Re: Godel proved maths inconsistent not incompleteness theorem

On Mar 14, 2:47 pm, Alan Smaill <sma...@xxxxxxxxxxxxxxxx> wrote:
Charlie-Boo <shymath...@xxxxxxxxx> writes:
On Mar 14, 7:28 am, Alan Smaill <sma...@xxxxxxxxxxxxxxxx> wrote:
Charlie-Boo <shymath...@xxxxxxxxx> writes:
On Mar 13, 8:54 am, Alan Smaill <sma...@xxxxxxxxxxxxxxxx> wrote:
Charlie-Boo <shymath...@xxxxxxxxx> writes:
On Mar 12, 12:11 pm, Alan Smaill <sma...@xxxxxxxxxxxxxxxx> wrote:
Charlie-Boo <shymath...@xxxxxxxxx> writes:
On Mar 11, 1:07 pm, Alan Smaill <sma...@xxxxxxxxxxxxxxxx> wrote:
...
where can I find the list of all CBL axioms?

Here:

1. Program Synthesis e.g. for PHP programs

"e.g." doesn't cut it.

Please read the rest and comprehend.  There are an infinite number of
programming languages.  I show the axioms for one enough to synthesize
a useful program nobody else has ever synthesized, the test for being
a factor.

That's just it ... I ask for the list of *all* axioms, and
you reply with examples.

There are an infinite number of programming languages.  For the ones
used as output to your Program Synthesis system, you give axioms for
the constructs in that language.  Most languages are terribly
redundant - theoretically all they need is constants, if, addition,
loops.  But there are bigger constructs such as multiplication and it
makes better programs if it can use that as well, so we need to
include enough to cover the domain we are in.

And if you end up with a system that can't prove associativity of
multiplication, you chuck in an extra axiom, etc etc etc.

CBL was designed to prove metamathematical statements about truth,
provability and related concepts.  As far as applying CBL to simple
mathematical facts, I have recently considered that as it may in fact
enhance the metamathematical proofs.

If P expresses a representable set then P(a) <=> |-P(a) ?  I may be
able to prove associativity of addition simply by showing that a
particular relation is representable and adding this new,
"Mathematical" rule to CBL:

P(x) <=> P(a) , |- P(a)

great, eh -- a new rule.

truly CBL is a never-ending mystery.

CBL proves properties of proving. Now you want to prove properties of
number and relations.

Why not crank the handle and find out if CBL proves associativity
when you add the rule?  After all, that's its great advantage, isn't
it -- automatic generation of proofs?

Yet you can't tell us whether your new enhanced version can prove
one of the most basic facts about addition.

You'll just have to make that an official challenge, I'm afraid
(directions above.)

C-B

--
Alan Smaill
.

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