This post is a follow-up on Catarina's excellent post "non-monotonicity is a fever". I want to defend one interpretation of Van Benthem's comment that Catarina says "always puzzled" her: "Many observations in terms of structural rules address mere symptoms of some more basic underlying phenomenon. For instance, non-monotonicity is like ‘fever’: it does not tell you which disease causes it." I have not read the relevant book, so this may not be what he had in mind, but I think it is right.
Say that A "i-implies" B in a situation iff the material conditional "if A is true then B is true" is true.
Say that A "s-implies B" in a situation if the subjunctive conditional "If A were the case, then B would be the case" is true.
Now these are certainly different. There are lots of cases in which the two famously come apart. (If Booth didn't shoot Lincoln, someone else did. If Booth hadn't shot Lincoln, he would have finished his term without being shot.) But both are non-monotonic forms of reasoning, made explicit by different conditionals. I have a paper - here - in which (along with Heath White) I argue that these two systems of non-monotonic inference are distinct but essentially related. That is, they form functional subsystems of any rational critter, systems neither of which is rationally functional without its inter-relation to the other.
I also think, that both are distinct from certain forms of non-monotonic probabilistic reasoning, but haven't argued this in detail.
To draw out one other type of inference that I have discussed, there is what Maggie Little and I - in several papers - call "defeasible laws." We claim that there are defeasible laws in ethics, biology, social science, etc. that again make explicit a form of inference that is both necessary and non-monotonic. (Example: Lying is defeasibly wrong-making.) And it is distinct from both i-implication and s-implication.
Now I (we) might be wrong about any of this, but it seems to me that there is at least prima facie reason to think that there are many distinct inferential practices, practices playing related but quite distinct rational roles in the function of a rational critter, each of which exhibits the structural feature of non-monotonicity.
That's what I would mean by claiming that non-monotonicity is a symptom, or feature, of a wide variety of underlying phenomena.