On 09 Mar 2015, at 22:06, LizR wrote:
On 10 March 2015 at 07:16, spudboy100 via Everything List <[email protected]
> wrote:
Ha! Your points seem unassailable, yet, buy example, how many
neurobiologists are believers in God? This is the crux of the
materialism argument. If God is not wearing cowboy boots and barking
out orders, they do not concede there could be this fellow.
Now that's a god I could believe in.
My question to you is, does the universe, to you, look non-
mathematical, quasi-crytsals included?
I don't believe there is anything in the universe that looks non
mathematical (to date). Some of it is intractable, but that doesn't
stop it being mathematical.
What would a non-mathematical universe look like? (Maybe one with
genuine randomness?)
Why do you say so?
You might need to revise your note Lisz. We have prove that the
computable functions from N to N is an enumerable set (even if not
constructively, and necessarily non constructively).
A computable function admit a finite code/program, and the finite
words are enumerable, lexicographically.
But we have seen that the set of all functions from N to N is not
enumerable.
A similar argument can show that most functions are random, like
almost all binary sequences are random, like almost all subset of N
are random.
Are they not mathematical?
Something which does not look, a priori mathematical, is the taste of
coffee, for example.
Matter is different: it looks both mathematical, with circles,
ellipsed, distances, volumes, ... But it has non mathematical aspect,
indeed the one which makes people believe it is made of elementary
substances, the atoms, or the strings, or the singularities in a
quantum field, which are supposed to be described by the quantum
filed, but be different from it, or from its mathematical
specification. But with comp, that is an illusion. yet, consciousness
is not an illusion, and is not 100% mathematical, because it is does
not admit a 3p definition at all.
That is not new for the mathematician: like arithmetical truth cannot
have a 3p definition in arithmetic, mathematical truth is suspected by
most has not having a mathematical definition. Attempts to describe
the entire mathematical universe leads to inconsistent theories, or to
incomplete theories.
Consciousness, knowledge are like that, we cannot define them
mathematically, even if we can prove they have to exist, by using meta-
theorem and the computationalist hypothesis.
Few concepts have the chance to have a consistent "Church-Turing-Post"
*thesis*, which provides a very solid and non trivial notion of
universality. The notion of machine is very ell defined mathematically
(with Church's thesis), but when self-reference is taken into account,
machine get some ,attributes (like the first person) which escapes
arithmetic and the realm of the computable, seen from inside.
There is a "Skolem Paradox" here. Some mathematical structure can look
small, seen from outside, and gigantic when seen from inside. It is
like in Alice in Wonderland, or in Yellow Submarine. The notion of
cardinality of a set is relative. Our reality can be enumerable "seen
from outside", or "objectively", and yet it can contain *very* high
cardinals, and even non mathematical feature, like consciousness,
assuming computationalism.
We might need God, because God might be the only one capable of being
conscious.
Consciousness is not an illusion. What might be an illusion is the
consciousness of the little ego, or the personal identity, which with
computationalism is a pure indexical notion.
BTW, I recall you have participated to the debate with Bill Taylor on
the FOR-list, on Church thesis. Bill taylor defend the idea that
Church thesis is a definition, and I refute that point. Do you
remember the refutation?
Church's thesis cannot be a definition, because it implies almost
directly Gödel's incompleteness theorem. In fact it is the
incompleteness which makes Church's thesis consistent, and thus
computationalism consistent.
If you, or someone, want me to prove or explain this, just ask.
Bruno
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