While thinking about the possible and impossible I came into the following conclusion. Some people say that nothing is impossible. But by saying that "nothing is impossible" they automatically preclude the possibility of the impossible. Which means that the possibility of the impossible is impossible. (If there's is something that is impossible, it's the impossible itself). Then it's not true that nothing is impossible.
(I don't know if I'm getting crazy or dumb by thinking this way or am I actualy right)

  • You are doing correct. It is just recursion. Impossible is a conception. So it is already real the minute you think/mention it. What people are meaning by the nothing is impossible phrase is that NO ONE yet found what is truly impossible. Sometime somebody thought its impossible to fly, yet planes are here, and so forth. SO! it is VERY difficult to find something that is truly impossible. BUT. Impossibility itself is possible, because we already understand what it means.
    – Asphir Dom
    Apr 6, 2014 at 20:27

1 Answer 1


Let Γ be the class of all impossible sentences, i.e., Γ = {φ : ¬◊φ}. Someone claiming that nothing it impossible is simply claiming that Γ = ∅. That commits them to the thesis that no formula is necessarily false, not that "the impossible is impossible" (whatever that means). The thesis is obviously false (i.e. Γ is nonempty), not because "impossible is impossible" is a tautology, but simply because there are sentences, such as (φ ∧ ¬φ) that are necessarily false (i.e. impossible) and thus belong to Γ. That's it.

It's always a good idea to model some interpretation of what's being said in a precise framework that will allow you to settle questions of truth without getting into contradictions and paradoxes. So for example, instead of formulas being impossible we could talk about actions beings unrealizable. The claim that nothing is impossible would then be that the set of realizable actions (for a given agent) is the entirety of the action space. In that framework, we would isolate an action that because of practical or theoretical reasons couldn't be realized (by the agent), contradicting the claim that she can do anything.

  • 1
    This is absolutely right. The question as asked involves an abuse of language.
    – user5172
    Apr 6, 2014 at 11:53
  • It's a bit of a leap of faith to go from "nothing is impossible" to Γ = ∅ - the common usage of such a sentence is more like 'for all practical results/states there exists some course of actions that has a nonzero chance of success', or 'all imaginable world states have a nonzero chance of existing'. And certainly there are formal logics where (φ ∧ ¬φ) is not neccessarily false; a logic system can only be complete or noncontradictory but not both, so any complete logic will have possibilities of (φ ∧ ¬φ).
    – Peteris
    Apr 6, 2014 at 16:28
  • You understand that by writing "math" you did not levitate above language paradoxes but rather dived even deeper? Without LANGUAGE around them your math symbols are meaningless.
    – Asphir Dom
    Apr 7, 2014 at 23:58
  • @AsphirDom (1) Where's the paradox? My aim was to explicate "nothing is impossible" in one particular way in order to avoid getting tangled in nonsense. Fitch's is a paradox, Preface is a paradox, Surprise is a paradox, Russell's is a paradox, Burali-Forti's is a paradox, Curry's is a pradox, you get the idea... (2) As regards the symbols, I could eliminate them, but that would not be helpful to anyone. I could rewrite what I said using simpler symbolism, but like everyone else, I have my tastes and yesterday I felt like talking of sets of sentences instead of using quantifiers explicitly. Apr 8, 2014 at 0:28

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