Re: My talk about Godel to the post-grads.

On Thu, 03 Jul 2008 22:32:22 +0100, John Jones <jonescardiff@xxxxxxx>
wrote:

MoeBlee wrote:
On Jul 3, 4:36 am, John Jones <jonescard...@xxxxxxx> wrote:

For example, I made no mention of the use of "+" in 'PA + "PA is
inconsistent' which looks idiosyncratic: statements are hardly arraigned
to display consistency by being added.

You ignoramus, '+' in that context is informal shorthand for the
binary union operation.

Go on, tell me that "binary union operation" is formal longhand for +.

But if the sign is 'technically'
employed, to mean "inclusion" perhaps, then it seems that by taking it
for granted we can include pretty well anything we want, whether it
makes sense or no.

No, it is understood informally as standing not for inclusion but for
union.

So, this 'union', it must be somehow, kinda, special, sort of technical.
Like grandmother's heiroglyphic fudge recipe, mysterious.

You _really_ don't know what the union of two sets is?


And it does not make sense in the instance you presented, for how would
one 'include' in a consistent system an inconsistent statement?

No one did.

You are right. They didn't include it, or add it- they unionised it.

Any
formal statement that tries to represent that is, as another author put
it, unsound.

Yes, the theory is unsound, but not inconsistent.

That allows two different ideas of theory, one relative, one absolute,
respectively. I.e. the statement
"the theory is unsound, but not inconsistent" is neither unsound nor
inconsistent, but equivocal.


Now answer that. For it looks as though the statement 'PA + "PA is
inconsistent"

It's not a single statement. It's a theory.

It's a statement.

obviously proves "PA is inconsistent"' doesn't get out the
starting gate.

David C. Ullrich

"Understanding Godel isn't about following his formal proof.
That would make a mockery of everything Godel was up to."
(John Jones, "My talk about Godel to the post-grads."
in sci.logic.)
.

Relevant Pages

  • Re: My talk about Godel to the post-grads.
    ... inconsistent' which looks idiosyncratic: statements are hardly arraigned ... to display consistency by being added. ... tell me that "binary union operation" is formal longhand for +. ... Ux is the set of all members of members of x and ...
    (sci.logic)
  • Re: My talk about Godel to the post-grads.
    ... out to you exactly what is incorrect in your remarks (such as, ... A better word than unsound is contradiction. ... But better than both unsound or contradiction is 'inconsistent'. ...
    (sci.logic)
  • Re: My talk about Godel to the post-grads.
    ... inconsistent". ... And on that basis, at least for this example, we can prove the inconsistent by the unsound. ... unsoundness would seem to require a meta-theory in order to assert that statements are false when a theory shows them to be true. ... "If PA is consistent, then the statement 'PA is inconsistent'" is unsound! ...
    (sci.logic)
  • Re: My talk about Godel to the post-grads.
    ... out to you exactly what is incorrect in your remarks (such as, ... A better word than unsound is contradiction. ... But better than both unsound or contradiction is 'inconsistent'. ...
    (sci.logic)
  • Re: My talk about Godel to the post-grads.
    ... inconsistent' which looks idiosyncratic: statements are hardly arraigned ... to display consistency by being added. ... '+' in that context is informal shorthand for the ... binary union operation. ...
    (sci.logic)