Eyes,
That is a tautology. The definition of "random" is "non-deterministic". If you mean something else by the word "random", you need to define what you mean by it.
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It doesn't mean non-deterministic if we believe in libertarian free will. Randomness means innately uncertain.
And that is different from "non-deterministic" how? If something is deterministic, then it is necessarily certain. If it is innately uncertain, then it cannot be deterministic.
Put simply, something that is random is clearly non-deterministic. If you are going to claim that non-determinism alone is not enough for something to qualify as random, then you need to explain what the additional criteria are.
So all you have done is add another set of laws. The "will laws".
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Crucially though what the Will decides is not determined from without, but is a spontaneous decision by an individual. Thus from one second to another second we do what we do because of what we are, but what we intrinsically are is not something imposed upon us externally, but is an elementary reality which cannot be further analysed. In other words what we do is a consequence of ourselves. But the self itself is self-determining.
Our decisions are clearly influenced by outside factors. Even if you allow for some non-reducible "will" that makes the decision, it is affected by outside influences. That will is either deterministic or random, and the mechanism of the influence is also either deterministic or random. Thus the overall process is either deterministic (if both are deterministic), or random (if either or both are random). Either way, Libertarian free-will goes out the window.
Libertarian free-will is incoherent because it asserts that the will is not constrained by any natural laws. It literally asserts that the will is neither deterministic nor random. It must be one or the other.
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No it mustn't. If you mean by deterministic, imposed from without, so that our behavior is circumscribed by physical laws or some sort of mental laws, then I do not see this as being necessarily true.
That is not what deterministic means.
Behavior could be determined from within.
Not completely. And even if it were, it would still be deterministic.
In this situation behavior might not exhibit any patterns which can either be captured by any physical laws or "mental laws", but nevertheless the behaviour isn't random in that the behavior is dictated by the Will and is in general accordance with how a person might be expected to behave in certain given specific circumstances.
This is contradictory. The will interacts with the physical and mental world. The laws that describe it are therefore necessarily a part of the natural laws describing the physical and mental.
If the will is not described by any natural laws, then nothing it interacts with can be either. If it can be, then those laws manifest in the laws describing how the will interacts with other things. Indeed, our decisions
are those interactions. The will can be thought of as a black-box algorithm, with our environment as the input, and our decisions as the output. If the will is deterministic, then there is a set of rules that dictate what our decisions will be for any input. If it is random, then those rules are probabilistic.
No, it isn't. If it is not random, then it is determined by something, which means it is not random.
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ok but determined by the self whose decision is not compltely dictated by factors external to the self.
That is also contradictory. If the self is deterministic, then its state at any point in time is determined entirely by its initial conditions, and its external influences. What determines those initial conditions? Either they are random, or they are determined by something outside of the self.
You are asserting that there is something to the self which is not determined by anything outside of itself, and yet which is not random. That is contradictory. It must be one or the other.
Dr. Stupid
And I can see why for you the syllogism wouldn't hold - but what about if you were a Hard Materialist? Would it hold then - in your opinion?
curses to reality imposing limits on my virtual time 
) that I've never done formal logic - all I know about it is what I've read on the boards.