On 10 Sep 2015, at 03:28, Jason Resch wrote:
Gödel left in his papers a fourteen-point outline of his
philosophical beliefs, that are dated around 1960:
The world is rational.
Human reason can, in principle, be developed more highly (through
certain techniques).
There are systematic methods for the solution of all problems (also
art, etc.).
There are other worlds and rational beings of a different and higher
kind.
The world in which we live is not the only one in which we shall
live or have lived.
There is incomparably more knowable a priori than is currently known.
The development of human thought since the Renaissance is thoroughly
intelligible (durchaus einsichtige).
Reason in mankind will be developed in every direction.
Formal rights comprise a real science.
Materialism is false.
The higher beings are connected to the others by analogy, not by
composition.
Concepts have an objective existence.
There is a scientific (exact) philosophy and theology, which deals
with concepts of the highest abstractness; and this is also most
highly fruitful for science.
Religions are, for the most part, bad– but religion is not.
Which is pretty much what you get when taking computationalism, and
thus computer science and mathematical logic, seriously. But Gödel
missed the Church's thesis, and disbelieved Church until his reading
of Turing.
It takes time to understand the impact of the discovery of the
universal machines or numbers and the consequence of the assumption
that this is what we are (in the global 3p view, or 0p view). From
inside "we" are different, and no more machine, or even anything 3p
definable, except by reference to truth (which we can do for simpler
machine than ourselves). Here simplicity is measured by the set of
provable, by the machine, arithmetical sentences.
But I like Gödel when defending that theology can and should be done
seriously. That seems obvious to me. It makes me more bizarre to me
that he did not realize that his incompleteness theorem determined a
non trivial theology, in the original sense of the greek, to a
machine. Theology is a bit of just a meta-semantic of self-referring
machines, relatively to probable continuations.
Of course Gödel distinguish religion and human use and misuse of
religion.
In 10. Materialism is wrong, it is really "materialism" in the
philosophy of mind, that is "matter and only matter".
But Gödel remains Aristotelian in the (of course quite common) belief
in a physical primary reality.
Gödel was mute on QM, and find any question on possible relationship
between incompleteness and quantum uncertainty indecent (or some other
word). But that is not maintainable when you take into account the
(sigma_1) arithmetical FPI.
Gödel was realist on sets, which I am not that much. I am 100%
confident in PA, but only 99,999...998% confident in ZF, mainly due to
the axiom of infinity. I love the ZF machinery but I think the machine
might hallucinate a little bit. I don't know. I have no doubt for the
use and the consistency, but it mushes the extensional viewpoint to
far somehow. The modal quantified predicate logic of ZF, its qG*, is
not well defined, nor definable. ZF is Löbian, but its beliefs are so
strong and rich that its theology get the Quine-Marcus "essentialist"
defect. No problem with PA and theories having a recursively countable
set of primitive terms.
Bruno
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