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 isthat we each can access memories that the other can not, and weprocess information in slightly different ways, in other words wehave different personalities.

OK.

The only difference between objective and subjective is that in onecase information is universally available and in the other case theinformation only exists in 3 pounds of grey goo inside oneparticular 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 aoil company not what a baby does to a diaper. I could probablyfigure out what you mean if I thought about it enough, but if youdon't take the effort to make yourself understood I don't see why Ishould 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/ -- You received this message because you are subscribed to the Google Groups "Everything List" group. To unsubscribe from this group and stop receiving emails from it, send an email to everything-list+unsubscr...@googlegroups.com. To post to this group, send email to everything-list@googlegroups.com. Visit this group at http://groups.google.com/group/everything-list?hl=en. For more options, visit https://groups.google.com/groups/opt_out.