On 05 Feb 2015, at 20:56, meekerdb wrote:
On 2/5/2015 11:27 AM, Bruno Marchal wrote:
On 05 Feb 2015, at 01:16, meekerdb wrote:
On 2/4/2015 10:13 AM, Bruno Marchal wrote:
With computationalism, physics is not causally closed,
Even with computationalism it seems physics is causally closed
except for the apparent randomness of QM. But if you believe in
MWI that is closed too. The UD is not casually closed because it
is always starting new threads of computation - with no cause.
No cause? It start new threads because it generate them all,
What "it"? How does "it" cause new threads to start?
Facts on the type "2+2=4".
I don't see that causation even means anything in arithmetic,
You can translate "p causes q", at the bottom level by either "p -> q"
or better []p -> []q.
it only imagining proofs as sequences of inference that we get
something like causation.
But it is enough to have a notion of running a program, with the
computer-science notion of execution/emulation. That's why we don't
need to *assume* a physical reality. We get it or not in a verifiable
way.
and dovetail on them. The universal dovetailing is equiavlent with
the proofs, and attempt of proofs, of the sigma_1 sentences.
a bit like arithmetic is not arithmetically closed either, the
universal machine put a mess in Platonia which is beyond the
possible control by the universal machines.
But all computation is closed. What does it matter that there are
uncomputable parts of arithmetic? They don't affect the
computations.
You forget the FPI on the arithmetical reality.
All the instances that produce FPI are also computable.
What produces the FPI is computable/emulable. But the FPI itself is
not, and physics comes from the FPI itself, and the measure, if it
exists (as it seems, technically).
You are speculating on a god "Matter" who by its magical power,
singularize you with that matter, and makes your infinitely many
brothers living in arithmetic into zombies.
And you are assuming that (some) axioms and their consequences
simply exist by the magic of being self-consistent.
No. I assume only that x + 0 = x, and things like that. Those axioms
does not exist. Only 0 and its successors exist. Then it happens that
those axioms can be represented in arithmetic, with the rules, by the
embedding of meta-arithmetic in arithmetic (what Gödel showed).
I have to go. Busy days and week-end. I will probably comment your
other posts a bit later. Sorry.
Have a nice week-end,
Bruno
http://iridia.ulb.ac.be/~marchal/
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