3 ms·
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.
by 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 agoYou 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.