[FRIAM] Thanks again Marcus

[Frank Wimberly]

Philosophically different.  Give the axioms of the rational numbers we can
construct, using ZF set theory, a set of equivalence classes of ordered
pairs of integers which satisies those axioms.  We can also construct a set
of equivalence classes of Cauchy sequences of rational numbers which
satisfy the axioms for real numbers, including algebraic and transcendental
numbers.

---
Frank C. Wimberly
140 Calle Ojo Feliz,
Santa Fe, NM 87505

505 670-9918
Santa Fe, NM

On Sat, Jun 20, 2020, 10:45 AM Jon Zingale <jonzingale at gmail.com> wrote:

> The isomorphism *isn't*, in some sense, enough. For instance, the rationals
> can be philosophically different than the integers. Sure we can identify
> them via diagonal argument, but when we want a field we don't reach for the
> integers. I claim that something similar is happening here and that the
> point of the article is missed when we jump to the isomorphism. Gisin would
> have just talked about the rationals if he meant the rationals, instead, he
> invokes Chaitin and computability on purpose. The truncation simplification
> obfuscates the deeper point. He is making an ontological claim about the
> universe and one that theoreticians of quantum theory may appreciate but
> applied mathematicians will not. The subjectivity of an observer is forced
> on us by classical logic. Here he constructs a physics over a completely
> different topos and what follows is not needing to make the observer
> interpretation. This point is significant enough to think about as being
> *more* than just truncation, it establishes what can be meant by randomness
> and the possibility that determinacy may be an illusion, even in
> macroscopic
> physics.
>
>
>
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