Hi Mirek,
On 05 Aug 2009, at 00:52, Mirek Dobsicek wrote:
> I've ordered the dialogue from a second-hand book shop :-) The
> Stanford
> encyclopedia says
> "Arguably, it is his (Plato) greatest work on anything."
> So I'll give it a try :-)
I love that book, and it is also my favorite piece of Plato.
To be sure, I don't think it is needed to understand neither UDA nor
AUDA, but it can help.
> This is probably the key problem for me. I know next to nothing about
> provability, the logic of provability, PA/ZF provers.
>
> I know that quite often you reference Boolos 1993 - The Logic of
> Provability. I took a look at it at Google Books preview but ... there
> is something missing in my education. From the beginning I am puzzled
> with "Why?, what?". What a headache :-)
You miss an introductory course on mathematical logic.
Have you herad about Gödel's incompletness theorem. Boolos book
explains the sequel.
I thought that, after Hofstadter best selling book on Gödel's theorem
(Gödel, Escher, Bach), it would be possible to talk on mathematical
logic to the layman, like we can talk on physics to the layman. But I
was wrong. Gödel's theorem is not yet part of the common knowledge,
and when it is used by non mathematician, in general it is abused.
>> x divides y if and only if it exists a number z such that y = x*z.
>
> I don't dare to correct your english but "there is/exists a
> number ..."
> is what I would write.
Thanks.
>
>
>>> Ad 3) If natural numbers and their relations are the only entities
>>> which
>>> do exist then me, you, everything is a recipe of a Turing-computable
>>> number.
>>
>> No. Not at all. Sorry. Gosh, you will be very surprised if you follow
>> the UDA-7. On the contrary. Arithmetical truth VASTLY extends the
>> computable domain. Most relations between numbers are not Turing
>> emulable.
>
> Aha! Then I really have a wrong mental picture of your work. I
> understood to arithmetical realism along the lines of this quotation
> from the Stanford article on realism:
>
> "According to a platonist about arithmetic, the truth of the
> sentence '7
> is prime' entails the existence of an abstract object, the number 7.
> This object is abstract because it has no spatial or temporal
> location,
> and is causally inert. A platonic realist about arithmetic will say
> that
> the number 07 exists and instantiates the property of being prime
> independently of anyone's beliefs, linguistic practices, conceptual
> schemes, and so on."
That is quite correct. All mathematicians are realist about
arithmetic, and most are realist about sets. But set realism is a much
more stronger belief than arithmetical realism.
Comp necessitates arithmetical realism if only to be able to state
Church thesis. Theoretical computer scientist are realist, because
they belief that all machine either stop or not stop.
>
>
> So I thought that you essentially take
> a) Numbers and their properties and relations exists.
Yes, but some people put to much sense in "exists". It is the
mathematical usual sense, like when you derive "there exists a prime
number" from the statement "17 is a prime number". No need to invoke
Plato Heaven, in the assumption.
>
> b) Now, since you don't assume existence of anything else => your
> body,
> your bike and coffee must emerge as patterns in the world of numbers.
I am agnostic. I assume neither that something else exists nor that it
does not exist, and then I prove from the assumption that we are
turing emulable, that physics is no more the fundamental science. I
prove that if we are machine then matter has to be an emerging
epistemological concept, and physics is a branch of machine biology/
psychology/theology, or mathematical computer science.
"b)" is obviously non valid. The fact that bike an coffee must emerge
from numbers is really the conclusion of the whole UD reasoning. It is
not because I don't assume them, it is because their independent
existence is shown contradictory.
I show that mechanism makes physicalism epistemologically
inconsistent. Even if matter really exists, it cannot be used to
justify our belief in matter. A slight application of Occam razor
eliminates matter, at that stage.
>
> c) Taking the Church-Turing thesis, these patterns are Turing-
> computable.
Not at all. The world of number is provably not Turing-computable.
Only a very tiny part of the world of number is computable. There is a
whole branch of mathematical logic devoted to the study of the degree
of non computability of the relations existing among the numbers.
Church thesis asserts only that the *computable* patterns are Turing
computable. It is just the assertion that Turing computability can be
used to define computability.
>
> d) Definitely, the vast majority of all patterns is not Turing-
> computable.
I don't understand.
>
>
> This is how I have thought about your working framework. Notice,
> that I
> don't talk about what you try to show, argue for, want to end up
> with etc.
My framework, comp, is just the hypothesis that I can survive with an
artificial digital brain (even material, if you want). That's all.
The negation of comp is "my soul/person/consciousness" is not Turing
emulable. Or I say "no" to all doctors. Or "I don't survive classical
teleportation done at any level".
I use the term "computationalism" in its standard usual traditional
sense. If you assume explicitly that computationalism needs the brain
to be a material object, then the UDA can be seen as a reductio ad
absurdo.
The conclusion of UDA is that Materialism is incompatible with
Computationalism. It is not obvious, but given that the numerous
attempts by materialist to solve the mind body problem have failed, it
is not so astonishing that a solution of the mind body problem needs
some "scientific revolution". The "revolution" is the reversal between
physics and the "theology of numbers" (the study of what numbers can
believe in, can know, can bet on, etc.).
Bruno
http://iridia.ulb.ac.be/~marchal/
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Received on Wed Aug 05 2009 - 10:42:48 PDT