Does free will exist? I can't see any way to disprove the idea that we may have free will in the following sense:
We have a will which is able to choose between two or more options, without that choice being determined by anything else.
However, when you think this through, it seems that the choice is arbitrary.
Imagine you are faced with competing choices. One in what you desire to do. The other is what you think you should do, or that you believe you have reason to do, or whatever.
If you recognise that one choice is the rational one etc., then presumably you will do it if you are rational, see that you have the most compelling reasons to do it, etc. It might be said that you still have the option of doing the other thing. But how could you then be said to be rational etc.?
Now imagine you simply do what you desire. The above dilemma assumed that this wasn't the choice that it made sense or you had reason to do. But then you must have been more drawn to doing that than being rational. Maybe you could say that you still had the option of being rational.
But how do you decide whether you are going to be a rational person, or a person who acts on their desires, whatever reason says? Well, if this is even something that you can decide (and maybe it's not) then you need to decide on some basis, or else on no basis, which would be arbitrary. But if you decide on some basis, then it would not make sense to say you still have the option of choosing to be the other kind of person. As if you did choose the second option, you would not be choosing on what you take to be the basis of the first option - as that would lead you to take the first option. So you are either choosing on some basis which supports the second option, or else though you want to choose the first option, some other aspect of your psychology is getting in the way and you end up choosing the second option.
Now if the choice between the two options is arbitrary, then you can choose either, and, if you have free will as described above, then your choice isn't determined by anything beyond your caprice. But then you aren't choosing either on any basis. But if you can think of a basis for one or the other, then if you accept that basis, and you don't get deflected by some other part of your psychology, then you will act on that basis. If you can think of a basis for either choice, then you can either evaluate those bases comparatively, or not. But if you can evaluate them comparatively, then you will go for the one which wins out in the comparison, unless something throws you off course. And if you can't evaluate them comparatively, then the choice between them lacks any deciding basis, and hence is in a certain way arbitrary. If you have free will, you can then decide for either, but there won't be anything counting for one or the other distinctly (it might be that both have something going for them, but we furthermore need a way to arbitrate between them).
If I remember, Sartre's view of freedom was very similar to this, and the criticism was much along these lines, as free will ends up bring arbitrary. I guess what I think is that Sartre's view was correct, if free will exists, but it suffers from the kinds of criticisms pointed out at the time. What people want of course is for us to have free will and be morally culpable for doing the right thing or the wrong thing. But I think these things come apart and can't be essentially connected.
If a person recognises the reason for doing the right thing, but ends up doing the wrong thing, that can either be because their motivation to do the right thing was stymied by some other aspect of their psychology (weakness of will), or because they decided there was more reason to do the wrong thing (i.e. they aren't a good person), or because they chose arbitrarily. If we move the choice one stage back, and ask them to chose between the reasons to be righteous, and the reasons not to be, then either they compare them on a common scale and chose one which wins out, or they chose one but chose it for no overall reason, i.e. an arbitrary reason. If they end up being a bad person at the end of all this, I think it is fine to call them that, but we can't then say they are ultimately choosing badness because they are bad, because they either see badness as having the most considerations behind it, or because they have chosen it arbitrarily and not because it is bad.
Sorry if this is more verbose than it should be. I guess this is a forum.