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