On 27 May 2013, at 19:28, John Clark wrote:

On Mon, May 27, 2013  Bruno Marchal <marc...@ulb.ac.be> wrote:
>> Can non-materialism do better and if so how?

> Yes, by using the mathematical theory of self-reference.

I've never heard of  "the mathematical theory of self-reference".

Have you heard about Gödel's theorem?


The mathematical theory of self-reference is the general theory, containing Löb theorems, many other fixed points theorem, and eventually axiomatized by Solovay who showed that the modal logic G and G* formalize respectively the provable and the true (but not necessarily provable) part about self-reference, provable by machine, or some more general entities.

Here is one "non modal" paper, three good textbooks, and a recreative introduction.

Smorynski, C., 1981, Fifty Years of Self-Reference in Arithmetic, Notre Dame Journal
of Formal Logic, Vol. 22, n° 4, pp. 357-374.

Smorynski C., 1985, Self-Reference and Modal Logic., Springer Verlag.

Boolos G., 1979, The Unprovability of Consistency, an Essay in Modal Logic,
Cambridge University Press.

Boolos, G. (1993). The Logic of Provability. Cambridge University Press, Cambridge.

The recreative introduction:

Smullyan R., 1987, Forever Undecided, Alfred A. Knopf, New York.




And it's no great mystery, the only difference between you and me is that we each can access memories that the other can not, and we process information in slightly different ways, in other words we have different personalities.

OK.


The only difference between objective and subjective is that in one case information is universally available and in the other case the information only exists in 3 pounds of grey goo inside one particular bone box.

There are other important difference. You can doubt the whole objective part, but you can't doubt the whole subjective part. Also, the term "information" has many different meaning, from something you can measure (Shannon) to something interpreted by some machine, or other entities.




>The details of this explains that the knower (Bp & p)

Yet another of your homemade anagrams, this time it sounds like a oil company not what a baby does to a diaper. I could probably figure out what you mean if I thought about it enough, but if you don't take the effort to make yourself understood I don't see why I should make an effort to understand you.

You need to read the book above, or to read my papers where I re- explain this from scratch, but concisely. It is computer science and mathematical logic. That is of course useful to reason when you assume computationalism.

Bp & p is for an arithmetical proposition asserting Beweisbar("p") & p, with p some arithmetical proposition, and 'p', the Gödel number of the arithmetical sentence representing p.



Bruno


http://iridia.ulb.ac.be/~marchal/



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