Prediction, incentive, and free will

Originally posted by DoctorScribbles
My concern isn't with the existence of the algorithm. My concern is more of a metaphysical one - could the algorithm actually be implemented and brought into physical existence, given that M already physically exists?

That is, if one doesn't dismiss the original problem out of hand by saying that obviously the man has free will to defy the mac ...[text shortened]...
P.S. Could any M have predicted that I would have required 19 edits to disprove its existence?

Why don't we ask M whether we can build M', in a predictive way so that a 'yes' answer is equivalent to eventual construction of M'. Clearly this results in a contradiction in which M' denies its own existence. If M answers no, then we get no M. Thus these machines cannot coexist if we start with M.

Starting with M' is kind of a non-starter based on following the machine metaphor too closely, because M' doesn't do anything, by definition, unless it has answers from M.

Originally posted by royalchicken
Why don't we ask M whether we can build M', in a predictive way so that a 'yes' answer is equivalent to eventual construction of M'. Clearly this results in a contradiction in which M' denies its own existence.

This is a good idea for a refutation of my proof, but I don't think it works.

M' is defined to be simply a machine that maps Yes to No, and No to Yes. Its definition doesn't entail that it says anything accurate about the rest of universe. If I ask M if M' can exist, and M says yes, then M' will say No. But M' saying No is not a contradiction; M' isn't asserting its own non-existence by saying No - it's asserting only that its input was Yes.

Its definition doesn't entail that it always supplies correct answers about the universe. Just like Magic 8 Balls can get wrong answers when you ask them, "Do you exist," and not vanish in a puff of logic when they do, M' is also allowed to get wrong answers about the universe. M, however, is not, since its definition says that it makes perfect predictions. Magic 8 Balls can exist, but Magic 8 Balls that make perfect predictions cannot.

Regarding your second point, I intended to define M' to be a machine that can function independently of M. Give M' any Yes or No input, regardless of the source of that input, and M' will return No or Yes. It can be designed and built prior to any physical or even conceptual existence of M.