On 12 Jun 2016, at 00:44, John Clark wrote:
On Sat, Jun 11, 2016 at 3:03 PM, Brent Meeker <[email protected]>
wrote:
>There are no "incorrect calculations".
2+2=5
> It's just a universal Turing machine that runs all one step
programs, all two step programs, etc. Some programs stop. Some
programs fall into infinite loops. Some just keep computing.
And some are consistent with the Peano postulates and some are
not, those that aren't physicists have no use for because they can
attach no meaning to them. Mathematicians could start with 2+2=5 as
an axiom and build some form of arithmetic from that, it would be a
pretty silly thing to do but it wouldn't surprise me if some
mathematician had actually done it. And that's the trouble with
mathematicians, sometimes when they drift higher and higher into the
stratosphere they start to sound like Minnie Mouse on helium.
Physicist are bound by something, observational facts, but
mathematicians have no such bound so sometimes they end up moving in
all directions and going nowhere.
> These are all abstract processes that "exist" in the
mathematical sense.
What sense is that?
> There is no sense in which they can be correct or incorrect.
What about non-sense?
PA + the axiom "PA is inconsistent" give ... a consistent theory. It
even gives a more powerful theory than PA, in which you can prove more
theorems than in PA (and my friend and late student Eric Vandenbussche
succeeded in proving that some new theorem can be non trivial and
"interesting" (in some technical sense).
Arithmetic is open to some form on nonsense, which is good for a
theory of consciousness. The only question is: do we have to add the
nonsense at the start, and rationalist prefer not.
Bruno
John K Clark
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