John Conway – The Free Will Lectures (2009) [video]

> Despite this, you (whatever 'you' is) are still free to accept or reject this proposition.

The outcome happens from all the previous moments you lived. Randomness doesn't make a person have free will and randomness may just be an illusion from our lack of understanding when it comes to what's resulting in the outcome we appear as random.

We're the sum total of genetics, environmental factors and all the external forces upon us since birth. That means if we're being punished it was outside the realm of it could have been different.

Bell's Theorem implies that if there is some kind of hidden variable controlling the outcome of a random quantum event like a seed, then it must work non-locally, which maybe doesn't completely rule it out, but it's really suggestive given that locality is one of the common assumptions like conservation of energy that has lead to a lot of progress in physics.

Interestingly, there is a local deterministic interpretation of quantum mechanics: the Many-Worlds Interpretation. The interpretation is considered by many to be what the Schroedinger equation by itself with nothing extra added (like wave function collapse) implies about the world. There is no objective randomness. The 10,000-foot view of it is that any random quantum event with multiple possible outcomes causes the world to branch into a separate world for each outcome. (Generally random quantum events have a continuous outcome space instead of discrete outcomes, but it's harder to talk about a continuous spectrum of "worlds". The "worlds" of MWI aren't necessarily discrete atomic things; the word "world" is more of a fuzzy label for our convenience, like the word "pile". Also, per the Schroedinger equation, there's situations where multiple histories leading to equivalent worlds can cancel out, decreasing the measure and therefore observed probability of that world occurring; that's how we could possibly know this whole splitting business is going on.)

However, a system like this would still have subjective randomness, in the sense that there's no way for you to predict the value of a random quantum event. (Say you have a device that when you press the button, it will measure radiation from a radioactive object inside it for a period of time, and then output "heads" if it measured more than the average amount and "tails" if less.) Assuming it's set up as advertised, the idea of predicting the result doesn't even make sense, because after the measurement, there will be a cluster of worlds with a version of you that sees "heads", and a cluster of worlds with a version of you that sees "tails". Predicting which one you'll be makes as much sense as predicting who you will be before you were born. (I find it interesting that no matter how deterministic of a universe you imagine, there's always the subjective randomness resulting from the indexical uncertainty in who you find yourself being. MWI extends indexical uncertainty like that to more situations.)

Right: if you are a brain-in-a-vat observing some powerful play, what can you say about the world in which the vat is embedded? (or for that matter, how is it that you can even be made aware of the vat’s existence?)

We can perform some measurements [0] which show that spin exists. So, the 101 lemma used in the Kochen-Specker Theorem is related to existing laboratory experiments, and not just thought experiments. But indeed this doesn't say whether people have free will.

We might instead interpret the Free Will Theorem as demolishing a position otherwise claimed: People have free will, but people are special; most other things don't have free will, and certainly particles don't! But the Free Will Theorem explicitly contradicts this position.

In terms of philosophy, there are several nuances to consider. There's Kochen-Specker itself [1], its untestability and its applications. There's free will itself [2], including whether free will is definable, is useful for ethics, and indeed whether free will exists. I think it's interesting that [2] has no mention whatsoever of [1] or the Free Will Theorem more generally.

[0] https://en.wikipedia.org/wiki/Stern%E2%80%93Gerlach_experime...

[1] https://plato.stanford.edu/entries/kochen-specker/

[2] https://plato.stanford.edu/entries/freewill/

I think the invulnerable argument for it is even simpler than that: whatever apparently non-determined behavior we observe may only appear that way because we don’t yet know the rules underlying it.

Any system will appear unsystematic until the precise rules governing it are known.

Since we can’t ever demonstrate that we’ve exhausted all possible theories of a system, the possibility always remains that tomorrow we would discover a perfectly effective one, and from that point the system would be as plainly deterministic as anything else.

In other words: we lack the capability to definitively distinguish between our own lacking knowledge and a system’s (potential) intrinsic non-determinism.