Abstract
The goal of this chapter is to disentangle several related—but importantly distinct—notions of evidential defeat. The broadest distinction in the literature on epistemic defeat is that between rebutting and undercutting defeat; very roughly, the idea is that rebutting defeaters provide a “positive” reason to disbelieve the conclusion, whereas an undercutting defeater merely “blocks” existing reasons to believe the conclusion. In this chapter, I formalize these two notions and explore some related (and under-discussed) phenomena such as “hybrid” defeat (where a single defeater can both rebut and undercut), “bidirectional” defeat (where some information that serves as evidence for a conclusion can become a defeater in the presence of another piece of evidence for the conclusion), and “redundant” defeat (where an undercutting effect is generated by the non-independence of two pieces of information, rather than by the “blocking” phenomenon that occurs in more typical cases of undercutting).
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20 June 2019
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Notes
- 1.
This latter class is more commonly referred to as “rebutting” defeaters; for reasons that will become clear later, I prefer the term “opposing.” The term is due to Jim Pryor.
- 2.
There has been a lot of discussion in the literature recently on so-called “higher-order” defeaters, which work by inducing doubts about the reliability of the cognitive process(es) that produced a belief. See, e.g., Christensen (2007a, b, c, 2009, 2010), Elga (unpublished), Kelly (2010), Lasonen-Aarnio (2014), and Schechter (2011). I consider these sorts of higher-order defeaters to be undercutting defeaters, though I will for the most part focus on lower-order kinds of undercutting defeat in this chapter.
- 3.
Here and throughout, I will assume Conditionalization—i.e., I will assume that the new rational credence for me to have in H, after collecting exactly evidence E, is my old p(H|E).
- 4.
- 5.
Here and throughout, I have changed the notation of the theories I’m discussing for the sake of consistency.
- 6.
Namely, that p(H|E) > p(H).
- 7.
Some positions in metaethics—notably, some versions of non-cognitivism—entail that my attitudes about Ada’s moral upstandingness are non-cognitive in nature, and hence do not involve my being related to a proposition about Ada’s moral upstandingness. For the purposes of simplicity, I simply ignore these positions here; I assume in the text that being confident that Ada is morally upstanding is simply a matter of having a high credence in the proposition that Ada is morally upstanding. However, nothing essential turns on this choice, and the example could be modified (at the cost of simplicity) to avoid this complication.
- 8.
For the purposes of this example, suppose that the hallucinogen at issue causes visual, but never auditory, hallucinations; thus, there is no reason for concern about whether your experience as of your friend speaking to you is veridical.
- 9.
- 10.
One purpose of taking the log of these quantities is so that the measure counts as a so-called “relevance measure,” where the measure is positive if E confirms H, negative if E disconfirms H, and 0 if E is neutral to H. Another purpose is to ensure scale-invariance. For our current purposes, the log can be ignored. Since log is a monotone increasing function, it will follow from the fact that A > B that log A > log B (and conversely). So if we want to compare two degrees of confirmation, all we need to do is to compare the argument of the log.
- 11.
- 12.
Of course, if there is no “one true measure” of degree of confirmation but rather just a plurality of different measures, then my account entails that there will be many different notions of undercutting defeat—one relative to each of the confirmation measures. But I think that this is precisely the right result; if there is no one privileged way to measure evidence, then I don’t think that there can be one privileged way to measure undercutting of evidence either.
- 13.
Clearly, we could play with the details here so that p(H| E & D) = p(H|E), which would also violate Defeater IFF Credence-Lowering’s condition.
- 14.
For any relevance measure of confirmation, since p(H|E) > p(H), dc(E, H, K) > 0. Similarly, for any relevance measure, if p(H|D) > p(H| E & D), then dc(E, H, K & D) < 0. So, if Bidirectional IFF D Flips E From a Confirmer to a Disconfirmer’s condition holds, then dc(E, H, K) > 0 > dc(E, H, K & D), so Undercutting IFF Degree-of-Confirmation Lowering’s condition holds.
- 15.
Note that while this argument provides some reason to believe that all opposing defeaters are undercutting defeaters, it provides no reason to think that all undercutting defeaters are opposing defeaters.
- 16.
The idea here would be that this information is an opposing defeater, since it’s morally bad to put drugs in people’s coffee without their consent, even if the drug has a vision-enhancing effect. However, this information wouldn’t be an undercutting defeater of the evidence that my visual experience provides for the proposition that Ada is morally good; if anything, this information would tend to strengthen the impact of my visual experience on that hypothesis, since it reduces the probability of a visual error.
- 17.
I’m assuming here that if p and q are logically equivalent, then p is a hybrid opposing defeater iff q is a hybrid opposing defeater, but I think that’s overwhelmingly plausible here.
- 18.
By “pure,” I mean to refer to defeaters that aren’t also hybrid undercutting defeaters.
- 19.
If dc is a relevance measure (which I’ve been assuming it is), then dc(E, H, K & D) = 0 when p(H|D) = p(H| E & D). But it’s clear here that p(H|D) = p(H| E & D) = .9.
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Kotzen, M. (2019). A Formal Account of Epistemic Defeat. In: Fitelson, B., Borges, R., Braden, C. (eds) Themes from Klein. Synthese Library, vol 404. Springer, Cham. https://doi.org/10.1007/978-3-030-04522-7_14
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