Misleadingness simpliciter

It is quite routine that learning a truth leads to rationally believing new falsehoods. For we all rationally believe many falsehoods. Suppose I rationally believe a falsehood p and I don’t believe a truth q. Then, presumably, I don’t believe the conjunction of p and q. But suppose I learn q. Then, typically, I will rationally come to believe the conjunction of p and q, a falsehood I did not previously believe.

Thus there is a trivial sense in which every truth I learn is misleading. But a definition of misleadingness on which every truth is misleading doesn’t seem right. Or at least it’s not right to say that every truth is misleading simpliciter. What could misleadingness simpliciter be?

In a pair of papers (see references here) Lewis and Fallis argue that we should assign epistemic utilities to our credences in such a way that conditioning on the truth should never be bad for us epistemically speaking—that it should not decrease our actual epistemic utility.

I think this is an implausible constraint. Suppose a highly beneficial medication has been taken by a billion people. I randomly sample a hundred thousand of these people and see what happened to them in the week after receiving the medication. Now, out of a billion people, we can expect about two hundred thousand to die in any given week. Suppose that my random sampling is really, really unlucky, and I find that fifty thousand of the people in my sample died a week because of the medication. Completely coincidentally, of course, since as I said the medication is highly beneficial.

Based on my data, I rationally come to believe the importantly false claim that the medication is very harmful. I also come to believe the true claim that half of my random sample died a week after taking the medication. But while that claim is true, it is quite unimportant except as misleading evidence for the harmfulness of the medication. It is intuitively very plausible that after learning the truth about half of the people in my sample dying, I am worse off epistemically.

It seems clear that in the medication case, my data is true and misleading in a non-trivial way. This suggests a definition of misleadingness simpliciter:

• A proposition p is misleading simpliciter if and only if one’s overall epistemic utility goes down when one updates on p.

And this account of misleadingness is non-trivial. If we measure epistemic utility using strictly proper scoring rules, and if our credences are consistent, then the expected epistemic value of updating on the outcome of a non-trivial observation is positive. So we should not expect the typical truth to be misleading in the above sense. But some are misleading.

From this point of view, Lewis and Fallis are making a serious mistake: they are trying to measure epistemic utilities in such a way as to rule out the possibility of misleading truths.

By the way, I think I can prove that for any measure of epistemic utility obtained by summing a single strictly proper score across all events, there will be a possibility of misleadingness simpliciter.

Final note: We don’t need to buy into the formal mechanism of epistemic utilities to go with the above definition. We could just say that something is misleading iff coming to believe it would rationally make one worse off epistemically.

The unavoidability of misleading evidence

Three definitional assumptions:

1. E is only evidence if there is some hypothesis H to which E makes an evidential difference, i.e., P(H|E)≠P(H).

2. E is incomplete if and only if it is evidence such that there is a hypothesis H such that 0 < P(H|E)<1, i.e., E doesn’t make everything certain.

3. E is misleading with respect to a hypothesis H if and only if either H is true and E is evidence against H (i.e., P(H|E)<P(H)) or H is false and E is evidence for H (i.e., P(H|E)>P(H)).

Then:

4. Every piece of incomplete evidence is misleading (with respect to some hypothesis).

[Proof: Suppose E is incomplete evidence. Either E is or is not true. If it is not true, it is misleading, since it lowers its own probability to zero. So, suppose that E is true. Let H₁ be a hypothesis such that 0 < P(H₁|E)<1. Replacing H₁ by its negation if necessary, we can assume H₁ is true. Note that the fact that E is evidence implies that 0 < P(E)<1. Let H be the disjunctive hypothesis: ∼E or (H₁&E). This is true as the second disjunct is true. Now, note that P(H₁&E)<P(E) as P(H₁|E)<1. Thus, (1 − P(E))P(H₁&E)<(1 − P(E))P(E). Thus, P(H₁&E)<P(E)P(H₁&E)+(1 − P(E))P(E). Thus: P(H₁|E)=P(H₁&E)/P(E)<P(H₁&E)+(1 − P(E)) = P(H₁&E)+P(∼E)=P(H). Thus, E is evidence against H even though H is true.]

In particular, we should not take misleadingness of evidence to be an evil. Misleadingness of evidence is a normal part of reasoning with incomplete information.

Yet another theory of ineffability

There is a long-standing tradition of trying to explain (!) the attribute of divine ineffability. Theories that are metaphysical in flavor rule the roost:

1. The only true assertions we can make about God are negative. (Eastern tradition)

2. The only true assertions we can make about God are analogical. (Aquinas)

3. The only true assertions we can make about God are non-fundamental. (Jacobs)

I want to add one more theory to the mix, one that can either be stand-alone or a complement to (1)–(3). This one is more epistemological:

4. The only assertions we can make about God are misleading.

One can illustrate the misleadingness of true, and even literally true, statements by examples.

• “Alice did not treat minorities as badly as Hitler” (when Alice was in fact an exemplary promoter of social justice).

• “Bob is somewhere in this building” (when he is standing right behind you).

• “I saw Carl in a car on I-35 this morning” (but the car was being towed by a truck).

• “Davita passed some of her exams” (when she passed all of them).

• “On a good day, Roger Bannister could run an 8 minute mile.”

Note that while (1)–(3) are limited to true statements, (4) does not have this restriction. After all, all false statements are misleading.

For concrete theological examples, think of how the doctrine of the Trinity shows that the doctrine of the unity of God is misleading, or the doctrine of the Incarnation shows that the doctrine of the transcendence of God is misleading. In a similar same way, when the doctrines of the Trinity and Incarnation are taught apart from the doctrines of unity and transcendence, they are misleading. But by (4) something more pessimistic is true: even when we teach Trinity and unity (or Incarnation and transcendence) together, we still mislead. I suspect that in heaven we will learn something that changes our understanding of unity and Trinity at least as much as the doctrine of the Trinity changed our understanding of unity.

Alvin Plantinga gives this counterexample to the thesis that we cannot say anything literally true of God: “God is not a bicycle.” If (4) is true, even this statement is misleading. In what way? Well, maybe it leads us to forget the intimate link between all reality and God: that all the reality in a bicycle is a participation in God.

Note that if (4) is true, then it is misleading. But that’s not a refutation.

One could also restrict (4) if one wanted to. For instance, one could restrict (4) to non-negative statements, or to non-analogical ones, or to non-fundamental ones.

I don’t know if (4) is true.