On 2/25/2019 8:55 AM, Bruno Marchal wrote:

Fictionalism does not apply to the arithmetical reality, nor tophysics, but to the naïve idea of a “physical universe” as being thefundamental reality. The theology of the universal machine is a prioriquite non Aristotelian: there is no Creator, and there is no Creation.Just a universal dreamer which lost itself in an infinitely surprisingstructure 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.`

Brent

I need no more than a partial applicative algebra, and each choice ofthe phi_i makes N into one, simply by defining an operation “*” in Nsuch 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 thearithmetical language, and those statements are, for each n, m, r,provable in RA. I have shown that the converse is true. It is a veryelegant Turing complete theory. With Indexical Digital Mechanism, itis absolutely undecidable if the Universe is bigger than the sigma_1reality. (But here I do a blasphemy: that can only be entirelyjustified by G* *only*!, It is where I have to insist that this ispresented as a consequence of YD + CT (“yes doctor” + Church-Turingthesis).Such theories are essentially undecidable. It means that not only theyare arithmetically incomplete, but all their effective consistentextensions are too. They are creative, you cannot capture the semanticin the way it could become complete, even in some imaginary domainconcevable by the machine/theory/number. The universal machine arenever entirely satisfied and a computation is always an escapeforward, but their self-reflection create a mess, and illusions.The sigma_1 arithmetical reality, as seen by the universal numberswhich lives there, in the first person undetermined sense, issomething *very big*. It generates infinitely many surprises. Thereare consistent histories.

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