On 04 Sep 2017, at 01:00, spudboy100 via Everything List wrote:
I cannot see Math Not being real, because it would fail, enormously,
if "laws" of the cosmos, did not work. In other words, we could
describe the world via phlogiston mist, or, luminiferous ether (tip
o' the hat to the 19th century scientists), so it works. If math
didn't work, simple objects like planets would not reliably work,
circling their parent star. Are there any counter-examples, where
Math fails to describe? Or, does Math have real examples of failure?
Please cite these. G'wan!
I agree math is real in that sense, but for a TOE it can be important
to agree at least that some part is real, in its meaning, and
everybody do agree on first-order classical arithmetic without
induction (even Nelson and the ultrafinitist). I think that doubting
that entails the doubting that "doubting" means anything.
And with mechanism, we don't need more than that, as that characterize
universal computability (in the sense of Turing, Post, Church, Kleene).
So I put the "induction axioms" (the formula (F(0) & F(n) -> F(n+1)
for all n -> F(n) for all n) already in the epistemological tools.
In mathematics, all attempt to get a theory of everything failed, and
there are quasi logical reason to bet that the mathematical reality is
not mathematically describable. This does not mean that set theories
and category theories (the "TOE" for math) are not interesting, even
for mechanism in the long run.
Only the computable has that miraculous property of being able to
invite its god, the universal machine, at the table of discussion! To
be sure, this applies to machine with oracles and other relativized
notions.
With mechanism, the physical has a mathematical origin, which at least
explain why the physical is so much mathematical.
Bruno
-----Original Message-----
From: David Nyman <da...@davidnyman.com>
To: everything-list <everything-list@googlegroups.com>
Sent: Sun, Sep 3, 2017 6:07 pm
Subject: Re: Is math real?
On 3 September 2017 at 17:46, Brent Meeker <meeke...@verizon.net>
wrote:
On 9/3/2017 7:06 AM, Bruno Marchal wrote:
On 01 Sep 2017, at 19:57, Brent Meeker wrote:
On 9/1/2017 1:03 AM, Bruno Marchal wrote:
This leaves, as Bruno says, lots of white rabbits.
That leaves us in the position of showing that there is no white
rabbits or, to refute computationalism by showing there are still
white rabbits, and then you can try to invent some matter or god
able to eliminate them, but that will in any case refute mechanism.
What if getting rid of those white rabbits tightly constrains
consciousness and physics to something like what we observe?
Exactly. Getting rid of the white rabbit = proving the existence of
the relevant measure = deriving physics from machine theology (alias
elementary arithmetic).
Then it will have been shown that physics entails consciousness as
well as the other way around.
OK. But arithmetic is a subtheory of any physical theory. The
progress are the following
Copenhagen QM: assume a physical reality + a dualist and unclear
theory of mind
Everett QM: assume a universal wave + the mechanist theory of mind
(+ an identity thesis).
Me: the mechanist theory of mind (elementary arithmetic).
Brent wrote to David:
I am agreeing with you. I only disagree with Bruno in that he wants
to take arithmetic or computation as more really real than physics
or consciousness and not derivative. It seems to me that the very
possibility of computation depends on the physics of the world and
is invented by evolution.
But that is plainly false. I can prove the existence of computation
in arithmetic.
After you assume arithmetic. I can prove anything if I get to
choose the axioms.
On the contrary, we can only speculate on a primary physical reality
for which there are no evidences at all.
You can't prove primary arithmetic either. "Primary" is just a word
you stick on "physical" to make it seem inaccessible.
I don't think that's right. Primary just means that part of a
theory that is assumed rather than derived. In the case at hand the
theory is mechanism, in which it is assumed that concrete or
phenomenal reality is ultimately an epistemological consequence of
computation. That being the case, the theory relies on computation,
or its combinatorial basis, as its ontology (i.e. that part of the
theory that is taken to exist independently of point-of-view). It
then sets out to derive its phenomenology by means of an
epistemological analysis (i.e. that part of the theory that is
understood to be point-of-view relative) based on the generic or
universal machine as unique subject or agent. Physics, as an
observationally-selected subset both of the computational ontology
and its derived phenomenology, cannot thus be considered primary, in
the sense given here. Rather, it makes its appearance as a tightly-
constrained extensional infrastructure in terms of which the
machine's phenomenology is enabled to play out in action.
David
I don't need to prove the physical, I observe it.
Your argument is 100% the same as saying "It seems to me that the
very possibility of computation depends on God".
If God or Matter plays a role in a computation, then you are not
taking the word "computation" in its standard meaning (cf Church-
Turing-Post-Kleene thesis), and I have no clue at all what you are
talking about.
So you put words in my mouth and then complain that you don't know
what I'm talking about?
Brent
Bruno
Brent
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