Re: Thanks again Marcus

Posted by Frank Wimberly-2 on
URL: http://friam.383.s1.nabble.com/Thanks-again-Marcus-tp7597319p7597333.html

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.

On Sat, Jun 20, 2020, 10:45 AM Jon Zingale <[hidden email]> 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.



--
Sent from: http://friam.471366.n2.nabble.com/

- .... . -..-. . -. -.. -..-. .. ... -..-. .... . .-. .
FRIAM Applied Complexity Group listserv
Zoom Fridays 9:30a-12p Mtn GMT-6  bit.ly/virtualfriam
un/subscribe http://redfish.com/mailman/listinfo/friam_redfish.com
archives: http://friam.471366.n2.nabble.com/
FRIAM-COMIC http://friam-comic.blogspot.com/

- .... . -..-. . -. -.. -..-. .. ... -..-. .... . .-. .
FRIAM Applied Complexity Group listserv
Zoom Fridays 9:30a-12p Mtn GMT-6  bit.ly/virtualfriam
un/subscribe http://redfish.com/mailman/listinfo/friam_redfish.com
archives: http://friam.471366.n2.nabble.com/
FRIAM-COMIC http://friam-comic.blogspot.com/