Here's my argument:
Premise 1: The belief "There is no free will"(~F) must be based on good reasoning (G) if we are to regard it as true (T).
Premise 2: However, if the belief ~F is true, then everything is determined (D).*
Premise 3: If everything is determined (D), then the belief ~F is also determined (A).
Premise 4: If ~F is determined, then it is not based on good reasoning (~G).
[In other words, if I am merely compelled by a necessary chain of events to believe something, then it is not a result of weighing the evidence, carefully deliberating, and discovering the best explanation of the facts. In such a case I would find "reasons" to be compelling not for their merits, but because I am determined to do so.]
Conclusion: ~F cannot be regarded as true (~T).
Now, for the sake of style I have been a little sloppy with my symbolization. The predicate form would be clearer for those familiar with the discipline, and pure symbol is not convenient in this format. Still, here's a somewhat clarified version:
1. If ~F=T, then ~F=G.
2. If ~F=T, then D.
3. If D, then ~F=A.
4. If ~F=A, then ~[~F=G].
Therefore, ~[~F=T]
To put it more succinctly, determinism implies that one is determined to be or to not be a determinist. End of story. No argument is possible or helpful for one who ascribes to such a view. Common sense, however, suggests that a rational person forms his beliefs upon good reasons. He looks at the evidence, he weighs his own experience, and he judges accordingly. By contrast, all forms of determinism (as generally understood) necessarily undermine rationality by eliminating the principles of deliberation and decision that are intrinsic to any informed judgment. Adherents to determinism, if consistent, must accept that such beliefs are the products of events or circumstances beyond their control. There is, therefore, no good reason for them to hold their beliefs (they simply must), and there is no good reason for us to listen to or adopt their perspective (since, according to them we don't choose our "wrong" beliefs anyway).
I'm amazed sometimes that this simple argument (my articulation of which is definitely not the first) is overlooked for more complex refutations. Determinism is necessarily irrational, and if you believe in humankind's capacity for reason, rational deliberation, and ethical decision making then you must reject it. The implications are significant, but we'll leave further discussion for another time.
Nighty-night.
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*For the sake of this argument I define the word "determined" to mean "part of a closed causal process, either physical of psychological." A closed causal process is one in which each event is necessarily caused by a prior series of events and circumstances. No choice or act of volition can violate or initiate anything except as a part of what the causal process effects. It cannot be otherwise, so it cannot be "free" in the normal sense of the word. A fair analogy might be a chain of dominos each successively causing the adjacent domino to fall (supposing that the impetus in such a series could be construed without personal agency).
Beauty.
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