On 23 Jan 2014, at 00:45, meekerdb wrote:
On 1/22/2014 1:38 AM, Bruno Marchal wrote:
On 22 Jan 2014, at 01:02, meekerdb wrote:
On 1/21/2014 3:30 PM, Jason Resch wrote:
On Tue, Jan 21, 2014 at 3:30 PM, meekerdb <[email protected]>
wrote:
On 1/21/2014 8:13 AM, Jason Resch wrote:
Why would you want to do that? It seems like an unnecessary
extra axiom that doesn't have any purpose or utility.
It prevents the paradoxes of undeciability, Cantor
diagonalization, and it corresponds more directly with how we
actually use arithmetic.
I'm not sure it helps. What you may gain from avoiding paradoxes
makes many of our accepted proofs false. E.g. Euclids proof of
infinite primes. Or Euler's identity. Most of math would be
ruined. A circle's circumference would not even be pi*diameter.
Would this biggest number be different for different beings in
different universes? What is it contingent on?
You're taking an Platonic view that there really is an arithmetic
and whether there's a biggest number is an empirical question.
Ah! I just said that is was not. Somehow you deny the reality of
math.
Which math? Finite arithmetic, Peano arithmetic, set theory,
homotopy theory,...? Or in short, yes.
I was thinking of arithmetic.
I see your point as a reductio ad absurdo for my case.
A long time ago, someone told me that the consequence of comp is so
startling that people will come with a critics of even "1+1=2". he
advised me to not answer that critics, except by mentioning that it
helps to complete the reduction ad absurdo.
I'm saying it's an invention. We invented an system in which you
can always add 1 because that was convenient; you don't have to
think about whether you can or not.
So to use this same line of reasoning, would you say there is no
definite (a priori) fact of the matter of whether or not a given
program terminates, unless we actually build a machine executing
that program and observe it terminate?
That's kind of mixing categories since 'program' (to you) means
something in Platonia and there you don't need a machine to run
it. In the physical world there is no question, all programs
running on a machine terminate, for one reason or another. Non-
terminating programs are the result of over idealization.
What makes you sure that the idea that all programs terminates is
not also an idealisation (about a finite universal reality)?
Also, if all programs terminate, there is no more real numbers. I
guess you will say that there are idealisation. You seem to "know"
that there is a concrete reality, but the comp approach to the mind-
body problem asks to, temporarily perhaps, doubt such "certainty".
Of course I'm not *certain*, all theories are defeasible outside of
Platonia.
Inside too.
But it seems like a well supported theory; at least as certain as
"you can always add one more".
All right. But the you see the conflict. You cannot have both, and
that is the point. I don't pretend that we can always add one. I
assume that because it is the only way to give sense to comp. You just
agree that comp is false, which is out of my topic.
You critics of comp is valid, if you assume that there is a bigger
natural number.
We do agree. But then, explain me what is the (small) physical
universe, where does it come from, and why it hurts? you invent a new
arithmetic, just to block an explanation. Is that not gross wishful
thinking?
Bruno
Brent
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