Is 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) > 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. (shrink)

There are many scientific and everyday cases where each of Pr and Pr is high and it seems that Pr is high. But high probability is not transitive and so it might be in such cases that each of Pr and Pr is high and in fact Pr is not high. There is no issue in the special case where the following condition, which I call “C1”, holds: H 1 entails H 2. This condition is sufficient for transitivity in high (...) probability. But many of the scientific and everyday cases referred to above are cases where it is not the case that H 1 entails H 2. I consider whether there are additional conditions sufficient for transitivity in high probability. I consider three candidate conditions. I call them “C2”, “C3”, and “C2&3”. I argue that C2&3, but neither C2 nor C3, is sufficient for transitivity in high probability. I then set out some further results and relate the discussion to the Bayesian requirement of coherence. (shrink)

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. (shrink)

The probabilistic support relation is known to violate transitivity. But over the years, philosophers have identified various conditions under which it does not, most notably screening-off and weak screening-off. In this short discussion note, I wish to highlight another condition that, unfortunately, is often neglected in the literature. This condition is due to Mary Hesse who recognized its transitivity-ensuring property long before other conditions entered the stage. I show that her condition is logically independent of screening-off and weak screening-off, but (...) that, just like the two aforementioned, it entails the recently proposed very weak screening-off condition due to Jeanne Peijnenburg and David Atkinson. (shrink)