On 16 Oct 2014, at 13:46, David Nyman wrote:
On 15 October 2014 19:32, Bruno Marchal <[email protected]> wrote:
If Churchland logic is applied in the case of comp, it leads to the
the idea that not only the first person is eliminated, but also all
references to the gluons, quarks, electron, bosons, fermions, waves,
probability, taxes, etc. All we have is elementary arithmetic.
Interesting. In an earlier conversation, I suggested to you that
realism about composite entities such as those you list above (and I
guess even quarks would be composite with respect to elementary
arithmetic) could ultimately be justified only by including the
logic of the knower. You seemed to disagree, but perhaps your point
is that such realism is epistemological rather than ontological?
Exactly.
In fact, physics, psychology, theology, are invariant for the change
of the fundamental ontology, once it is rich enough to prove he
existence of an effective (Turing) universal entity, like elementary
arithmetic (*), or any first order specification of any Turing
universal system.
Then incompleteness, is unavoidable for the "sound/correct" machines,
but if they obeys K4, they can justify that it has to be like that.
Löbian machine can know that they are universal, and they know the
price of consistency (the possibility of inconsistency).
Such machines looking inward will know (in the weak sense of
Theaetetus applied to provability) the difference between proof and
truth, and between provable, and provable-and-true, and will get all
Platonist internal nuances between rationally believing, and knowing,
and then also observing/betting (where proofs are attached to
consistency, or possibility, that is what is provable-and-consistent).
Gerson fears that the Theaetetus definition makes knowledge
propositional, but incompleteness prevents the machine to even define
"provable-and-true" in (any) of its available languages. The first
person "I" of the machine is not a machine, but it can still be
studied with mathematical tools, and its existence makes sense with
the usual classical analysis (which is not effective or constructive a
priori, especially theology, which will be essentially negative? You
and God are not this, nor that, ...
Bruno
(*)(that is not entirely obvious, but proved since a long time, a
proof begun by Gödel, but made definite with Church thesis by Turing,
Post, Church, Kleene, and the birth of recursion theory which studies
mainly the degrees on non-computability),
David
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