On 27 May 2012, at 23:56, John Mikes wrote:
Thanks, Brent and Bruno. You are kind to respond.
The point I wanted to approach (far approach, indeed) is that
whatever we derive (mentally) about Nature comes from our human
mind, be it binary or not.
We don't know that. We believe that.
I might be a butterfly only dreaming that he is human.
I might be an amnesic God, just playing to himself that he is a human.
Nor do we know if something like Nature exist.
We do know that we are conscious, but not much more. We believe more,
and that's OK, if we grant that those are beliefs, which means that we
are aware that they might be wrong.
And: it is not BINDING (restricting?) upon Nature, there may be more
we cannot even imagine within our limited capabilities.
And here computationalism, the theory or hypothesis, makes it possible
to say more, like the fact that Nature is necessarily, in that theory,
a sort of surface emerging from the vaster volume of a sort of mind,
itself emerging in a precise way from arithmetic or alike.
We think in our 'model of knowables' and it is incredible how far we
got.
Except that I can argue that if COMP is true, then we have regressed
since +500. We have made some progress in technology, and even, I
think, in politics (at least conceptually), but we have transformed
science into religion, and religion into superstition. As long as we
oppose mysticism and rationalism, we can only regress. We are hiding
the data since 1500 years. Modernity has existed from -500 to +500, in
some limited circle. Since then we are in the obscurantist era. The
most fundamental science, theology, is still abandoned to
authoritarians.
A figment of a physical world, an 'almost' perfect technology with a
reductionist (conventional) science and I don't even mention: math.
I read your discussions with awe and keep my agnostic indeterminism.
That is the genuine scientific attitude.
Bruno
JohnM
On Sat, May 26, 2012 at 6:06 PM, meekerdb <[email protected]>
wrote:
On 5/26/2012 9:35 AM, John Mikes wrote:
Brent wrote:
1. Presumably those true things would not be 'real'. Only provable
things would be true of reality.
Just to be clear, I didn't write 1. above. But I did write 2. below.
2. Does arithmetic have 'finite information content'? Is the axiom
of succession just one or is it a schema of infinitely many axioms?
Appreciable, even in layman's logic.
In '#1' - I question "provable" since in my agnosticism an
'evidence' is partial only, leaving open lots of (so far?) unknown/
able aspects to be covered. In the infinity(?) of the "world" also
the contrary of an evidence may be 'true'.
As Bruno said, "Provable is always relative to some axioms and rules
of inference. It is quite independent of "true of reality". Which
is why I'm highly suspicious of ideas like deriving all of reality
from arithmetic, which we know only from axioms and inferences.
#2 is a technically precise formulation of what I tried to express
in my post to Bruno.
IFF!!! "anything" (i.e. everything) can be expressed by numerals,
the information included into arithmetic IS infinite,
I see no reason to suppose that. Everything ever expressed so far
has been done with a finite part of arithmetic. Assuming every
integer has a successor is just a convenience for modeling things;
you don't have to worry about running out of counters. There is a
book "Ad Infinitum, The Ghost in Turing's Machine" by Rotman that
proposes what he calls "non-euclidean arithmetic" which does not
assume the integers are infinite. I can't really recommend the book
because most of it is written in the style of French
deconstructionist philosophy, but the Appendix has some interesting
ideas.
however as it seems: in our (restricted) view of "the
world" (Nature?) there seem to be NO numbers to begin with.
In our human 'translation' we see 1,2, or 145, or a million "OF
SOMETHING" - no the (integer?) numerals.
Axioms? in my vocabulary: imagined things, necessary for certain
theories we cannot substantiate otherwise.
Axioms are just part of a logical, i.e. self-consistent, system.
Mathematicians don't even care if they are "true of reality". They
may or may not refer to imagined things; they are just assumed true
for some inferences. I could take "I am typing on a keyboard" as an
axiom, which I also happen to think is true, or I could take "I am a
projection in a Hilbert space" which might be true, but is much more
dubious.
In another logic than human, in another figment of a "physical
world" different axioms would serve science.
Logic is about the relations of propositions, statements in
language. Humans already have invented different logics.
2+2=4? not necessarily in the (fictitious) "octimality" of the
'[Zarathustran' aliens in the Cohen-Stewart books
(still product of human minds).
2+2=11
Brent
"The world consists of 10 kinds of people. Those who think in
binary and those who don't.
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