On 18 Aug 2014, at 20:11, meekerdb wrote:
On 8/18/2014 1:49 AM, Pierz wrote:
Ah no, I'm not mistaking the map for the territory. I don't know
why you say that. I'm saying the territory is infinite in all
directions (according to my guess), but our maps are finite and so
have to have false boundaries drawn around them.
I said that because it is our maps that are infinite. If you take
the natural numbers and arithmetic as the ontology of your TOE,
you've assumed an infinite map.
I disagree. The natural numbers will give the ontology, and it is an
infinite realm, even infinitely complex, and not unifiable by any
effective theory. But the map are the effective theories, not the
realm that they attempt to describe. Map, theories, needs to be
finite, or at least axiomatizable (= recursively enumerable, by a
theorem of Craig).
There is no observable infinity, it's an abstraction we've
invented. It might be right or it might not. The very title of
this list implies it consists of people whose preferred map is
"everything". So it is not modest agnosticism to suppose the
territory is infinite - that not something known.
The comp is eminently finite: it is Kxy = x and Sxyz = xz(yz), and
nothing more except some identity axioms.
Bruno
Brent
That allows them to be accurate to some approximation, but I am
hypothesizing we'll never close the loop completely.
Brent
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