On 30 Jul 2012, at 16:20, David Nyman wrote:
On 30 July 2012 13:11, Bruno Marchal <marc...@ulb.ac.be> wrote:
If we are removing ourselves from the object of our study we must
remove all things that are implied. It is the observer that acts,
not the object alone. All of the properties, such as reflexivity,
transitivity, symmetry, do freeze and cease to be anything active.
You come back with your solipsist anthropomorphic conception of the
arithmetical truth. It does not work with comp at the start.
This seems moot to me. Could you be more precise about why we might
be justified in thinking of arithmetical truth as eternal but
nonetheless subject to change?
I think it is better to say that the arithmetical truth are atemporal,
for they are not depending on time or on space at all.
So arithmetical truth, as opposed to our human (or any machine)
knowledge of it, is not subject to change.
"We" and most machines are subject to change, relatively to our most
probable supporting universal system, which themselves might be
subject to change, relatively to some other universal system, ll this
up to the once we choose as a basis (of the phi_i).
The changes are relative, and entirely defined relatively to universal
numbers (the arithmetical computer existing in arithmetic).
A computation is a sequence of states related by computational steps
through the operation of some universal number, like phi_i(j)^0,
phi_i(j)^1, phi_i(j)^2, etc. (that is, the computation of the ith
program on the input j). Such a computation, which can be defined in
arithmetic, might support a self-referential universal program (Bp),
which will develop discourses on its conditions and possible
expectations. As far as that program is self-referentially correct, it
will inherit a distinct (from its code/body) first person notion (Bp &
p), which obeys a logic of subjective time, where time is an ordering
on some of its individuating accessible knowledge states. But it will
also inherit the first person indeterminism on its arithmetically
consistent personal continuations.
All this contribute to its illusion of change and time (and space),
despite everything is statical and relational in the big picture
(arithmetical truth). Time and space are mental indexical
constructions that numbers naturally develop relatively to local
universal structure(s).
I was just opposing Stephen's idea with the comp idea that numbers and
arithmetical truth is a (human) mental construct necessitating some
primitive time, space or physical reality. With comp, I argue that
arithmetical truth is simpler and can explain why the numbers (or
better the person associated to those numbers) construct ideas of time
and space, and why they can believe in some genuine way in them, and
be deluded in believing that they are primitive.
Bruno
http://iridia.ulb.ac.be/~marchal/
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