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Why isn't building a decision theory equivalent to building a whole AI from scratch?

I understand, what I wrote was wrong. What if we use n%3=0 and ~(n%3=0) though?

A natural number n can be even or odd: i.e. n%2=0 or n%2=1.

If X = {n is natural number} then you showed that we can use P(n%2=0|X) + P(n%2=1|X) = 1 and P(n%2=0|X) = P(n%2=1|X) together to get P(n%2=0|X) = 1/2.

The same logic works for the three statements n%3=0,n%3=1,n%3=2 to give us P(n%3=0|X) = P(n%3=1|X) = P(n%3=2|X) = 1/3.

But then the same logic also works for the two indistinguishable statements n%3=0,n%3=1 \/ n%3=2 to give us P(n%3=0|X) = P(n%3=1 \/ n%3=2) = 1/2.

But 1/2 = 1/3 is a contradiction, so we find that axiom 3 leads to inconsistencies.

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1gRR
n%3=0 is distinguishable from n%3=1∨n%3=2. If A="n%3=0", B="n%3=1", and C="n%3=2", then an isomorphism f that maps B∨C to A must satisfy f(B∨C) = f(B)∨f(C) = A, which is impossible.

Isn't it just strategy stealing? Calling it tit-for-tat maybe focuses away from the fundamental reason why it wins.

I'd like to ask him for an explanation of what the hard problem is and why it's an actual problem, in a way that I can understand it (without reference to undefinable things like "qualia" or "subjective experience"). Would probably have to discuss it in person with him and even then doubt either of us would get anywhere though.

1XiXiDu
Oh yeah, I'd love to see a consciousness for dummies or consciousness 101 written by him. So far I haven't read up on the whole issue but merely thought a few times about consciousness myself and ran into intractable problems rather quickly. To read up on the vast amount of literature on the topic, and the hard problem in particular, won't become a priority any time soon due to the massive amount of time it would take me to digest it, and given that the expected payoff I assign to doing so is virtually zero. It would also be interested if he is able to circumscribe the problem in layman's terms. It might hint at the possibility that a lot of the literature is made up of language games throwing around mysterious terminology that nobody ever bothered to define.