On justified yet logically inconsistent beliefs
I recently read that “a person can be justified in believing an inconsistent set of propositions, even when this person recognizes the inconsistency.”¹
This caught me off guard. I always thought that rationality requires logical consistency. The author is Paul K. Moser and the book is his first monograph, Empirical Justification (1985). He makes his point by way of Henry Kyburg’s lottery paradox. This seems like a valuable lesson worth sharing.
Suppose that we observe a lottery in which one ticket out of one hundred will be chosen as the winner. What sort of beliefs can we hold in a justified way about this lottery?
First, we should believe that one of the one hundred tickets will be chosen. We believe that either ticket number 1 will win, or ticket number 2 will win, or ticket number 3 will win, etc. Let’s say that we are justified in believing that one out of the many tickets will win.
Second, we should also believe that any given ticket is likely to lose. Not convinced? Just add more tickets to the lottery until the likelihood of any particular ticket winning becomes minuscule. Unless justified belief requires certainty — which would be an extreme requirement — there is a point at which the odds of a given ticket winning are low enough that we ought to believe that it will lose.
Taken together, we are justified in believing:
(a) that some ticket will win; and
(b) that any given ticket will not be chosen.
Justified beliefs (a) and (b) turn out to be logically inconsistent in the sense that they cannot both be true. By the nature of the lottery, we are justified in believing that some ticket will win, that all the losing tickets will lose, but also that the winning ticket will lose. One of our justified beliefs about the lottery is a justified false belief.
Furthermore, our justified false belief that the winning ticket will lose is logically inconsistent with our justified true beliefs about the lottery. If we believe that ticket 1 will lose, that ticket 2 will lose, that ticket 3 will lose, and so on, then the logical conjunction of those beliefs is that no ticket will win. i.e. that all the tickets will lose. But we also believe with justification precisely the opposite — that some particular ticket will win.
Something has to give. Paul Moser argues that we ought to abandon the idea that the logical conjunction of our justified beliefs is also a justified belief.
In terms of the lottery, my justified beliefs about each ticket, that it will lose, do not add up to justified belief that every ticket will lose. On the contrary, although we expect each ticket taken separately to lose, we also expect one of them to win. We just don’t know which one. In the case of this lottery, we are therefore justified in believing logically contradictory beliefs.
Moser concludes that “there can be logically inconsistent sets all of whose members we can justifiably believe, even when we recognize the inconsistency.”³
Upon learning this lesson, I immediately wondered how it would apply to mystery in theology and human limits upon theological knowledge. A couple days later, I came across a passage by John Wesley to the same effect. He writes,
although every man necessarily believes that every particular opinion which he holds is true (for to believe any opinion is not true, is the same thing as not to hold it); yet can no man be assured that all his own opinions, taken together, are true. . . . “To be ignorant of many things, and to mistake in some, is the necessary condition of humanity.” This, therefore, he is sensible, is his own case. He knows, in the general, that he himself is mistaken; although in what particulars he mistakes, he does not, perhaps he cannot, know.³
This principle seems to me above reproach. What we think is true, that we believe. We also expect to be wrong. We just don’t know wherein lies our error. We ought therefore to admit that we can, in certain cases, be justified in believing logically inconsistent beliefs.
How far does this principle go in practice? Well, the smaller the lottery the more uncomfortable I feel. There are plenty of problems in theology involving two or three apparently (and often obviously) inconsistent potential beliefs. In the past I faced such dilemmas and trilemmas intending to choose one logical option for the sake of logical consistency.
But if we think of theological dilemmas and trilemmas as tiny lotteries, it seems possible to have strong evidence for multiple incompatible options. In fact, this is often the case. Were it not so the choice would be easy and our difficult decisions would vanish. Yet faced with these decisions, perhaps it is reasonable to hold incompatible justified beliefs based on their supporting evidence whilst expecting to be wrong about we know not which one.
References
1: Paul K. Moser, Empirical Justification, Philosophical Studies Series in Philosophy 34 (Dordrecht: D. Reidel, 1985), 18.
2: Ibid., 20.
3: John Wesley, John Wesley’s Sermons: An Anthology, ed. Albert C. Outler and Richard P. Heitzenrater (Nashville, TN: Abingdon Press, 1991), Kindle edition, chap. “Catholic Spirit: Sermon 39–1750.”
