Does Conway's Free Will Theorem imply the the universe has free will? or that we do not?

neither... I would go directly to the source.

Conway is a great mathematics writer.

good luck! .

Jim has answered most of your question and has a good link. But it should be added that Conway's "Free Will Theorem" defines free will as something "not determined" by prior conditions. If we make the substitution and call it "Conway's Theorem of Things Not Determined By Prior Things", then it's an interesting statement about certain quantum phenomenon. The fallacy is dragging a philosophical notion like free will into a subject of quantum physics. Free will does not necessarily mean that you are totally unpredictable, it means that YOU feel free to exercise your decisions. For example, put a kid in front of a cookie. You and I and his mother all know that he'll probably reach for it, but that does not mean he won't reach for it out of his own volition.

Addendum: KV, did you see my answer posted in your OTHER place you've posted this question? As I have said, questions about free will belong in philosophy, not physics or mathematics, until it's sufficiently defined to be described mathematically. Conway clearly has failed to do this, or has made some strong presumptions that may not even apply to humans.

It does neither, based on the Wikipedia article I read.

According to the article:

IF the universe has free will, THEN so do elementary particles.

The rule for logical implications like this is that they are true unless the hypothesis is true and the conclusion is false.

So if elementary particles don't have free will, according to the theorem, we can conclude that neither does the universe. (This is called the contrapositive: "If a, then b" is true if and only if "If not b, then not a" is also true.

If, however, elementary particles DO have free will, then the universe might or might not have free will. Either way, the theorem would be true.

That's how I read it.

I've answered KV's question elsewhere, but just wanted to correct previous answerers.

Conway's theory is 'observer has free will' implies 'particles have free will' (and not the more obvious reverse!).

Because:

A implies B == not A or B

the theory is equivalent to:

'observers don't have free will' or 'particles have free will'.

So KV's quesion was correct, assuming one allows KV's transposition of 'the universe' for 'elementary particles', of course.