On 2/26/2019 2:39 AM, Bruno Marchal wrote:
On 26 Feb 2019, at 01:04, Brent Meeker <meeke...@verizon.net> wrote:



On 2/25/2019 8:55 AM, Bruno Marchal wrote:
Fictionalism does not apply to the arithmetical reality, nor to physics, but to 
the naïve idea of a “physical universe” as being the fundamental reality. The 
theology of the universal machine is a priori quite non Aristotelian: there is 
no Creator, and there is no Creation. Just a universal dreamer which lost 
itself in an infinitely surprising structure and wake up from time to time, or 
from numbers to numbers.
There is according to St Anselm, who also thought that definitions bring things 
into existence.

Yes, but God is defined by being perfect, and existence is considered as being 
good, and better than non existence. So, of course, God has to exists. Then 
Gödel made St-Anselmes more rigorous, by making that proof in the modal logic 
S5, which unfortunately presuppose a metaphysics incompatible with Mechanism.
Such notions of God are quite away from Plato, and makes sense with physicalism, and 
not much sense with Mechanism, where the notion of “fundamental truth" is the 
closer notion to the God of Plato. There is an understanding that such a notion of 
“fundamental truth”, at the origin of all types of truth, is transcendant, and this 
fits very well with the theology (G*) of the sound machines.

Right.  Truth and existence are quite different things.

Brent


Only strong-atheists believe in the God of the (Roman) Christians. Educated 
christians usually does not, although they fake it since 529 (due to violence 
and authoritative argument only).

Of course, no argument at all can prove any existence, but all experiences 
makes some existence true, although not in a rationally justified way.

Bruno




Brent

I need no more than a partial applicative algebra, and each choice of the phi_i 
makes N into one, simply by defining an operation “*” in N such that n * m = 
phi_n(m). There exist numbers k and s such that

((k * n) * m) = n
(((s * n) * m) * r) = (n * r) * (m * r),

for all m, n, r in N.

And, the key point, the operation “*” can be defined in the arithmetical 
language, and those statements are, for each n, m, r, provable in RA. I have 
shown that the converse is true. It is a very elegant Turing complete theory. 
With Indexical Digital Mechanism, it is absolutely undecidable if the Universe 
is bigger than the sigma_1 reality. (But here I do a blasphemy: that can only 
be entirely justified by G* *only*!, It is where I have to insist that this is 
presented as a consequence of YD + CT (“yes doctor” + Church-Turing thesis).

Such theories are essentially undecidable. It means that not only they are 
arithmetically incomplete, but all their effective consistent extensions are 
too. They are creative, you cannot capture the semantic in the way it could 
become complete, even in some imaginary domain concevable by the 
machine/theory/number. The universal machine are never entirely satisfied and a 
computation is always an escape forward, but their self-reflection create a 
mess, and illusions.

The sigma_1 arithmetical reality, as seen by the universal numbers which lives 
there, in the first person undetermined sense, is something *very big*. It 
generates infinitely many surprises. There are consistent histories.

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