`At 13:53 30/01/04 +1100, Stathis Papaioannou wrote:`

fact vs. value; formal vs. informal; precise vs. vague; objective vs. subjective; third person vs. first person; computation vs. thought; brain vs. mind; David Chalmer's easy problem vs. hard problem of consciousness:

To me, this dichotomy remains the biggest mystery in science and philosophy. I have very reluctantly settled on the idea that there is a fundamental (=irreducible=axiomatic) difference here, which I know is something of a copout. I really would like to have one "scientific" theory that at least potentially explains "everything". As it is, even finding a clear way of stating the dichotomy is proving elusive.

`Actually that *difference* is not *really* fundamental. Although I could have taken it as axiom, it appears`

that the mechanist hypothesis literally forces us to introduce that difference. It is hard to explain this without being a little bit technical. The main fact. is that, in the apparently crisp domain of formal provability by correct machine or correct theorem prover, once the machine are sufficiently powerful, we get this

that the mechanist hypothesis literally forces us to introduce that difference. It is hard to explain this without being a little bit technical. The main fact. is that, in the apparently crisp domain of formal provability by correct machine or correct theorem prover, once the machine are sufficiently powerful, we get this

`provable(p) does not entail provable(p) and true(p)`

`This should be astonishing, because we have restricted ourself to correct machine, so obviously`

`provable(p) entails the truth of p, and thus provable(p) entails "provable(p) and p"; so what ????`

`What happens is incompleteness; although provable(p) entails true(p), the machine is unable to prove that.`

That is the correct machine cannot prove its own correctness. By Tarski (or Kaplan &Montague 1961)

such correctness is not even expressible by the machine (unlike provability and consistency).

But, (and that's what the "meta" shift of level makes it possible); we can define, for each proposition p, a modal connective knowable(p) by "provable(p) and p". Accepting the idea that the first person is the knower, this trick makes it necessary for any correct machine to have a different logic for something which is strictly equivalent for any omniscient outsider. In some sense this explains why there is necessarily a gap between (3-person) communicable proof and (1-person) non-communicable (as such) knowledge.

This is so important that not only the knower appears to be variant of the prover, but the observables, that is: physics, too.

But that could lead me too far now and I prefer to stop.

That is the correct machine cannot prove its own correctness. By Tarski (or Kaplan &Montague 1961)

such correctness is not even expressible by the machine (unlike provability and consistency).

But, (and that's what the "meta" shift of level makes it possible); we can define, for each proposition p, a modal connective knowable(p) by "provable(p) and p". Accepting the idea that the first person is the knower, this trick makes it necessary for any correct machine to have a different logic for something which is strictly equivalent for any omniscient outsider. In some sense this explains why there is necessarily a gap between (3-person) communicable proof and (1-person) non-communicable (as such) knowledge.

This is so important that not only the knower appears to be variant of the prover, but the observables, that is: physics, too.

But that could lead me too far now and I prefer to stop.

Some previous posts in the current thread have attacked this idea by, for example, explaining ethics in terms of evolutionary theory or game theory, but this is like explaining a statement about the properties of sodium chloride in terms of the evolutionary or game theoretic advantages of the study of chemistry. Yes, you can legitimately talk about ethics or chemistry in these terms, but in so doing you are talking meta-ethics or meta-chemistry, which I think is what Bruno means by "level shift".

`Yes, ok. And indeed evolutionnary theory and game theory and even logic are sometimes used to just put that difference under the rug making consciousness a sort of epiphenomenon, which it is not, for incompleteness is inescapable, and introspective machines can only build their realities from it. All this can be felt as highly counter-intuitive, but the logic of self-reference *is* counter-intuitive.`

`Bruno`