived example). Now consider the statement: "It's not impossible for God to exist." That's equivalent to saying "It's possible for God to exist." The two statements are totally equivalent. Sure, we don't know whether or not God exists, but that doesn't make the statement "It's not impossible for God to exist" fundamentally different from "It's possible for God to exist."
Now consider the headline: "I think faster than light travel is possible." And the suggestion is to change this to "I think faster than light travel is not impossible." Again, the two statements are totally equivalent because whether or not something is possible is a binary state and the law of the excluded middle.
> I was trying to explain why the arguments saying it's impossible are inconclusive and we shouldn't throw out the possibility too quickly
Specifically the point is that the author believes that impossibility has not been adequately proven. Not that possibility has been proven.