Evidential support, transitivity, and screening-off

AbstractIs evidential support transitive? The answer is negative when evidential support is understood as confirmation so that X evidentially supports Y if and only if p(Y | X) &gt; p(Y). I call evidential support so understood “support” (for short) and set out three alternative ways of understanding evidential support: support-t (support plus a sufficiently high probability), support-t* (support plus a substantial degree of support), and support-tt* (support plus both a sufficiently high probability and a substantial degree of support). I also set out two screening-off conditions (under which support is transitive): SOC1 and SOC2. It has already been shown that support-t is non-transitive in the general case (where it is not required that SOC1 holds and it is not required that SOC2 holds), in the special case where SOC1 holds, and in the special case where SOC2 holds. I introduce two rather weak adequacy conditions on support measures and argue that on any support measure meeting those conditions it follows that neither support-t* nor support-tt* is transitive in the general case, in the special case where SOC1 holds, or in the special case where SOC2 holds. I then relate some of the results to Douven’s evidential support theory of conditionals along with a few rival theories.</jats:p

Is evidence of evidence evidence? Screening-off vs. no-defeaters

I argue elsewhere (Roche 2014) that evidence of evidence is evidence under screening-off. Tal and Comesaña (2017) argue that my appeal to screening-off is subject to two objections. They then propose an evidence of evidence thesis involving the notion of a defeater. There is much to learn from their very careful discussion. I argue, though, that their objections fail and that their evidence of evidence thesis is open to counterexample

Evidence of Evidence as Higher Order Evidence

In everyday life and in science we acquire evidence of evidence and based on this new evidence we often change our epistemic states. An assumption underlying such practice is that the following EEE Slogan is correct: 'evidence of evidence is evidence' (Feldman 2007, p. 208). We suggest that evidence of evidence is best understood as higher-order evidence about the epistemic state of agents. In order to model evidence of evidence we introduce a new powerful framework for modelling epistemic states, Dyadic Bayesianism. Based on this framework, we then discuss characterizations of evidence of evidence and argue for one of them. Finally, we show that whether the EEE Slogan holds, depends on the specific kind of evidence of evidence

Explanation, confirmation, and Hempel's paradox

Hempel’s Converse Consequence Condition (CCC), Entailment Condition (EC), and Special Consequence Condition (SCC) have some prima facie plausibility when taken individually. Hempel, though, shows that they have no plausibility when taken together, for together they entail that E confirms H for any propositions E and H. This is “Hempel’s paradox”. It turns out that Hempel’s argument would fail if one or more of CCC, EC, and SCC were modified in terms of explanation. This opens up the possibility that Hempel’s paradox can be solved by modifying one or more of CCC, EC, and SCC in terms of explanation. I explore this possibility by modifying CCC and SCC in terms of explanation and considering whether CCC and SCC so modified are correct. I also relate that possibility to Inference to the Best Explanation

Defeaters and Disqualifiers

Justification depends on context: even if E on its own justifies H, still it might fail to justify in the context of D. This sort of effect, epistemologists think, is due to defeaters, which undermine or rebut a would-be justifier. I argue that there is another fundamental sort of contextual feature, disqualification, which doesn't involve rebuttal or undercutting, and which cannot be reduced to any notion of screening-off. A disqualifier makes some would-be justifier otiose, as direct testimony sometimes does to distal testimony, and as manifestly decisive evidence might do to gratuitous evidence on the same team. Basing a belief on disqualified evidence, moreover, is distinctively irrational. One is not necessarily irresponsible. Instead one is turning down a free upgrade to a sleeker, stabler basis for one's beliefs. Such an upgrade would prevent wastes of epistemic effort, since someone who bases her belief on a disqualified proposition E will need to remember E and rethink her belief should E ever be defeated. The upgrade might also reduce reliance on unwieldy evidence, if E is relevant only thanks to some labyrinthine argument; and if even ideal agents should doubt their ability to follow such arguments, even they should care about disqualifiers

Evidence of evidence is evidence under screening-off

AbstractAn important question in the current debate on the epistemic significance of peer disagreement is whether evidence of evidence is evidence. Fitelson argues (persuasively in my view) that, at least on some renderings of the thesis that evidence of evidence is evidence, there are cases where evidence of evidence is not evidence. I introduce a ‘screening-off’ condition and show that under this condition evidence of evidence is evidence.</jats:p

Dwindling Confirmation

We show that as a chain of confirmation becomes longer, confirmation dwindles under screening-off. For example, if E confirms H1, H1 confirms H2, and H1 screens off E from H2, then the degree to which E confirms H2 is less than the degree to which E confirms H1. Although there are many measures of confirmation, our result holds on any measure that satisfies the Weak Law of Likelihood. We apply our result to testimony cases, relate it to the Data-Processing Inequality in information theory, and extend it in two respects so that it covers a broader range of cases.</jats:p

Knowledge-First Theories of Justification

Knowledge-first theories of justification give knowledge priority when it comes to explaining when and why someone has justification for an attitude or an action. The emphasis of this entry is on knowledge-first theories of justification for belief. As it turns out there are a number of ways of giving knowledge priority when theorizing about justification, and in what follows I offer an opinionated survey of more than a dozen existing options that have emerged in the last two decades since the publication of Timothy Williamson’s Knowledge and Its Limits. I first trace several of the general theoretical motivations that have been offered for putting knowledge first in the theory of justification. I then go on to examine existing knowledge-first theories of justification and their standing objections. These objections are largely, but not exclusively, concerned with the extensional adequacy of knowledge-first theories of justification. There are doubtless more ways of giving knowledge priority in the theory of justification than I cover here, but the resulting survey will be instructive as it highlights potential shortcomings that would-be knowledge-first theorists of justification may wish either to avoid or else to be prepared with a suitable error theory

Higher-Order Uncertainty

You have higher-order uncertainty iff you are uncertain of what opinions you should have. I defend three claims about it. First, the higher-order evidence debate can be helpfully reframed in terms of higher-order uncertainty. The central question becomes how your first- and higher-order opinions should relate—a precise question that can be embedded within a general, tractable framework. Second, this question is nontrivial. Rational higher-order uncertainty is pervasive, and lies at the foundations of the epistemology of disagreement. Third, the answer is not obvious. The Enkratic Intuition---that your first-order opinions must “line up” with your higher-order opinions---is incorrect; epistemic akrasia can be rational. If all this is right, then it leaves us without answers---but with a clear picture of the question, and a fruitful strategy for pursuing it