Bruno Marchal wrote:
Some embeddings that could be represented by this number relations
could
"prove" utter nonsense. For example, if you interpret 166568 to
mean
"!=" or
"^6" instead of "=>", the whole proof is nonsense.
Sure, and if I interpret the soap for a pope, I can be in trouble.
Right, but that's exactly what Gödel is doing. 11132 does not mean
"="
anymore than "soap" means "pope", except if artificially defined.
But even
than the meaning/proof is in the decoding not in 11132 or "soap".
If we just take Gödel to make a statement about what encodings
together with
decoding can express, he is right, we can encope "pope" with "soap"
as well,
but this shows something about our encodings, not about what we use
to do
it.
Bruno Marchal wrote:
That is why we fix a non ambiguous embedding once and for all.
How using only arithmetics?
Bruno Marchal wrote:
Thus Gödel's proof necessarily needs a meta-level,
Yes. the point is that the metalevel can be embedded non ambiguously
in a faithfull manner in arithmetic.
It is the heart of theoretical computer science. You really should
study the subject.
You should stop studying and start to actually start to question the
validity of what you are studying ;)
Sorry, I just had to say that, now that you made that remark
numerous times.
It is like saying "You should really study the bible to understand
why
christianity is right.".
Studying the bible in detail will not reveal the flaw unless you
are willing
to question it (and then studying it becomes relatively superfluous).
Bruno Marchal wrote:
I don't see how any explanation of Gödel could even adress the
problem.
You created a problem which is not there.
Nope. You try to talk away a problem that is there.
Bruno Marchal wrote:
It
seems to be very fundamental to the idea of the proof itself, not
the proof
as such. Maybe you can explain how to solve it?
But please don't say that we can embed the process of assigning
Gödel
numbers in arithmetic itself.
?
a number like s(s(0))) can have its description, be 2^'s' * 3^(... ,
which will give a very big number, s(s(s(s(s(s(s(s(s(s(s(s...
(s(s(s(0))))))))))))...))). That correspondence will be defined in
term of addition, multiplication and logical symbols, equality.
I don't see what your reply has to do with my remark. In fact, it
just
demonstrates that you ignore it. How to do this embedding without a
meta-language (like you just used by saying 'have its description'
- there
is no such axiom in arithmetic).
Bruno Marchal wrote:
This would need another non-unique embedding
of syntax, hence leading to the same problem (just worse).
Not at all. You confuse the embedding and its description of the
embedding, and the description of the description, but you get this
trivially by using the Gödel number of a Gödel number.
Maybe actually show how I am wrong rather than just saying that I
confuse
everything?
Bruno Marchal wrote:
For more detail and further points about Gödel you may take a look
at this
website: http://jamesrmeyer.com/godel_flaw.html
And now you refer to a site pretending having found a flaw in
Gödel's
proof. (sigh).
You could tell me at the start that you believe Gödel was wrong.
I tried to be fair and admit that Gödel did prove something (about
what
numbers can express together with a meta-level).
If you believe that Gödel proved something about arithmetics as
seperate
axiomatic systems, then the site clearly shows numerous cricitical
flaws. It
is not pretending anything. It is clearly pointing out where the
flaws lie
(and similar flaws in other related proofs). I haven't even see any
real
attempt to show how he is wrong. All responses amount to little
more than
denial or authoritative argument or obfuscaction.
The main reason that people don't see the flaw is because they
abstract so
much that they abstract away the error (but also the meaning of the
proof)
and because they are dogmatic about authorities being right.
That's why studying will not help much. It just creates more
abstraction,
further hiding the error.
benjayk
