Le 10-août-07, à 22:32, David Nyman a écrit :
>
> On 10/08/07, Bruno Marchal <marchal.domain.name.hidden> wrote:
>
>> OK. Have you seen that this is going to made physics a branch of
>> "intensional number theory", by which I mean number theory from the
>> points of view of number ... ?
>
> Insofar as we accept that the foundation of 'comp reality' is the
> number realm, comp physics must indeed be a branch of this (e.g. as
> per my previous example of 'digital digestion').
That the 'comp reality' is founded on the number realm, is almost
trivial. What is not trivial at all, and this is what the UDA shows, is
that, once you say "yes" to the digital doctor, for some level of
substitution, then your immateriality (somehow like the quantum
superpositions) is contagious on your most probable neighborhoods. So
that physics has to be shown to emerge statistically from the "measure"
on the UD accessible relative states. Withouth this, the arithmetical
interview would not lead to making comp testable.
This reasoning shows really the incompleteness of Everett's work: once
you accept the observer can be locally described by its digital memory
states, the laws of physics have to emerge from all comp histories.
We can discuss that too, although it is not entirely needed for
grasping how to derive physics from comp. To be sure, it is needed,
however, for the understanding that with comp, we *have to* derive the
physics from "intensional numbers prevailing discourses". With comp,
postulating a physical world cannot be used as an explanation relating
mind and appearance of matter (memory-stable observations).
It is not that (aristotelian primary )substance does not exist, but
that such primary substance is provably (with the comp hyp) void of
explanation power.
>
>> OK. Don't buy it if you decide to buy only one book on Godel, and let
>> me think which is the best one. But if you are willing to buy/read two
>> books, then get it asap.
>
> 'In for a penny, in for a pound' (old English saying) - I've ordered a
> cheap(ish) copy of Franzen on Godel. But let me know which you think
> is the best one.
Well, I should perhaps take the opportunity of your book open mindness
to suggest some books I have already advertized on the list.
Comp is related to computations, computing, and computability.
Fortunately we will need mainly the computability theory, which in some
sense is more easy than computing theory. The best book is without
doubt the one by Cutland:
CUTLAND N. J., 1980, Computability An introduction to recursive
function theory,
Cambridge University Press.
Then, you have a "recreative" introduction to the modal logic of
self-reference, the system known as G (but also GL, Prl, K4W, etc.).
Unfortuantely the most important chapter "the heart of the matter" need
a good understanding of Cutland (say) to make the link.
SMULLYAN R., 1987, Forever Undecided, Alfred A. Knopf, New York.
Then, the best textbook on mathematical self-reference is the book by
Boolos 1993. But this one is probably a bit heavy to begin with. So
wait to see if your curiosity will be enough high. It does contain a
full chapter on the "third hypostase"; alias the first person, alias
the knower, alias the modal logic S4Grz, or its purely arithmetical
interpretation.
BOOLOS, G. 1993, The Logic of Provability. Cambridge University Press,
Cambridge.
Or perhaps better (lighter) is its predecessor book on the subject, in
the lucky case you find it (in a library?). I would be Dover Edition, I
would print a paperback of that book;
BOOLOS, G. 1979, The unprovability of consistency. Cambridge
University Press, London.
Actually, if you have good eyes, the textbook by Smorynski is also
quite valuable (and complementary to Boolos on many aspects):
SMORYNSKI, C., 1985, Smoryński, P. (1985). Self-Reference and Modal
Logic. Springer Verlag, New York.
>>> I think we may have to come back later to this question of subjective
>>> time. But for now I rely on you to set the agenda of our more
>>> structured modus operandi.
>>
>>
>> Ok thanks.
>
> Then for the rest, I'll wait for your next post.
OK. I will begin by saying two words on the language we will use when
discussing with the machine. I can already explain the difference
between the layman (or grandmother) and the logician. This is not just
for you (I guess you know what I will say) but for those who just
abandon logic for reason of notation.
The main difference is that where a layman says "Alfred is serious",
the logician says serious(Alfred).
Where the layman will say there is a ferocious dog, a logician will say
that it exists something such that that something is a dog and is
ferocious. Because of laziness he will write Ex(dog(x) & ferocious(x)).
For saying that all dogs are ferocious, he will say that for all dogs
(i.e. choose any thing that is a dog) that things will be ferocious:
and he will write Ax (dog(x) -> ferocious(x)).
Of course, there is perhaps no effective test to see if a dog is
ferocious or not, perhaps the notion is not well defined, but we have
to live with things like that: even in the pure realm of numbers we
will encounter some unexpected (I guess) complexity.
By the way, David, do you know what is called "classical propositional
calculus", the truth table method? Do you need some refreshing?
Some refreshing is in Smullyan's FU, but I can do it, or focus on some
difficulty (classical propositional calculus is not so simple indeed,
even if simpler than most other logics).
Bruno
http://iridia.ulb.ac.be/~marchal/
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Received on Sat Aug 11 2007 - 10:36:41 PDT