(I think you got confused in the post and thought that having fixed points shows LFW, but if anything it’s the opposite; Bryan’s point is that he can avoid fixed points. So the deterministic setting is the more favorable one for his argument, and since it doesn’t work there, it just doesn’t work period.)
Not at all. Having fixed points proves LFW wrong, not right.
The whole point of my post is that LFW advocates would say that they can avoid fixed points, while if some theory such as hard determinism or compatibilism is correct then this argument shows that there’s a situation in which you can’t avoid fixed points.
Bryan is saying he can avoid fixed points. This is trivially true in the deterministic setting, and your post is asking whether it’s also true in the probabilistic setting. But it doesn’t matter whether it’s true in the probabilistic setting! The entanglement argument shows that even if you have a function without fixed points, this still doesn’t give you LFW.
The point of my post is not that not having fixed points implies LFW, it’s that LFW implies not having fixed points. Obviously there are other arguments for why you would not have fixed points, e.g.g might fail to be continuous.
Not at all. Having fixed points proves LFW wrong, not right.
Okay; I got the impression that you had it backward from the post, one reason was this quote:
Fortunately for the argument, the assumption of continuity for g is plausible in some real-world settings
Where I thought “the argument” refers to Caplan, but continuity is bad news for Caplan, not good news.
Anyway, if your point is that showing the existence of fixed points would disprove LFW (the contrapositive of LFW → no fixed points], then I take back what I said about your post not being relevant for LFW. However, I maintain that Caplan’s argument has no merit either way.
I think we agree that Caplan’s argument has no merit. As I’ve said in another comment, the reason I quote Caplan is that his remark in the podcast is what prompted me to think about the subject. I don’t attribute any of my arguments to Caplan and I don’t claim that his argument makes sense the way he conceived of it.
Not at all. Having fixed points proves LFW wrong, not right.
The whole point of my post is that LFW advocates would say that they can avoid fixed points, while if some theory such as hard determinism or compatibilism is correct then this argument shows that there’s a situation in which you can’t avoid fixed points.
The point of my post is not that not having fixed points implies LFW, it’s that LFW implies not having fixed points. Obviously there are other arguments for why you would not have fixed points, e.g.g might fail to be continuous.
Okay; I got the impression that you had it backward from the post, one reason was this quote:
Where I thought “the argument” refers to Caplan, but continuity is bad news for Caplan, not good news.
Anyway, if your point is that showing the existence of fixed points would disprove LFW (the contrapositive of LFW → no fixed points], then I take back what I said about your post not being relevant for LFW. However, I maintain that Caplan’s argument has no merit either way.
I think we agree that Caplan’s argument has no merit. As I’ve said in another comment, the reason I quote Caplan is that his remark in the podcast is what prompted me to think about the subject. I don’t attribute any of my arguments to Caplan and I don’t claim that his argument makes sense the way he conceived of it.