Keep in mind I'm a complete novice in philosophy, especially when it comes to the literature. I might misrepresent some positions completely. Please call me out.
The determinist states: Our decisions are bound to causation, and thus we are not truly free.
This statement implies that the only way for free will to exist would be to detach an agent from causation; as long as some factors affect out motivation to do something, we are not truly free.
The determinist thus claims that the only way for a choice to be free is that there would be some force acting above the physical reality, especially when it comes to cognition and decisionmaking. Thus only in a dualistic reality is free will possible.
I have a few problems with this:
1. This method of defining free will seems to consequentally destroy the agent. If we were to be able to decide what we want, we'd, at least apparently, fundamentally be nothing. How would it be possible to even assign a different "want" to ourselves without that want...
You wrote, "The determinist states: Our decisions are bound to causation, and thus we are not truly free." In the context of free will, what you say describes not determinists in general but only hard determinists, i.e., those determinists who also say that determinism rules out free will. The other kind of determinists -- soft determinists -- accept determinism but say that it doesn't rule out free will and may indeed be essential to acting freely. Unlike hard determinists, soft determinists allow for the combination of determinism, free will, and moral responsibility. You'll find details in this SEP entry .