You are saying 2+2=4 is a "static timeless relationship that just exists", I am saying "summation" is an action. Similarly, "constructing a set" is an action even if "the set of all things contains the number 1" is a timeless relationship which just exists. The axiom addresses our capability to perform or not be able to perform the action of constructing a set from sets who have indistinguishable elements. If we take the axiom, I can choose elements from those sets despite their indistinguishability, if we do not take the axiom I cannot.


At this point, I think you are just misunderstanding my use of the AoC. Allow me to reintroduce the context of when I originally brought it up:
The AoC is not proof that we can make choices independent of cause and effect, and it is not a refutation that we can either. The point of this all in the greater context of our discussion, is that even in rigorously defined mathematics, some obvious "truths" in set theory are not possible to arrive at without taking choice as an axiom. In our discussion of free will, I find it similarly difficult to prove anything, but perhaps exploring the mathematical analog could yield some insight into our less rigorous exploration of free will.



There is no Motte and Bailey fallacy - what I said is still true and I offer no lesser idea. If the Axiom of Choice were somehow proven false, and became for instance "The Theorem of Non-Choosability without distinguishing characteristics", that would show, in my opinion of course, strong support for determinism. As to whether its possible to prove the AoC false, this bit "The Axiom of Choice will never become a theorem." is quite a strong statement mathematically speaking. If you were able to justify that in some rigorous way I would be very interested to hear it.



Yes I certainly admit I don't know how to prove the existence of an uncaused choice, but this is an incorrect use of a razor. If we had some decision to make here, we could use a razor to make it, but we're looking for rational proof of difficult things, and a razor is not a proof.

On a similar vein, I also don't know of any proof of causality ("caused" choices). We certainly have a lot of empirical evidence that cause-and-effect exists, but why not examine all cross-products of the following:


---------------------------Method
________________________
---------------------| empirical | rational |
---------------------________________________
Choice | causal | A | B |
-------------------------
| non-causal | C | D |
-------------------------
I hope you like my ASCII art.

I think A has a lot of empirical evidence, C perhaps has some, but B and D I've got nothing for. Can you rationally prove that choices are causal? (Yes yes shifting-the-burden-of-proof fallacy or whatever, but we're on the search for truth here!!!)


I would just like to point out I agree with this in general. Though I think for this to work you need a viewpoint which is able to balance determinism and free will - evaluating the various deterministic factors in society are important, but without free will I don't see a mechanism to assign responsibility (other than utility, but that brings us back to the moral questions and might makes right).

Again I generally agree with these courses of action but I don't see the connection to determinism. You're making a leap from a particular physical mechanism to a moral judgement that we should act a certain way in response to the physics. Insofar as I asked a question prior to this, and you tried to answer with the weather example, the answer I see in your explanation is just that we allow the "not-figure-out-able" part to be modeled indeterminately, aka allow for non-determinism until we can convert it to determinism (or indefinitely if we can't).

I suppose for more clarity, I was asking with respect to the idea of what do you do if your worldview is "purely" deterministic. If you allow for a mix of determinism and non-determinism these questions seem pretty easy to answer.