On 15 Jan 2014, at 16:59, Edgar L. Owen wrote:
Bruno,
If you assume the basic axioms of arithmetic are the basic axioms of
reality then you ARE effectively saying that "Arithmetic exists
because arithmetic exists."
That is true.
But the premise is incorrect.
I do not assume that the basic axioms of arithmetic are the basic
axioms of reality.
That is, on the contrary, what I *prove*, from the computationalist
assumption.
UDA proves it quickly, (in 8th step) and AUDA extracts constructively
the quanta (and the qualia).
whether you verbalize it or not, and that is your implicit unstated
fundamental axiom.
That is certainly not less circular than my fundamental axiom, and
considerably less convincing....
If that is not your fundamental axiom then what is?
The intuitive theology (comp) is the bet that I would survive, or even
that I would not notice the difference, once a computer simulating my
body, at some level of description, is provided. ("yes doctor")
UDA shows, or is supposed to show, that if that is true, then physics
has to be recovered by a relative statistical calculus on all
computations (modalized by internal points of view, or indexicals) in
arithmetic.
UDA shows that the TOE is anything Turing complete "thing". I use
Arithmetic because it is taught in school.
AUDA does a part of that recovering, so we can already compare that
physics with the actual observation.
Bruno
Edgar
On Wednesday, January 15, 2014 8:50:44 AM UTC-5, Bruno Marchal wrote:
On 15 Jan 2014, at 13:41, Edgar L. Owen wrote:
Bruno,
Of course it is circular - but it is meaningful.
Without further ado, circular statements are *to much* meaningful.
The fundamental axiom MUST be circular,
Is that anew meta-axiom? Again, that is not obvious at all.
but it must be so in a meaningful way. I already noted that when I
said it was 'self-necessitating'.
"self-necessitating" contains two hot complex notions: "self" and
"necessitate".
We want to explain the complex from the simple, not the other way
round.
So far as I know my Existence Axiom is the most meaningful
fundamental axiom.
If that was true, you would not need to say so.
What is YOUR fundamental axiom? 'Arithmetic exists because
arithmetic exists' perhaps? Sounds like a similarly circular axiom
to me....
You should also never put statements in the mouth of others,
especially when they are completely ridiculous, like if I would have
said that "arithmetic exists because arithmetic exists".
I am working at two levels: an intuitive meta-level, where the
assumption is a precise version of Milinda-Descartes old mechanist
assumption. To put it shortly it says that not only I can survive
with an artificial heart, kidney, skin, but that the brain is not
excluded from that list. It means that my body functions, at some
level, like some sort of machine. As far as I understand you, it
is implied by your "computational stance".
So my assumption, at that level, is a tiny part of your assumption.
By reasoning at that meta-level (UDA), we get as "meta-theorem" that
the TOE does not need to assume more than the usual elementary
axioms of arithmetic. One precise theory is classical logic + the
axioms, where you can read s(x) by "the successor of the number x".
0 ≠ s(x)
s(x) = s(y) -> x = y
x+0 = x
x+s(y) = s(x+y)
x*0=0
x*s(y)=(x*y)+x
Then, in that theory, all the terms I need are defined. It is in
that theory that we define the observers and derive physics (and
more). That's AUDA, or "the machine's interview" (in the sane2004
paper). Comp makes the whole thing both mathematical and
experimentally testable.
Bruno
Edgar
On Wednesday, January 15, 2014 3:10:30 AM UTC-5, Bruno Marchal wrote:
On 14 Jan 2014, at 19:05, Edgar L. Owen wrote:
> Bruno,
>
> 'Non-existence cannot exist', obviously refers to the existence of
> reality itself,
Then it is circular.
> not to milk in your refrigerator! Existence must exist means
> something must exist, whether it's milk or whatever. Individual
> things have individual localized existences, but existence
(reality)
> itself is everywhere because it defines the logical space of
reality
> by its existence.
That is not intelligible.
>
> The Axiom of Existence means there was never a nothingness out of
> which somethingness (the universe) was created.
Assuming that there is a "universe". But then you do not explain why
there is something. You just assume this. You axiom is "something
exists".
>
> Milk is created by female mammals in case you had some doubt?
> :-)
>
> Next question: Reality IS a computational MACHINE in the general
> sense of machine.
That is digital physics, which is refuted.
> Thus of course consistency applies to it.
That does not follow. Machines can be inconsistent.
Bruno
http://iridia.ulb.ac.be/~marchal/
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