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) ((KK) 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 LĂ¶bian 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 otherwisethey 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

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