A determinist would likely agree that if determinism is true, then everything we do was directly necessitated by physical causation. That is, the way things were in the distant past, given the laws of physics, directly implied that the world would end up exactly as it is. They might add that quantum particles changed things unpredictably between then and now, but we may take that as one with the previous for my purposes.
Given that account of determinism, let's analyze the concept of physical causation. We make two observations.
1. First, we observe that it is distinct from the bare concept of motion. When we say that entity A caused entity B to do something, we mean more than just that entity A moved, then entity B moved. For example, if we say "the bat caused the ball to fly out of the park", we mean more than: "the bat swung, then the bat touched the ball, then the ball flew out of the park." So part of the concept of physical causation is the idea that entities can in some sense move because of one another, i.e., that they can in some sense generate motion in one another.
2. Second, we observe that it is not perceptually evident in the external world. That is, although there is an important difference between "A moved, then B moved" and "A moved, causing B to move," there is not a perceptual difference between the two. Return to the ball and bat example. We would not be able to tell the difference between a situation in which the ball simply performed the motions that it did perform (situation 1), and a situation in which it performed those motions because of the bat (situation 2). The two situations appear to be different from one another, however. There appears to be an additional element in situation 2 that does not exist in situation 1, i.e., a physical cause.
If you doubt that there is an additional element in situation 2 that does not exist in situation 1, think about the relationship between the ball and bat in situation 2. The relationship between the two of them appears to be unique in an important way. We can clarify that as follows. Suppose the bats in situations 1 and 2 and my bat sitting at home are identical in physical composition. My bat sitting at home clearly does not stand in the same sort of relationship to the ball as the bat in situation 2 does at the moment of impact, even after we ignore the positions of the bats. Further, there seems to be a way in which the relationship between the bat and ball in situation 1 is more like the relationship between my bat and the ball than the relationship between the bat and ball in situation 2. So there is something different about situations 1 and 2, even though there is nothing *perceptually* different between situations 1 and 2.
Let’s put all of that together. If nothing in the external world or introspection could provide us with the idea of physical causation, then it is reasonable to conclude that we would not have the idea. (The only alternative is that we are born with it. If you hold that position, you have the burden of proof. I cannot be expected to prove a negative.) So, from our second observation, it must be something introspective that provides us with the idea. And it could not be any part of the introspective realm that is independent of the self, for the same reason that I cited to exclude the external world.
So, the only way we could acquire the concept of physical causation is if the irreducible self first observes directly that it is a direct source of physical causation, then applies the concept of physical causation by analogy to those things that appear to stand in the same sort of relationship with one another as it does to the things it acts as a cause upon. The acquisition of the concept of physical causation therefore demands an irreducible self which is a cause, and therefore, physical causation would be unintelligible to a being without free will. Since determinism holds that physical causation exists and that free will does not (this is true in both the QM and non-QM variants), determinism contains an implicit contradiction.
Q: Why didn't you address (post x) that I made in response to you nine minutes ago???
A: Because I have (a) a job, (b) familial obligations, (c) social obligations, and (d) probably a lot of other atheists responded to the same post you did, since I am practically the token Christian on this site now. Be patient, please.