On 20 Jun 2016, at 06:09, Bruce Kellett wrote:
On 20/06/2016 3:34 am, Bruno Marchal wrote:
On 18 Jun 2016, at 02:59, Bruce Kellett wrote:
Smolin's book with someone-or-other is possibly more useful: he
rejects platonism and says that a better way is to seem
mathematics as "evoked" -- i.e., it has properties independent of
us, but we 'evoke' it by specifying some axioms. These axioms (and
their consequences) are not pre-existent in any sense.
That expression is misleading.
An axiom is supposed to be true in some structure, not existent.
Then the axiom itself might be existent in some other theories.
Axioms are what we say they are -- they are neither true nor false.
We talk about machines and numbers, and we do have a good intuition
before chosing the axioms and definitions. Indeed, in math we don't
formalize our theories, even in logic. We study formal theories, but
we use informal theories.
They might be true statements about some model or domain, but that
does not define them as axioms.
To just define "digital machine", or "computationalism" we need the
Church-Turing thesis, we need a good intution of the natural numbers
(but less that we need in trigonometry, so it is usually considered as
being a very weak theory).
If you believe that Euclid is false, or that Diophante is false, just
say so at once. I use less assumptions than most scientists.
The Peano axioms might find expression in the integers, but that
does not imply that the integers "exist" in any meaningful sense.
It exists in the sense that either a counter-example to Riemann
hypothesis exists, or it does not.
Now in the case of "rich" (Gödel-Löbian), in fact in the case of
all essentially undecidable theories, (like RA, PA, ZF, ...) the
theory are rich enough so that their axioms and consequences are
reflected in the relation between the objects they talk about. That
is why both "2 + 2 = 4" and "ZF proves "2 + 2 = 4"" are elementary
arithmetical propositions (even provable by the very weak non
Löbian RA). In that sense the axiom are pré-existent, but only in
the mind of the universal numbers. It is like the distribution of
primes is well defined, even before the first mathematician
discovered the prime number and look at its distribution.
Mathematicians are not universal numbers!
Of course there are, provably.
I guess you mean that they are more than that. That can be true.
All I say is about those mathematicians (or not) saying "yes" to the
doctor. Then a mathematician is a universal number, but admittedly in
a sense close to just say that the sun is a star. Which does not say
much.
The axioms exist only in the minds of mathematicians, not in
"universal numbers",
Then mechanism is false. But with Church thesis and "yes doctor",
which are my assumptions, then it is a theorem that even you right now
and here are in infinitely many number relations.
whatever they might be. The distribution of primes is determined by
the existence of integers and the definition of prime numbers -- and
both are the inventions of mathematicians.
In which theory? Well, it is wrong. Some insects use them since much
more than humans.
May be you could try to formalize your physicalist theory to see if
it assumes or not the numbers or any universal system at the start.
To use numbers, or mathematics in general, in physics does not
require that these things exist at the start.
I don't do philosophy.
I just show that mechanism and materialism are inconsistent when taken
together, or required some supermagical phlogiston.
They are simply descriptions of objects in the universe we observe
-- mind-dependent, like colours, emotions, or sensations. Take a
Humean stance -- the "laws of physics" are not handed down from on
high; they are not pre-existent in any sense -- they are the
mechanisms we construct to formalize the regularities we observe
around us.
Excellent. I agree. A reason more be able to variate the explanation
of such regularities, as we don't observe that they are "real". Oh,
the simplest explanation is that it is universal coherent number
dreams, as those exists, even once we suppose the numbers, like
phsyicists already suppose.
That is why the "laws of physics" are only ever provisional, subject
to revision in the light of new and better data.
You miss that we need also a theory to relate the observer as a person
to what we infer the possible existence, and *that* is what is debated
here. The use of your identity link simply does not work.
Bruno
Bruce
Then all what UDA shows, is that if you do assume it, adding Matter
just does not work for the mind-body problem.
Physicalism/computationalism is just testable. And then QM (without
the dualist collapse) adds evidence to digital mechanism.
Bruno
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