On 10 Nov 2014, at 02:00, meekerdb wrote:
On 11/9/2014 2:16 PM, Bruno Marchal wrote:
It is a matter of convention how much you put in the ontology, but
if we are machine, it is absolutely undecidable if the "universe"
has cardinality above aleph_zero.
So, with Occam, the motto would be to put as less as possible in
the ontology.
Is it mere convention? I don't think you can define the natural
numbers without the relation of successor.
That is a technical question, and it can depend on the axioms you
choose for multiplication and addition. But the usual axiomatization
that I often gave is just simpler.
But given relations, then structures (like the set of all primes)
are emergent.
OK. Once you have the basic 3p laws and object (like 0, and the
elementary axioms of RA or PA), many things will emerge. Some of those
things can be define in the theory, like "being a prime number". Of
course the set of prime number will emerge, but this will not make the
set of prime number an emelment of the theory (we cannot quantify on
sets). That set, unlike each prime number, is not in the basic
ontology, but the property of being a prime is definable in the
theiory, like the property of being a representation of a computations.
Now, by incompleteness, some other things can emerge, and yet not be
definable in the theory, although definable by observers which
existence can be proved in the theory.
And all such form of emergence are still of the 3p type.
Then you have, again by incompleteness, the emergence of things which
cannot be defined in any 3p way, but can be proven (in some
metatheiry) to correspond to properties of observers or numbers:
typically the first person notion 'associating the Gödel provability
of p to the truth of p) will be of that kind. usually, the
reductionist forgets that type of association, or consider it to be
trivial, by identifying (unconsciously) proof and truth.
I am uneasy with your conversation with David, because I agree with
both of view, but see you are not entirely talking about the same thing.
For example, I will not put the property of being prime in the
epistemology. Being prime is an objective 3p property which "emerges"
from the laws of +, *, and s. Similarly with "being a number coding
for a computation", or even "being a computation" itself. But
epistemology will be defined not by the 3p Gödelian provability
predicate, but by the Theaetetus method, at the meta-level, and this
gives rise to something that the machine will be confronted to, and
yet not definable in its language. that is where knowledge and
consciousness appears, and plays their role. Indeed, an important
role, as the physical reality will emerge from such non definable
objects.
Graziano approach assumes a physical universe, in a sense which is
epistemologically contradictory once we assume computationalisme. Such
approach just does not work. He put the mind, and the body (by UDA),
under the rug.
Bruno
Brent
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