There are two things I can hardly separate: UDA, that is the Universal 
Dovetailer Argument, which is an argument showing that if you take 
seriously enough the hypothesis that we are digitalizable machine then 
it follows that *necessarily* the physical laws, among more things (see 
below), emerge from the relation between numbers, in a verifiable way.
This includes relative relations between particular numbers and what I 
will call from now on Universal Numbers.
And UDA points on a way to explicitly extract the physical laws: just 
interview one of those universal numbers.
I say above that the physical laws emerges, among more things
Among more? Not only UDA forces the quanta to emerge from numbers, but 
the interview shows that they emerge in the company of many non 
communicable truth, even many sort of non communicable truth, some of 
which are good candidates for playing the role of qualia. In that case 
quanta appears to be sharable qualia.

It is in the UDA that I have introduce the first and third person 
discussion (the expression itself coming from philosophy of mind). In 
the UDA the definition of first person *discourse* is quite specific: 
it is the content of a diary, or of any local memorization of a result 
of self-localisation (like Washington and Moscow) after 
self-duplicating experiments. Note that here some "universe" or 
"universal story" is presupposed in the thought experiment. Third 
person person discourse are then defined by the content of a diary of 
some external observer, where external refer to the 
reading-annihilating (cut) and reading reconstituting (copy) pair of 

The last version of UDA has 8 steps: (CT is for Church's thesis)

1) classical teleportation (Here the 1-discourse is equivalent with the 
3-discourse, up to the use of the indexical "I" by the candidate)
2) Classical teleportation with delay (Here already the 1 and 3 
discourses diverge)
3) Self-duplication (Here the first person indeterminacy appears)
4) Self-duplication with asymmetric delay.
5) Teleportation without annihilation of the "original"
6) Virtual 1+2+3+4+5 (the preceding steps with virtual reconstitutions)
7) Universal 1+2+3+4+5 (Here appears the universal Machine and the 
Universal Dovetailer. CT is used)
8) Arithmetical 1+2+3+4+5 (Here the UD appears to be "just" Sigma1 

It follows from that that "ontologically" (perhaps in a weaker sense 
than usual, or at least in a weaker sense than Peter D. Jones' use of 
the term) the following theory is enough. It is often named Robinson 
Arithmetic and denoted by Q. It is a tiny segment of elementary 
arithmetic. As a theory, it is a very poor theory, completely incapable 
of making the slightest generalization. But yet able to prove all the 
sigma1 truth, which by Church thesis, makes it capable of representing 
all computable functions, that is the Fi and the Wi, etc. Put in 
another way, although Q has few provability abilities, it has the full 
universal power of a universal turing machine or of any (relative) 
universal number.


TOE 1 (Ontology, formally presented)

Classical first order logic with equality,   together with the symbol 
0, s, +, *

The intended meanings of 0, s, + and * are respectively the number 
zero, the successor function (which sends a number n on its successor 
n+1), and addition and multiplication.

The axioms are:   (where "Ax" should be read: "for any number x", and 
"Ex" should be read "it exists x such that ", and "x ­ y" abbreviates 
~(x = y))

Q1)   Ax        0 ­ s(x)
Q2)   AxAy    x ­ y -> s(x) ­ s(y)
Q3)   Ax        (x ­ 0  ->  Ey(x = s(y))

Together with the definition of addition:

Q4)   Ax        x + 0  =  x
Q5)   AxAy   x + s(y)  =  s(x + y)

and the definition of multiplication:

Q6)   Ax         x * 0  =  0
Q7)   AxAy    x * s(y) = (x * y) + x

Just remember that the roadmap point: UDA shows that "ontologically"  
Q1+Q2+Q3+Q4+Q5+Q6+Q7 is enough for a (comp) TOE.  As a machine, which 
dynamics is governed by the inference rules of logic (modus ponens, 
rule for the quantifiers), Q is recursively isomorphic to a UD.  By its 
Church-Turing completeness, it is universal for computability.

KEY REMARK: although computability-complete, the theory Q is very weak 
in term of provability power. It cannot even prove that any numbers has 
a successor (Ax Ey (y = s(x)), although Q can prove all individual 
statements Ey(y = s(0)), Ey(y=s(s(0))), Ey(y=s(s(s(0))), etc. Q can 
prove (modulo the notation) that 1+3 = 2*2,  that 1+3+5 = 3*3, that 
1+3+5+7 = 4*4, etc., but Q cannot, like the greeks, generalizes and 
concludes that the sum of any sum of the first odd positive integers 
are perfect squares. Q can prove, for each number n and m, that n+m = 
m+n, but cannot infer that (n + m = m + n) is true for all n. Still, Q 
has the full power of being able to prove ExP(x) in case P is decidable 
and true, and this makes Q sufficiently powerful to prove 
metamathematical statements like the theory "ZF can prove the 
consistency of me (Q)". Here we are invited to NOT DOING Searle's 
error, consisting in confusing computation (simulation, emulation) and 
provability (or any higher belief system notion). In a sense Q can 
imititate ZF proving Q's consistency, but Q can hardly believe (prove) 
ZF's consistency, and Q can certainly not infer her consistency from 
ZF's proof of it. Give me time and Einstein's brain, and I can emulate 
Einstein's opinion about the loop-gravity/string theory debate, but 
this will not entail I will understand it. It is capital to understand 
this, because it will explain eventually how from a little ontology (Q 
theory), we will get an infinitely rich and unbounded epistemology 
"from inside Q" or from inside the work of a UD.

TOE 2 (Epistemology, will permit the "universal interview" which will 
include "physics" and in fact all Plotinus' hypostases (n-person point 
of view).

An observer will be any consistent extensions of Q. Peano Arithmetic is 
probably the most celebrate one, like ZF, or axiomatizable second order 
arithmetic (Analysis), same+omega-rule (as example of angels), or 
("gods") the set of all statement of arithmetic (written in ZF) which 
are true in all transitive models of ZF, etc.

I will fix the idea by choosing Peano Arithmetic (PA) for the begining 
of the universal interview. Q, as the UD, generate (in a precise 
arithmetical sense) all the proofs, made by all the consistent 
extensions of itself, and we will keep an eye on what PA says about 
itself and its consistent extensions. This will be equivalent with the 
study of what a self-referentially correct machine can prove about 

Formally PA is just Q1+Q2+Q3+Q4+Q5+Q6+Q7 together with an infinity (but 
mechanically generable) of induction axioms:

For any predicate P definable in Q (or PA, they have the same 
language), PA believes that (think about an infinite range of 

[ if P(0) and Ax (P(x) -> P(s(x)) ]  -> AxP(x)

This gives to PA a tremendous ability to generalize. It is not even 
clear if not all current mathematic (except logician's set theories and 
categories) can be proved in PA. And of course PA is lobian, by which I 
mean PA's provability are captured by the modal logics G and G*.

Suddenly grand-mother stops me: Bruno, you get too much technical ... 
keep the hypostases for another posts, it will be too much ...

OK, it was an attempt. Please keep this post for letter references. But 
the extraction of physics (and the other hypostases/persons) is 
entirely based on the arithmetical self-reference logics, and I can 
hardly explain this without introducing the basic notions. Recall that 
once we have a modal logic we can use some canonical multiverse 
attached to it.

But don't hesitate to comment. Nevertheless in the next one we get the 
n-person arithmetical notions.



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