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Isn't it circular logic? B=H(B) - if circular logic doesn't work, why would it mean that some unrelated function H doesn't exist? Simplified proof: assume H ex
by GoblinSlayer 4y ago
Isn't it circular logic? B=H(B) - if circular logic doesn't work, why would it mean that some unrelated function H doesn't exist?
Simplified proof: assume H exists, then consider equation 1=0, it's a contradiction, therefore the assumption is false and H doesn't exist.
- lisper 4y agoBut 1=0 is not a contradiction, it is simply false. All contradictions are false, but not all false statements are contradictions. But that is neither here nor there. What matters is that a provably false statement (in this case a contradiction, but that doesn't really matter) follows from some assumption, and therefore the assumption must be false. This is not circular reasoning, it is proof by reductio ad absurdum (https://en.wikipedia.org/wiki/Reductio_ad_absurdum https://en.wikipedia.org/wiki/Reductio_ad_absurdum).
- Tainnor 4y agoThat'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.