According to the traditional account of defeater, defended by John Pollock in the paper “Defeasible Reasoning” (1987), the following definition of a “defeater” is accepted:
(DEF) Where D and E are jointly consistent propositions, D is a defeater for E’s support for P if and only if (i) E is a reason to believe P but (ii) E&D is not a reason to believe P.
A consequence of Pollock’s account is the following principle of symmetry:
(SYM) If both E and D provide a reason to believe P, D is a defeater for E’s support for P if and only if E is a defeater for D’s support for P.
But this traditional account has been challenged by some philosophers. Jake Chandler in his paper “Defeat Reconsidered” (2013) developed the following counterexample: Outside the door to Sam’s flat is a switch for the light in the staircase. Flipping the switch (ES) typically causes the light to go on (PS): ES is a reason to believe PS. When there is a power cut (DS), ES loses this probative force. Thus, DS is a defeater for ES’s support for PS. It is also part of DS that there is backup power system that is activated (and automatically turns on the lights) when the main system fails. So, just like ES, DS provides a reason to believe PS. But there is an asymmetry: while DS is a defeater for ES’s support for PS, ES is not a defeater for DS’s support for PS (since the position of the switch is irrelevant). In this way, the previous principle (SYM) fails and, consequently, so does the traditional definition of defeater (DEF). This conclusion can be presented in the form of a dilemma:
How can we solve this problem? Jake Chandler proposes an alternative to DEF that seems to solve the counterexample. His proposal is as follows:
(DEF*) Where D and E are jointly consistent propositions, D is a defeater for E’s support for P if and only if D is a reason to not believe that E is a reason to believe P.
This account has a different negational scope, requiring, not that E&D not be a reason to believe P, but that E&D be a reason to not believe P. This solves the previous counterexample, because DS provides grounds to hold that ES is no reason to believe HS. However, ES does not provide grounds to hold that DS is no reason to believe PS.
This solution seems intuitive. But in a recent paper presented by Tommaso Piazza, “The Traditional Account of Epistemic Defeat: a Defence”, he presents several replies to Chandler’s objections. Piazza’s first quick reply is as follows:
“The inference from the proposition (DC) that there is a power cut to the conclusion (PC) that the light is set to on is neither deductively valid nor inductively strong; hence, the first proposition is not a reason in Pollock’s sense for believing the second”.
However, I think there is a problem with Piazza’s reply. For, the propositional content of the DC premise is not only that there is a “power cut”, but also that there is a “backup power system” that automatically turns on the lights. According to Chandler, this latter propositional content is not “background knowledge”, but is part of DS itself.
Piazza points out that he wants better examples in which D is at the same time a defeater for E as a reason for P and a reason for believing P in Pollock’s sense. An example of this could be a standard Gettier case. However, according to Piazza, these examples do not raise a real dilemma for the defender of DEF. For, in such cases, “E and D are symmetrical with respect to their defeating potential”. Thus, according to Piazza, the traditional account remains plausible .
However, Piazza’s argument seems to me to be a “fallacy of begging the question”. For, Chandler’s counterexample is formulated in such a way that symmetry fails. So, one cannot suggest “better” examples in which symmetry does not fail. In other words, a good counterexample would be one in which D is a defeater for E’s support for P, but E is not a defeater for D’s support for P. In such cases, we have Chandler’s dilemma. So it seems to me that Piazza’s objections to Chandler’s argument are not viable. In short, it seems that we still have a good counterexample (that formulated by Chandler) to the traditional account of defeater.