Eager summarizes the positive use of analogy in the following terms:
It is lawful to argue from a resemblance of relations to the resemblance of other relations, provided that the two sets of relations can be shown to depend one on the other, or both on the same cause.
We find this principle used in law all the time, and Eager uses a legal example. Suppose we have no laws about landlords and tenants; we can then construct the relevant laws by borrowing from the laws we have about borrowers and sellers. This, of course, is constructive, but one can find nonconstructive examples. Being analogy-based, they all yield only probability, and can turn out to be wrong (just as the constructive case could turn out to be unworkable) but they do exist. For instance, if you had never come across a spore before, certain similarities of seeds to spores could allow you to conclude, defeasibly, that seeds and spores did much the same thing.
Eager describes the negative use of analogy in the following way:
It is lawful to answer an objection to the consistency of two terms, when related in any way to one another, by showing that other terms, admitted to be similarly related, are liable to the same objection.
In effect, the negative use of analogy is a parity argument. Thus the overall structure of Butler's Analogy consists in the argument, against the deists, that objections made against a divine moral government have analogues in objections made against a divine natural providence, and that objections against revealed religion have analogues in objections made against natural religion, and that therefore the replies made to the objections in one case have analogues in the other case.
Both of these uses bring out clearly that analogy, despite the fact that it is far from demonstrative, is a close friend of consistency. People often make objections that, given their other commitments, they could not reasonably accept because the underlying principle of the objection is inconsistent with some principle they rely on elsewhere; and negative analogy hunts those out, although, again, it does so only with probability.
Of course, I think it could be argued that there are more uses of analogy than these two. For instance, I think there is a neutral use of analogy that does not work to establish truth (as in positive analogy) or falsehood (as in negative analogy), but merely intelligibility -- for instance, Hume uses such analogy extensively in his account of belief. And there are probably as many uses of analogies as there are interesting modal operators or 'truth values'.
