5 ms·

That's certainly not the case. We can and absolutely have proven things to be impossible.

• mindcrime 6y ago
  We can and absolutely have proven things to be impossible. What would you consider to be an example of that? And how does that square with the Problem of Induction which is the hole in our entire system of empirical knowledge generation?
  • bawolff 6y ago
    Lots of things in math. Yes to apply that to the real world, we have to use some assumptions like, the universe isnt a giant trick, the sun will rise tomorrow, we dont live in the matrix, etc. However given the context of this discussion those are fairly reasonable assumptions.
  • baddox 6y ago
    You can’t make a Turing machine which can solve the halting problem or an algorithm which can determine whether any given mathematical statement is true.
    • deleted 6y ago
      [deleted]
    • lurquer 6y ago
      You can prove that 2+2!=5. You could even say that, given the rules governing math, it is ‘impossible’ that 2+2=5. The domain, however, is synthetic and composed of a system of axioms and rules. If I change the underlying axioms and rules, I could certainly prove that 2+2=5, just as I can prove that The sum of a triangles interior angles exceed 180 degrees, or that two identical number squared can equal -1. (Redefining what a straight line means for the former, and inventing an imaginary number system for the latter.) Proving what can and cannot follow given a set of rules, however, is not what philosophers mean when they speak or impossibility in the real world.