Le 10-août-07, à 22:32, David Nyman a écrit :

> On 10/08/07, Bruno Marchal <[EMAIL PROTECTED]> 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 

BOOLOS, G. 1993, The Logic of Provability. Cambridge University Press, 

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).



You received this message because you are subscribed to the Google Groups 
"Everything List" group.
To post to this group, send email to [EMAIL PROTECTED]
To unsubscribe from this group, send email to [EMAIL PROTECTED]
For more options, visit this group at 

Reply via email to