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If nothing is impossible, then would it be possible for something to be impossible?

Great question!

person in the air via parachute he parachute has the word impossible on it crossed out

15 February 2022

To get started, consider two claims:听

(1)听听 听nothing is impossible.
(2)听听 听everything is possible.听


Really, claims听(1)听补苍诲听(2)听are saying the same thing. (If that鈥檚 not immediately obvious to you, consider a similar pair of claims, like 鈥渘o question was unanswered鈥 and 鈥渆very question was answered鈥; you should be able to see that these claims hold in exactly the same situations.)听


翱办:听(1)听补苍诲听(2)听come to the same thing. So, if听(1)听holds, then certainly听(2)听holds too. Spelling this out:
(3)听听 听if nothing is impossible, then (certainly) everything is possible.


Or, to put it another way:听
(1)听听 听if nothing is impossible, then (certainly) there is not something which is impossible.
Maybe that answers your question!


I鈥檓 hesitating, though, because I used the word 鈥渃ertainly鈥 in my answer, and your question asked about what 鈥渨ould be possible鈥. Depending on what you had in mind, these notions might come apart. In particular, maybe you are asking whether we should accept that:
(4)听听 听if everything is possible, then necessarily everything is possible.
which is slightly different from听(3). We鈥檝e dealt with听(3), so let鈥檚 focus on听(4).


It turns out that it鈥檚 really hard to asses claims like听(4). This is because claims about what鈥檚 (im)possible often depend upon the notion of possibility you have in mind. In a mundane sense, it鈥檚 impossible to travel from London to New York in less than a minute: no plane can fly fast enough. But in another sense, it鈥檚 perfectly possible: someone with superpowers could do it, and it鈥檚 surely logically possible to have superpowers (even if it's very unlikely, and maybe even physically impossible).


This suggests that different notions of possibility might affect whether听(4)听is true or false. Indeed, it suggests a game: come up with different notions of possibility, and see how they affect听(4).听
I鈥檒l leave it to you, to come up with a notion of possibility, which makes听(4)听true. But it鈥檚 not obvious how you might come up with a notion of possibility where听(4)听is true; so, let me help with that.听

black and white chess rooks

When people playing Chess, they sometimes speak in terms of (im)possibility: they say things like 鈥渨hite can鈥檛 win from here鈥. Spelled out fully, they mean something like: 鈥渇rom this position, there is no way for white to place the black king in checkmate, whilst following the rules of Chess鈥. So, in Chess, talk about (im)possibility just means something about which board-positions which can(not) now be reached.


Of course, at the start of the game, nothing has happened. So (in the Chess sense):听
(5)听听 听everything is possible


However, if I move a pawn forward, then the rules of Chess prevent me from ever moving it back to where it was. This means that many positions, which were once possible (i.e. reachable from where I was), have now become impossible (unreachable from where I am).听


So, at the start of the game, it is possible to reach a position where not every (legal) position is reachable. So: at the start of the game, it鈥檚 right to say (in the Chess sense):听
(6)听听 听it鈥檚 possible that not everything is possible.
But if you put听(5)听补苍诲听(6)听together, you have to deny听(4)!听