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.


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.

You received this message because you are subscribed to the Google Groups 
"Everything List" group.
To unsubscribe from this group and stop receiving emails from it, send an email 
to everything-list+unsubscr...@googlegroups.com.
To post to this group, send email to everything-list@googlegroups.com.
Visit this group at https://groups.google.com/group/everything-list.
For more options, visit https://groups.google.com/d/optout.

Reply via email to