It seems to me, however, that most slippery slope arguments, even those put in causal language, are actually not really causal in precisely this way. Rather, they are justificatory. And I think these are in general the version that is least amenable to easy analysis and evaluation. The temptation is to try to put it down in premise-premise-conclusion form, and I think there are good reasons to be wary of such a glib approach. For it is glib in at least this sense, that it assumes the argument is deductive in structure. Or in Locke's terms, which are actually useful for once, it pretends that the argument must be ad judicium, when it is really ad ignorantiam; that, in particular, it is an argument in the premise-conclusion sense rather than a challenge.
Challenges are a class of argument that are common in rational argument, although often overlooked; it is difficult to find anyone besides Locke who even acknowledges that they exist. But that they do exist is clear. Here is a famous example from Berkeley's Principles of Human Knowledge (1.10):
Now, if it be certain that those original qualities are inseparably united with the other sensible qualities, and not, even in thought, capable of being abstracted from them, it plainly follows that they exist only in the mind. But I desire any one to reflect and try whether he can, by any abstraction of thought, conceive the extension and motion of a body without all other sensible qualities. For my own part, I see evidently that it is not in my power to frame an idea of a body extended and moving, but I must withal give it some colour or other sensible quality which is acknowledged to exist only in the mind.
This is undeniably an argument; indeed, it is probably the argument in PHK most people have historically found persuasive, despite the fact that he gives more sophisticated arguments. And, as with all of Berkeley's arguments, it is beautifully constructed. He gives a reason for the challenge (first sentence), the challenge (second sentence), and a reason for thinking it is genuinely challenging (third sentence). But how would one put this into premise-conclusion form without distorting the argument? To be sure, the first sentence is a conditional, but the third sentence is ineliminably in first person and if it were just taken flatly wouldn't be much of an argument at all, even combined with the first sentence -- certainly not one that would have much force for anyone but Berkeley himself. Any significant force the argument has comes from the second sentence. But the second sentence is not a premise; it is quasi-imperative in nature. It's not a premise, it's a request.
And this, I think, is the key. Challenges are part of a broader class of rational acts that we might call 'search requests'. In these arguments, key information is not provided; rather, what we have in its place is a request for one's interlocutor(s) to do something and return with information, which will be the premise (or complete it). What differentiates this challenge-argument of Berkeley's from other search requests is that it is specifically (1) an objection to an opposing position; (2) in which the person giving the request is fairly confident that the information returned due to the request will be unfavorable to that position. Berkeley is quite confident that no one will be able to "by any abstraction of thought, conceive the extension and motion of a body without all other sensible qualities." From this one can see that the possible good responses to such an argument are (1) reject the request for some good reason (e.g., if it weren't actually relevant) or (2) accept it and return information contrary to expectation (i.e., favorable to the position expected to). Another way to put it is that the argument here is itself simply a demand for an argument, combined with a reason for thinking the demand cannot be met: to counter it, you have to give an argument that you really and truly can "conceive the extension and motion of a body without all other sensible qualities."
Slippery slope arguments, I would suggest, are one kind of challenge. Unlike Berkeley's challenge, which is inquisitive, asking the interlocutor to perform an inquiry to answer a particular question, slippery slope arguments are admonitive, asking the interlocutor to show that a likely bad result can be avoided. I think this is true even of the causal version: the emphasis of the argument is not on "This may well lead to that" but on "Show me that this won't lead to that given that it looks like it might". The whole point of a slippery slope argument is to raise a warning flag. This flag can be raised with varying degrees of confidence; but it's a warning of something bad that seems to be reason to object to a position, and the arguer is insisting on the need to address it. And the possible responses are to argue (1) that the warning flag is misguided, i.e., that the apparently bad outcome is not bad at all; or (2) that there is a genuinely significant difference between this case and that case. Which, of course, are the kinds of responses reasonable people undertake when responding to slippery slope arguments.
I said above that I think most slippery slope arguments, regardless of how they are phrased, are really justificatory: the warning they raise in particular is that it's unclear how a justification (for an action or a position) used in this case would not also apply (perhaps equally, but perhaps with minimal adaptation) in situations where it would give bad results. Putting it this way shows the affinity between slippery slope arguments on the one hand and arguments by analogy and parity arguments on the other; this would be fruitful territory for exploring. But it's still the case that slippery slope arguments are admonitive challenges, not analogies or arguments based on parity.
