On 16 Aug 2014, at 21:46, meekerdb wrote:
On 8/16/2014 12:27 PM, Bruno Marchal wrote:
But not everything exist. Only K, S, (K K), (K S) (S K) (S S) ((K
K) K), etc.
etc. = .... And you also assume that a UD exists.
Not at all. It is a consequence of elementary arithmetic (addition and
multiplication laws). Equivalently
some combinators are UDs.
Or if you prefer, only 0, s(0), s(s(0)), etc.
Plus their respective laws.
That's your hypothesis.
No. It follows from comp ("yes doctor + Church's thesis).
Why not start with ZFC,
Because those assumes much more than elementary arithmetic. It would
not chnage the physics, but I prefer consider ZFC as a universal
numbers, a Löbian one with tough cognitive abilities, but I work
trying top be agnostic of set theory.
which most mathematicians consider the foundation of mathematics?
With comp, we have a simpler ontology. The question asking if the
cardinal of our "reality" is bigger than aleph_0 is absolutely
undecidable. The collection of all set is just too big, but it
wouldn't change anything to assume it or not, except from the view
from inside where some axioms in set theory might help to solve some
halting machine problem. Note that ZFC proves the same theorem in
arithmetic than ZF. ZF proves much more arithmetical proposition than
PA, indeed ZF can prove all translation in arithmetic of G* (the G* of
PA, of course, ZF is as ignorant about its own G* than PA is on its
own).
ZF + kappa proves even much more arithmetical propositions, more than
ZF.
For the ontology, it is simpler to not assume infinities. I let them
crop out of the machine's theology.
I hope the answer is that one of them, or some other hypothesis,
will provide testable predictions that are confirmed. But otherwise
they are just hypotheses.
You can't say that. The whole point of the reasoning is that the mind-
body problem isthat if we assume comp then we must derive the
physical laws from Kxy = x, and Sxyz = xz(yz). Or from the laws of
addition and multiplication.
It happens that it works, as we get a quantum logic of for the
observable (with definition mirror the case of "certainty" for the FPI.
It is long, as you need to define the provability predicate in that
theory, but it is typical stuff in mathematical logic.
UDA is the enunciation of a problem, and AUDA gives the solutions at
the propositional levels, and it is more like a theology than a
physics, because it points on the unprovable truth and the unnameable
truth, with different intensions (Z* \ Z, X* \ X, ...).
To see it as a theology (of machines numbers, combinators) helps to
understand the whole picture, especially for people acquainted with a
non aristotelian conception of reality (the mystics, Lao-Tseu,
Milinda, and the rationalist mystic Plotinus, Proclus, ...
Damascius ...).
It explains two things that QM does not explains: the very origin of
the many worlds/dreams, and the different views the universal internal
machines can develop from it, including the non justifiable truth
about the 1p views, and about the 3p outer god, etc.
Bruno
Brent
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