Re: Torkel Franzen on truth

Newberry says...

On Dec 12, 6:46 am, stevendaryl3...@xxxxxxxxx (Daryl McCullough)
wrote:

We already went throug this circe 15 times.

Yes, I know. I keep thinking that you can be convinced
about how ridiculous your argument. It's complete nonsense.

That's why I asked you to put it in the form of a syllogism,
so you can see that your conclusions *don't* follow from your
hypotheses.

a) The consistency of PA is provable
b) But the proof does not have any cogency

I don't grant that at all. Why not say what is actually
the case: "The proof of the consistency of PA (or *any*
theory, for that matter) requires principles that go
beyond PA". To conclude that that means that the proof
has no cogency is just silly.

c) Since we know that PA is consistent we surpass any machine

That's a non sequitur. You haven't demonstrated that
no machine can "know" that PA is consistent, because
you haven't defined the word "to know". Define it *first*.
*Then* demonstrate that humans know that PA is consistent
*using* this definition. *Then* demonstrate, using the
*same* definition, that no computer program can know that
PA is consistent.

So there are at least three gaps in your argument.
(1) You haven't defined what it means to "know" a
mathematical fact.
(2) You haven't demonstrated that humans know that
PA is consistent using that definition.
(3) You haven't demonstrated that machines cannot
know that PA is consistent using that definition.

There are several candidate definitions of "know"
under which humans can be said to know that PA is
consistent. There are other candidate definitions
of "know" under which nobody ever knows anything.

You are applying one definition to humans, and
a *different* definition to machines.

You have to *pick* one, and show that humans know
PA is consistent by that definition, and that machines
cannot know it, by that same definition.

--
Daryl McCullough
Ithaca, NY

.

Relevant Pages

  • Re: Laws of Intelligence -2
    ... >> reflect consistent basic patterns of mental activity? ... >> creative mental activity can be described in terms of laws. ... >humans because of the way our brains work. ...
    (talk.origins)
  • Re: Torkel Franzen on truth
    ... etc. Deriving what follows from those principles. ... humans believe that PA is consistent? ... No formal proof of PA has any cogency ...
    (sci.logic)
  • Re: Torkel Franzen on truth
    ... etc. Deriving what follows from those principles. ... Humans believe that PA is consistent. ... rely on mathematical principles that go beyond PA. ...
    (sci.logic)
  • Re: OT:Thanksgiving
    ... would be consistent with His nature." ... "the same" characteristics as a hand tool, ... that their creators (humans) wanted them. ... consistent with nature, I agree. ...
    (comp.lang.cobol)
  • Re: "true" AI Hardware Development
    ... resistance to functional description at all. ... that we can build functionally equivalent machines. ... no two humans are the same. ... Do you understand that all computers are physical machines that work by ...
    (comp.ai.philosophy)