I think there is free will. Those who think we do not have free will invariably arrive at this conclusion on the basis of this argument:

1. If everything we do is a product of external causes or indeterministic chance, then nothing we do is done freely. (If P, then Q)
2. Everything we do is a product of external causes or indeterministic chance (P)
3. Therefore nothing we do is done freely (therefore, Q)

The problem with it is that though premise 1 is well-supported by our rational intuitions, premise 2 is just a dogma. It may be true, but there isn't any evidence that it is.

Here is a stronger argument, because in this case both premises are well-supported by our rational intuitions (and demonstrably so):

1. If everything we do is a product of external causes or indeterministic chance, then nothing we do is done freely. (if P, then Q)
2. We do some things freely (not Q)
3. Therefore, not everything we do is a product of external causes or indeterministic chance.

Premise 1 is the same as in the previous argument and so enjoys powerful support from our rational intuitions, as even those who deny we have free will must admit.

Premise 2 is also well supported by our rational intuitions. For free will is something we learn about via our reason (we don't hear, touch, smell, taste or see free will - it is something our reason represents us to have). And clearly the reason of most people tells them that they have free will, for humans have believed in free will for as long as they have had powers of rational reflection.

Now, perhaps the intuitions that support 2 are false. But the burden of proof is on the person who makes this claim, for all arguments appeal to rational intuitions and so to just dismiss some because respecting them would lead to a conclusion you do not personally endorse is irrational. The only rational basis upon which one should reject widespread rational intuitions is conflict with other rational intuitions. And those that support 2 do not conflict with any others, so far as I can see. They just conflict with the dogma that eveything we do is the product of external causes or chance.

2. We do some things freely (not Q) — Bartricks

How do you define "freely" in a way that doesn't just boil down to "a mix of random and deterministic" though?

And clearly the reason of most people tells them that they have free will — Bartricks

It's not so much reason as intuition I think. If there was a reasonable argument for free will as you're presenting it and everyone knew we wouldn't be talking about it

for humans have believed in free will for as long as they have had powers of rational reflection — Bartricks

For as long as laws and punishment existed and needed to be justified*

Now, perhaps the intuitions that support 2 are false. But the burden of proof is on the person who makes this claim — Bartricks

The proof is simply that in EVERY OTHER CAUSAL CHAIN in the world, an event happens either randomly or deterministically. I'm pretty sure that puts the burden of proof on the one proposing the magical third method of causation "free"

I wouldn't start out by defining free will, as exactly what free will involves is a matter of inquiry. So it is something I think I have good evidence I possess - my reason tells me I possess it - even if I do not know exactly what having it involves.

For an analogy: I have excellent evidence my computer is working - it appears to be working. But I haven't the first idea 'how' it is working. Likewise, I think I have excellent evidence that I have free will - my reason tells me I have it (and it tells other people the same thing, for free will is almost universally believed-in). But when it comes to what having free will involves- well, about that I am far less sure and I think we only get insight into it by listening to our reason.

Anyway, why do most people think causal determinism is incompatible with free will? Well, because they think that if determinism is true then everything they do will be wholly the product of external causes.

Does that follow, though? No. Imagine an object that has always existed. That is, it never came into being - it exists of necessity. Now imagine that determinism is true and imagine that object in the company of other objects. Those other objects causally interact with the necessarily existing object, and the necessarily existing object causes some events to occur. Were those events wholly the product of external causes? No, for there was another ingredient - the nature of the object itself. And that nature, whatever it may be, was not itself the product of prior causes, for this object was never created.

Thus, it does not follow from determinism being true, that everything a person does will trace to external causes, for the person themselves may not have been created - they may be a necessarily existing thing.

So far as I can see, that is the only way it is possible for a thought or desire or will of mine to be something other than caused by external causes or a matter of pure chance. That is, if I am a contingently existing object (an object that has come into being), then everything I do will indeed be either a product of external causes or pure chance. It is only if I am a necessarily existing object that this will not be true. Thus, I conclude - tentatively - that free will requires being a necessarily existing thing.

That's a conclusion that is quite hard to swallow, I admit. But that's just due to intellectual fashions.

Plato, I should add, believed we are necessarily existing things. So I am not alone in this view. It is also supported by other evidence.

For instance, my reason tells me that I cannot be divided. I can have half an apple and half a cake and half a car and half a house. But I can't have a half a mind. Minds are indivisible.
Yet only something that lacked parts would be indivisible. That is, only something simple - something that is made of nothing simpler than itself - would be incapable of being divided.

If I listen to my reason, then, I am being told that my mind is a simple thing.

Simple things, if they exist (and some must), exist of necessity. For they cannot be created (from what could one create one?) or destroyed (for into what could one deconstruct one?). Thus, they exist 'a se' or with 'aseity'.

So, in so many words my reason tells me that my mind is a necessarily existing thing. Which confirms what it told me about my free will - namely that I have it, and that I could only have it if I was a necessarily existing thing.

I am being told that my mind is a simple thing — Bartricks

Shame on those people insulting you.

Seriously, the simplest are covariant quantum fields.

If all of our thoughts and actions were preprogrammed and merely passive responses to external causes, wouldn't one expect far more uniformity among people in general? Even if a supercomputer could mimic all of my behaviour, would it be able to copy other people's responses at the same time? We all seem to have a different 'operating system' in the sense that meeting one person is a qualitatively different experience to meeting another person. We have an ability to improvise and deal with uncertainty. There is so much diversity and contrast between people which seems beyond that possible than if our decisions were completely deterministic.

This overlaps with what i've said in another thread - but an event will not be wholly the product of prior causes and/or chance if the event is caused to occur by a necessarily existing object.

First, not all events can be caused by prior events, for that would land us with an infinity of prior events. So we know by rational reflection that some events must be caused by objects.

Of course, we'd have the same problem if every object had to be caused to exist. So we know that some objects are not caused to exist. And as nothing can come from nothing, we know that some objects exist of necessity. That is, it is in the nature of some objects to exist.

An object of that kind - an object that exists by its nature - has not been caused to exist by anything external or prior. And because it exists of necessity, its existence cannot be said to be chancy either. Thus, if we are objects of that kind, we would be capable of exercising free will.

I conclude that this is exactly what we are.