In his Stanford entry on defeasible reasoning, Koons says the following:
In particular, a logical theory of defeasible consequence will have epistemological consequences. It is presumably true that an ideally rational thinker will have a set of beliefs that are closed under defeasible, as well as deductive, consequence.
I’m not sure either of the two claims are true, but I want to focus more on the claim about the defeasible consequence relation. (For deductive consequences, I think some closure principle is true, but even ideally rational thinkers do not engage in every deduction within their intellectual purview.)
So suppose we consider a set S of claims, where S* is the set derived by adding all the defeasible consequences of S. Then the claim would be that it is impossible for an ideally rational thinker to believe S rather than S*.
A first thing to note is that the relation in question can’t be the Chisholmian one here. As I understand his views, Chisholm’s concept of defeasible consequence is clarified by epistemic principles, principles whose antecedents specify items that prima facie support certain conclusions. To sustain the above claim, however, one will have to limit the defeasible consequence relation to what S supports, all elements of S considered. So if S contains p, and p prima facie supports q, but is defeated by further information d (contained in S), then q is not a defeasible consequence of S.
There is another point to note as well. The notion of a defeasible consequence, if it is to be of any epistemological use, needs to be able to hold between things other than beliefs. Being appeared to redly prima facie warrants believing that something is red, even when the person doesn’t believe that s/he is being appeared to redly. So something’s being red should be a defeasible consequence of the claim that one is appeared to redly (at least when no defeaters are present).
This point gives us reason to reject the claim that an ideally rational thinker will have a set of beliefs closed under the defeasible consequence relation. For the set of beliefs might defeasibly support q, but be undermined by some experience one is having which is not encoded within the belief system at all.