Holbach is the exemplary hard determinist. He argues that freedom, in the sense that people are free to do or not to do an action that is within their power, is an illusion.
This is a strictly naturalist argument. Everything in Nature invariably acts according to the natural laws. This is a claim that is not too difficult to swallow; the next claim, which needs a little more support, is that people are completely natural, ie, there is no part of the metaphysical in them. But if people are completely natural, and everything in Nature acts invariably according to the natural laws, then people act invariably according to the natural laws.
The only thing that makes us believe that we are different from other natural things, is that we cannot see all of the factors that act on us. These factors are remote, many having occured in the relatively distant past, and many others that are not so distant, are yet obscure to us.
We can see most of the factors that cause rocks to remain on the ground, and so we see that the rock remains on the ground because of those factors. People, on the other hand, act on such remote and obscure reasons, that we say that they are free to choose what to do, to choose whether or not to do something. But Holbach argues that, being natural, we are acted upon by factors just as are rocks. We only think we are free, because we do not recognize all of those factors.
An example he gives is this: When arguing for free will, someone might say, 'but look: I can choose whether or not to move my hand just now. That proves my freedom.' To this Holbach replies that it is the influence of the desire to refute his opponent that causes the arguer to choose to move his hand.
Karl Popper offers a critcism of this argument, but it is not a very good one. He says that, granting that it is determined that I move my hand, it may yet not be determined which way I move my hand. But clearly, Holbach's argument can withstand this criticism: for the way in which I move my hand is simply the result of a host of remote causes. For instance, how tired are my muscles, did my brain transmit enough electricity to make x ganglia fire, what is my habitual way of moving my hand when making a point, etc. There are many more factors, many of which are very remote; so, if it is determined that I move my hand, then it seems to follow logically that which way I move my hand is also determined.
Popper gives a great argument for indeterminism (that is, against determinism), which I do not have the time to expound and argue against here. Suffice it to say that I am not conviced by it. If you are interested in it, see Karl Popper, The Open Universe.
Another example is this: A man who has not had water for a week, and who comes upon a spring, will be elated. His desire will be to drink. But if he knows that the spring is poisoned, he will refrain from drinking. This is taken to be evidence that the man is free. But Holbach replies that the man's desire to stay alive, to not be poisoned, is stronger than his desire to drink. He did not choose to not drink; one influence simply acted more strongly on him than the other did.
Holbach has more to say, but this is the core of it.
His argument assumes that humans are strictly natural, ie, have nothing like a soul. It is a nearly irrefutable argument, if we are prepared to accept that humans are entirely natural; if we are not prepared to do so, it is still a strong argument, but it is open to criticism.