Wolfgang Schwarz

Evidentialism and time-slice epistemology

Time-slice epistemology is the idea that epistemic norms are history-independent: whether an agent at a time satisfies an epistemic norm is always determined by the agent's state at that time, irrespective of the agent's earlier states.

One motivation for time-slice epistemology is a kind of internalism, the intuition that agents should not be epistemically constrained by things that are not "accessible" at the relevant time. Plausibly, an agent's earlier beliefs are not always accessible in the relevant sense. If yesterday you learned that yew berries are poisonous but since then forgot that piece of information, it seems odd to demand that your current beliefs and actions should nevertheless be constrained by the lost information.

Time-slice epistemologists usually endorse evidentialism, the hypothesis that one's beliefs should be proportioned to one's present evidence. Indeed, evidentialism is often presented as another motivation for time-slice epistemology: if evidentialism is right, then earlier beliefs are relevant only insofar as they are part of the present evidence. Earlier beliefs do not impose any direct constraints on present belief.

But it is important to distinguish time-slice epistemology and evidentialism. In my view, both are mistaken, but their combination is even worse: time-slice epistemologists should not be evidentialists, and evidentialists should not be time-slice epistemologists.

The main reason why evidentialists should not be time-slice epistemologists is that I think evidentialists ought to accept substantive diachronic norms on evidence. I might talk about that another time. Here I want to talk about the other claim, that time-slice epistemologists should not be evidentialists. The main reason for that is that time-slice epistemologists should endorse a principle of inverse reflection according to which one's rational credence at any time t in any proposition P, conditional on the hypothesis that one's previous rational credence in P, conditional on the evidence at t, was x, should be x. In symbols:

Cr(t)(P / Cr(t-1)(P/E(t)) = x) = x.

Here Cr(t) is credence at t and E(t) the evidence at t. The principle must be further restricted by the assumption that the previous credence at t-1 was rational. It should also be adjusted if we allow for self-locating propositions which change their truth-value over time, but I will not get into how exactly that should be spelled out.

Inverse reflection recommends a kind of self-trust or commitment to one's previous beliefs. In the simplest case where you acquire no new information about a proposition P, it says that if you know your previous degree of belief in P then you should stick to that degree of belief. In general, if the evidence E(t) at t includes full information about the agent's previous beliefs, then agents who obey inverse reflection also obey conditionalisation.

Inverse Reflection might seem compatible with evidentialism (Hedden 2015, for example, assumes that it is), but it is not. To be sure, very often the information that a rational agent has degree of belief x in P supports P to degree x. If I learn that you are 90 percent confident that your bicycle is at home and I have no further relevant evidence, I should become fairly confident as well that your bicycle is at home.

But there are cases where evidentialism and inverse reflection come apart. One such case are situations in which the evidence does not determine a uniquely rational degree of belief. Suppose the evidence E(t) licenses assigning credence 0.7 to P, but also credence 0.8. (Or it licenses assigning imprecise credence [0.6,0.7] and also [0.7,0.8], but let's stick with the precise case.) Suppose an agent rationally assigns credence 0.7 to P and neither gains nor loses any relevant evidence between t and t'. By hypothesis, the new evidence then still licenses assigning credence 0.8 to P. By contrast, the principle of inverse reflection requires the new probability to be 0.7.

One might respond that such cases are impossible because the information that one previously assigned credence 0.8 to P is actually evidence in favour of P over and above all the first-order evidence still retained from the earlier time. But that seems highly implausible.

In effect, inverse reflection ensures doxastic conservatism for agents who have access to their previous beliefs. And doxastic conservatism is a good thing. Among other things, it rightly predicts that one's credences should not fluctuate wildly in the absence of any relevant new information. It also gives the right verdict in Elga's (2004) Dr. Evil scenario and in the scenarios I discussed in the previous two blog posts (1, 2).

These examples further illustrate how evidentialism and inverse reflection can come apart -- even if we block the above example by postulating that the evidence always licenses exactly one state of belief.

Consider for example the case of the broken duplication machine from the previous post. Here Fred's new evidence supports the hypothesis that his machine works to degree 2/3, but Fred's credence in that hypothesis should remain at 1/2. That outcome is predicted if Fred obeys (a suitable version of) conditionalisation, but also if he obeys (a suitable version of) inverse reflection. For note that the story of Fred does not involve any memory loss. We can assume that Fred perfectly remembers his credal state before entering the machine. At that time, Fred's credence in Works was 1/2, and it was also 1/2 conditional on the hypothesis that Fred would learn whatever he actually learned when emerging from the machine. By inverse reflection, Fred's new credence should therefore be 1/2.