[prmph]

> Now describe something that is non-random and not-caused. I argue there is no such thing, i.e. caused and random are exhaustive just as zero and non-zero are, there is nothing left that could be both non-(zero) and non-(non-zero).

That's my point. The fail to exist only in a certain axiomatic system that is familiar to us. But in a certain mathematical/platonic sense there is nothing essential about that axiomatic system.

[danbruc]

Well, what does random mean? Unpredictable, right? Why is it unpredictable? Because the outcome is not determined by anything else. [1] So random just means not determined. And instead of caused I would say determined, because caused is a pretty problematic term, but for this discussions the two should be pretty much interchangeable. And this is probably the best place to attack my argument, to point out something wrong with that. Once you agree to this, it will be a real uphill battle.

So your non-random + not-caused just says non-(non-determined) and non-determined. Now you have to pick a fight with the law of excluded middle [2]. You are saying that there exists a thing that has some property but also does not have that property. Do you see the problem? Nothing makes sense anymore, having a property no longer means having a property, everything starts falling apart.

Maybe you can resolve that problem in a clever way, but you will have to do a lot more work than saying there is some axiomatic system where this is not an issue. Which one? Or at least a proof of existence? And even if you have one, does it apply to our universe?

[1] Things may also seem random because you do not have access to the necessary state, for example a coin flip is not truly random, you just do not have detailed enough information about the initial state to predict the outcome. Or you may not know the laws or have the computing power to use the laws and that bares you from seeing the deterministic truth behind something seemingly random. But all those cases are not true randomness, they are just ignorance making things look random.

[2] https://en.wikipedia.org/wiki/Law_of_excluded_middle

[prmph]

Yep, the law of the excluded middle is one place to start attacking your argument, I assume you know not all philosophers accept it.

Then, you are also right that semantics intertwine with logic in a way that needs careful interrogation and is open to different perspectives. I'd be very careful making the leap you make from:

> non-random + not-caused

to:

> non-(non-determined) and non-determined.

Your arguments also contain an interesting thing to think about: True randomness. If you really think about it, true randomness should not exist. And yet we think radioactive decay at the quantum level is truly, fundamentally, irreducibly random. If that is so, here is an example of things happening that we, by definition, cannot explain in any more fundamental way.

Which is to say, the universe is not bound by the logic of our experience. In the same way we had to break out of our basic intuition about numbers to create new ones that gave us more power, in the same way we could never have logically reasoned our way into quantum mechanics and needed experimental evidence to accept something so radical, yes in the same way math does not care that our minds/logic is currently too weak to conceive of a mechanism for free will.

Here is mind twister for you: Imagine a chain of antecedents for an action. In our intuition, the chain stretches backwards infinitely. But what is it could somehow wrap around to form a ring at infinity? Analogous to the way cosmologists think the universe is not infinite in all dimensions

[danbruc]

I was wrong about the law of excluded middle, that is not an issue. Intuitionistic logic rejects it, because it says P or not P is definitely true, whether or not we have any proof for P or not P. But that is not really relevant here, the real question is whether there are things that are neither determined nor random. If random means not determined, then no such thing can exist, unless you accept a violation of the law of noncontradiction [1]. So are random things and determined things complementary sets with respect to some universe of things under consideration?

[1] https://en.wikipedia.org/wiki/Law_of_noncontradiction