On 06/03/11 19:24, Bruno Marchal wrote:
Yes but! I have no problem with the idea of a Platonic realm of
mathematical structures simply existing, with or without the physical to
instantiate them. I am aware this is a deep philosophical debate, but
the Platonic concept seems somehow more straightforward than the
physicalist concept. But for there to be activity, change, time
evolution, 'in' that Platonic realm, seems to me a massive leap. That
all possible numbers simply exist seems simple and straightforward. And
as Russell S points out, all possible numbers is vastly simpler than
'the numbers we have discovered / used / instantiated / whatever. But to
posit the exercise of some computation requires something utterly
different. There has to be some kind of changing frame of reference, as
in a Turing machine in action. Are you saying you believe in this kind
of procedural process as a process active in an abstract arithmetical
Platonic realm? For it seems this is required in what you declare.
On 06 Mar 2011, at 14:16, Andrew Soltau wrote:
On 07/02/11 15:22, Bruno Marchal wrote:
You say "And the result is easy to describe: physics is not the
fundamental branch.". This is the leap of yours I never understand.
Do you posit that a mathematical universe with no physical content
somehow automatically computes?
Comp makes precise that saying to be a machine is equivalent with
saying that there is a level of functional substitution where my
(first person) consciousness is invariant for a substitution made at
that level. Comp can show that we can never known our level of
substitution, and my reasoning works whatever I mean by my brain (it
could be the entire galaxy or the entire observable universe if
someone asks for it). CTM is vague on the level, and miss the point
that we cannot know it, if it exists.
Comp is also much more general than CTM, which relies usually on
some amount of neurophilosophy, or on representationalist theory of
the mind, and CTM is often criticized by 'externalist', like brent
Meeker for example. But comp is not annoyed by externalism, given
that it defines the (generalized) brain by the portion of universe
you need, like possibly the matrix above.
So comp is a very weak, and thus general, hypothesis. And the result
is easy to describe: physics is not the fundamental branch.
Computations have been discovered by mathematicians, in mathematics.
Models of Sigma_1 complete theories automatically computes indeed. It
is a theorem, even without Church thesis. In physics people usually
bets that some physical devices can approximate such computation. But
apart from Landauer and some others, the notion of physical
computation is not yet even well defined.
But whatever physical computation is, or whatever the process we are
witnessing is, it requires an ongoing change. The Turing machine moves
along the tape, whether it is physical or simply a theoretical construct
of a physical machine. In order to actually move, and carry out the
computation, step by step, it requres more than to exist, it has to act.
There has to be a time evolution of the state of the system.
My leap is a consequence of step seven already, in case the apparent
universe is robust. Then the MGA eliminates the assumption of the
existence and of the robustness of a physical universe.
Irrespective of the existence of a physical universe, something has to
explain how change comes about. Or are you saying that in the
arithmetical universe change 'just happens', in the same way as all
possible numbers 'just happen' to exist?
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