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That's a standard proof by contradiction. Make an assumption, derive a contradiction, the conclusion is that the assumption must be wrong. There's indeed an ex
by Tainnor 4y ago
That's a standard proof by contradiction. Make an assumption, derive a contradiction, the conclusion is that the assumption must be wrong.
There's indeed an extra assumption in here, namely that we can write a program such as B that runs on "itself". That's not difficult to see though, if we think in terms of Turing Machines (or an actual computer with memory, for that matter).
I think the given proof is essentially correct.
- GoblinSlayer 4y agoCircular logic is a known source of paradoxes, it's difficult to assume it to be a priori correct.
- Tainnor 4y agoI don't think you know how circular logic, or proof by contradictions work. If you could indeed derive 1=0 from H, then that would indeed by reason to dismiss H, but you can't just "consider" 1=0, you have to prove it from H.
- GoblinSlayer 4y agoThat's the point, B=H(B) doesn't follow from H, it's a new independent construct, so you need an independent proof of its validity.