Model of induction

[Robert Wall]

Hey Glen,

Yes, on the first issue with respect to the Axiom of Choice, I think the word "choice" there does not map one-for-one to the same word used in probability theory. I think the two concepts are mutually exclusive, but this may be beyond my "pay grade" to worry or talk about. 🤐

However, I can most certainly see your point about the beneficial relationship between measurement theory and probability theory. The notion sigma algebra is spot on, especially for the mathematics of theoretical probability. Even though I may be considered an old dog professionally, I can still resonate with Grant's notion of probability spaces as well.  It's all good!

You know, I can still have fun while simultaneously being lost in the forest. This has been fun!  Thanks for letting me play in the sandbox ... 😊

Cheers

On Wed, Dec 14, 2016 at 6:50 PM, glen ☣ <[hidden email]> wrote:

Well, sure.  But the point is that the axiom of choice asserts, merely, the existence of the ability to choose a subset.  They call them "choice functions", as if there exists some "chooser".  But there's no sense of time (before the choice function is applied versus after it's applied).  The name "choice" is a misleading misnomer.

And that's my point.  Probability theory is a special case of measure theory.  Calling the set measures "probabilities" is an antiquated, misleading, and unfortunate name.

On 12/14/2016 01:41 PM, Frank Wimberly wrote:
> Don't think about choosing.  The axiom of choice says that there is a function from each set (subset) to an element of itself, as I recall.

--
☣ glen

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============================================================
FRIAM Applied Complexity Group listserv
Meets Fridays 9a-11:30 at cafe at St. John's College
to unsubscribe http://redfish.com/mailman/listinfo/friam_redfish.com
FRIAM-COMIC http://friam-comic.blogspot.com/ by Dr. Strangelove