I decided to look at how people use 'undercutting defeater'. Because it's a lazy Saturday morning, I am only using online sources and am not being very systematic; it's just to further make my point about the ambiguous use.
Undercutting defeat as local
Typically used in discussions of defeasible reasoning
* Robert Koons's SEP article on Defeasible Reasoning: "give one a reason for doubting that the usual relationship between the premises and the conclusion hold in the given case" and "provide a reason for doubting that q provides any support, in the actual circumstances, for r"
* Thomas Kelly's SEP article on Evidence: "Intuitively, where E is evidence for H, an undercutting defeater is evidence which undermines the evidential connection between E and H. "
* John Pollock, How to Build a Person: A Prolegomena: "Undercutting defeaters attack the connection between the reason and the conclusion rather than attacking the conclusion directly. Where P is a prima facie reason for Q, R is an undercutting defeater if and only if R is a reason for denying that P would not be true unless Q were true." [Note, incidentally, that this is an extraordinarily generous account of what counts as an undercutting defeater: an inference could have many undercutting defeaters in this sense and still be an excellent inference -- indeed, could still be the most rational inference available. This connects with another common ambiguity in discussions of undercutting defeaters, namely, whether they are supposed to be reasons to think the inference could give the wrong answer under some circumstances, or whether they are supposed to be reasons to think the inference fails, simply speaking. There are also very different things, since on one having an undercutting defeater is extremely common and no big deal and on the other it is devastating to an argument. I think this ambiguity arises a byproduct of the local/global ambiguity, but I'm not certain; it may just be due to the associations people have with the words 'undercut' and 'defeat' interacting with what one wants to use 'undercutting defeater' to talk about.]
* J. Anthony Blair, Groundwork in the Theory of Argumentation: "An undercutting defeater is an argument whose conclusion is the negation of the inference from the evidence to the conclusion of the argument it aims to defeat."
Undercutting defeat as global
Typically used in discussions of justification, reliabilism, etc.
* Michael Sudduth's article on Defeaters in Epistemology: "An undercutting defeater for some belief that p is a reason (in the broad sense) for no longer believing p, not for believing the negation of p (Pollock, 1986, p. 39). More specifically, it is a reason for supposing that one’s ground for believing p is not sufficiently indicative of the truth of the belief."
cf. also Michael Sudduth's article, "Reformed Epistemology and Christian Apologetics": "An undercutting defeater is an overriding reason for supposing that the grounds of some belief that p are inadequate, i.e., do not provide the appropriate sort of support for the belief that p."
* Thomas Grundman, "Reliabilism and the Problem of Defeaters": "evidence for the unreliability of the source of her belief....defeaters are evidence which removes justification"
* William P. Alston, Realism and Anti-Realism: "An undercutting defeater undermines the rationality of holding a belief not by entailing or supporting its denial but rather by calling into question the soundness of its grounds."
I found it much easier to find examples of people defining undercutting defeaters in the local way, but most of the examples of the phrase in use that I've come across are global -- I think it's just that people specifically talking about defeasible reasoning are much more likely to give an actual definition than simply take it as known to everybody or clarify by example alone.
