On 25 Sep 2017, at 02:01, Russell Standish wrote:
On Sat, Sep 23, 2017 at 10:34:14AM +0200, Bruno Marchal wrote:
Now, this does not necessarily concern us. I think. Even ZF and ZF
+Choice proves the same theorems in arithmetic. That is probably not
the case for ZF and ZF + CH, but the comp ontology will not change.
For the phenomenology, that might change something though, making
the measure problem more easy or more difficult. We are not yet
enough advanced on this to decide, i think. model theory and set
theory are *quite* complex compared to arithmetic!
If comp ontology does not depend on CH (seems plausible), but there is
an effect of phenomenology, then so much the worse for comp. Comp
predicts that phenomenology is purely derivable from comp.
The existence of the phenomenology is derivable.
Then it happens that its propositional part is entirely derivable, due
to Solovay arithmetical completeness of G and G*.
But the first order part can be shown being highly undecidable and
incomplete. For a theology, the contrary would have been embarrassing.
However, I tend to agree with Saibal that things like the CH will
prove irrelevant to phenomenology.
I agree for CH, which has no application at all (but of course: who
knows?, and Kiesler' work might change this, although I am not sure).
It is a different matter for the axiom of choice (needed for having a
base in all Hilbert spaces, for example). Anyway: the phenomenology,
and the ONE have a complexity which is unboundable from "inside
arithmetic". With Mechanism, all theories of mind are incomplete, and
cannot be completed effectively.
Bruno
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Dr Russell Standish Phone 0425 253119 (mobile)
Principal, High Performance Coders
Visiting Senior Research Fellow [email protected]
Economics, Kingston University http://www.hpcoders.com.au
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