We can distinguish four kinds of necessity:
Intrinsic (Natural) Necessity
1. Formal Necessity (e.g., on a Euclidean plane, the angles of a triangle are equal to two right angles)
2. Material Necessity (e.g., such-and-such material puts such-and-such constraints on what can be done with it)
Extrinsic Necessity
1. Necessity of the End (e.g., In order to keep living, it is necessary to eat)
2. Necessity of Compulsion (e.g., Such-and-such cause constrains the result in such-and-such way)
This can be applied to the question of the viability of determinism. I have come across determinists who puzzle over why it's usually referred to as causal determinism, since the necessity is one of logical implication. I think this is an odd thing to say. Logical implication only represents the necessity; it tells us that it is there. What it does not do is tell us why we believe the necessity to be there in the first place, and that is really what is always at issue in the question of whether any form of determinism is true. If determinism is the position that, given the initial state, the final state must follow, then the sort of necessity involved can't be material necessity - initial state and final state aren't related in that way. It can't be necessity of end, because the implication goes the wrong way (because it's an end-means necessity: given the final state, the initial state follows; but determinism requires the reverse). Further, necessity of end allows for alternative possibilities, which is why it hasn't usually been regarded as an issue in the free will debate. So this leaves only formal necessity and necessity of compulsion. For formal necessity to do the work determinism needs, there must be some intrinsic principle uniting initial and final states that makes the link between them necessary; a universal determinism, such as arises in the debate over freedom of will, requires that this principle not only make the link necessary, but that it apply to all relevant states (universal) and do so necessarily (if it is contingent we seem to have moved the necessity back to necessity of compulsion). So if formal necessity is to undergird universal determinism, there has to be something about states themselves that requires they be linked in this way. As determinism is usually formulated, the only conditions that are plausible candidates are space and time, which certainly don't seem to constrain things in this way. So while a formal determinism is perhaps possible, it would need considerably more defense than most determinists have been willing to make. So the necessity of determinism would appear to be a necessity of compulsion, i.e., a necessity due to the causes involved.
