Le 04-sept.-06, à 16:08, 1Z a écrit :
> Arithmetical statements use the word "exists", or the symbolic
> euivalen thereof. However, it is not to be taken literally
> in all contexts.
>
>> No need to add
>> metaphysics at this stage
>
> Yes there is. You need metaphysics to answer the question
> of whether the existence-claims of mathematics shouldbe takne
> literally.
"Metaphysics" is provided through the "yes doctor", which you have no
choice not to take literally.
I mean you would not say "yes" to a doctor who tells you that you will
survive the comp-substitution and then add: don't take this literally.
But even this is strictly speaking suppressed when defining the many
notion of contingency and necessity from the intensional (modal)
variant of the Godel Lob self-referential provability notions.
Recall the UDA and AUDA difference (AUDA = Arithmetical UDA = lobian
interview).
>
>> (nor at any other stage by the way, except
>> the yes doctor, which I prefer to range in "theology" than in
>> "metaphysics").
>
> Is theology better-foudned as a discipline ?
When done by rational theologians, like most of the greek one, it is.
Of course in our civilization "theology" has been appropriated by
"politics" since a long time. Still many Christian theologians have
been "rigorous" or "modest" or "scientific" since, but are generally
put on the margins, if not burned alive or ignored. Today the
aristotelian primary matter hypothesis is defended by the atheist and
the Christian, mainly.
> And Sherlock Holmes lives because Sherlock Holmes lives
> at 221b Baker Street.
Really? Could you give me his phone number please? I will verify.
Come on Peter, this is a diversion which has nothing to do with the
notion of existence of numbers.
You refer to possibly interesting nuances, but those are out of topics
here.
> Arithmetical statements use the word "exists", or the symbolic
> euivalen thereof. However, it is not to be taken literally
> in all contexts.
I don't care. The point is that with comp, the existence of an
electron, or of anything, cannot be taken literally too. The point is
that with comp you can derive from PEANO, why numbers have to believe
in electron, although electron existence is less literal than the
existence of 417.
You keep doing the 1004 fallacy. The question are not metaphysical at
all, and does not address any notion of metaphysical existence in which
I am not interested at all. The point is that the computationalist
hypothesis generates many different notion of existence, and the
interesting thing to do (with respect of explaining quanta, qualia,
where do we come from etc.) consists in finding the relation between
those form of existence, not some intrinsic meaning that they would
have.
Now the simplest notion of existence is the standard interpretation of
"Ex" in first order logic presentation of arithmetic, if only to begin
with. All other notion of existence (psychological, physical,
theological, etc.) are derived from it.
>
>>> Necessary truth
>>> can exist in a world of contingent existence -- providing
>>> all necessary truths in such a world are ontologically non-commital.
>>
>>
>> I don't understand.
>
> If necessary truths don't refer to contingently
> existing things, they cannot be "infected" by their contingency.
I don't understand. A necessary truth could refer to contingently
existing things. If you take (like we will do in the Lobian interview)
"provability B" for "necessity", and consistency D or "possibility",
Godel's second incompleteness theorem is already an example of
necessity about contingencies: it is necessary that if a tautology is
consistent then it is consistent that a falsity is necessary
G proves Dt->DBf, or G* proves B(Dt->DBf). Also B(Ex(x=x)) which is
enough.
>> AR does not ask you for believing in some metaphysical (still less
>> physical) existence of numbers.
>
> Then it does not show the UD exist, and it cannot follow
> that I part of its output.
You should have written: "Then it does not show the UD exists
physically, and it cannot follow
that I am a physical part of its output."
And I agree with you given that I already do not believe you exist
physically in any genuine (applicable) sense of the word (assuming
comp). BTW I have already makes long answer of this, and you did not
reply.
>
>> It ask you to agree that a proposition
>> of the type ExP(x) is true or false independently of any cognitive
>> faculty.
>
> It may well be true. It may well mean nothing more
> than "P(x) is non-contradictory"
No. ExP(x) means that it exist a natural number verifying the property
P.
"P(x) is non-contradictory" is the proposition DP(x),or ~B~P(x), i.e.
~Bew('P(x)') which is a completely different proposition. This one is
even undecidable by *any* lobian machine.
Example: Bf is false but is also non-contradictory for any sound theory
of arithmetic.
Contradictory
>
>> Cognitive abilities are needed to believe or know that ExP(x)
>> is true (or false), but that's all.
>
> Quite. So nothing in the argument can tell me about the nature of my
> existence.
?
> The Pythagorean rationalist *must* believe mater
> is impossible -- the argument becomes inconsistent otherwise.
Could you elaborate?
>
> The argument that matter is "useless" is more akin
> to empiricism than rationalism.
I agree.
But don't see your point unless you believe I am not an empiricist,
which of course I am, given that one of my main point in my PhD thesis
is that comp is empirically testable.
True, sometimes some people believe that I am not empiricist because I
show that if comp is correct the physics is entirely "in our head". But
I have never said that everything "in our head" should necessarily be
taken for granted. We can and must, from comp, extract the physics
which is in our head, and then compare it with the empirical physics,
and so we can test comp. OK?
(Again this is something I have already explain, I repeat the
explanation because I suspect others could still be confused, but I am
not sure I will repeat this an infinity of times, if only because I
will be more buzy. I will begin to concentrate myself on the
presentation of the "roadmap/hypostases". This should help you to
reevaluate more constructively your critics perhaps, imo.
Bruno
http://iridia.ulb.ac.be/~marchal/
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Received on Tue Sep 05 2006 - 10:26:24 PDT