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Ratiocination

Contradictory Beliefs


Some doxastic logics endorse the following principle: if S believes p at t, then it's not the case that s believes ~p at t. Call this rule No Contradictions.

No Contradictions gets some traction, I suppose, because of its similarity to the Law of Non-Contradiction. That contradictions aren't possible suggests to some that contradictory beliefs aren't possible either. And abiding by No Contradictions does seem to be a necessary condition for proper function or rational thought. It's natural to think that sane, rational, epistemically responsible agents just don't hold contradictory beliefs.

I'm inclined to think that this is mistaken. But first a distinction. It's one thing to believe p at t while also believing ~p at t. It's another to believe that (p&~p) at t. One can reject No Contradictions while still thinking that it's impossible for someone to believe the conjunction of a proposition and its negation (this view requires that belief not be closed under conjunction introduction).

So why reject No Contradictions? Here are two reasons. First, No Contradictions assumes that actual epistemic agents have a degree of rationality that they may not have. So it’s perhaps open to empirical falsification. This is something for the psychologists to tell us, I suppose; but for all I know we might actually find someone (perhaps someone who's not very epistemically responsible) who believes p and ~p at the same time.

But second, it seems to me that No Contradiction is subject to counterexample. If No Contradiction is going to be an axiom or a theorem of some doxastic logic based on K, then it will have to be broadly logically necessary. Any broadly logically possible case in which No Contradiction fails to hold will suffice to unseat it, then. Here's a counterexample which seems to me, at least, to be broadly logically possible: I believe that Hesperus is a star. I also happen to believe that Phosphorus isn’t (I’m convinced it’s a planet, say). In this case, I believe p and I believe ~p.

The case is interesting in that it doesn't require any acts of wild epistemic irresponsibility. So long as the subject doesn't know that Hesperus is Phosphorus, at least. To elaborate: ‘Hesperus’ and ‘Phosphorus’ are proper names that rigidly designate the same thing. The English sentence S1: “Hesperus is a star” expresses the same proposition (call it p) as the sentence S2: “Phosphorus is a star.” Suppose so. Then I’d think the sentence S3: “It’s not the case that Phosphorus is a star” expresses the negation of p. A subject believing the propositions expressed by both S1 and S3 will then hold a set of beliefs with contradictory propositional content (though not necessarily believing a contradiction proper, given that belief isn't closed under conjunction introduction). One cannot, of course, derive a contradiction from S1 and S3 without some further premise (viz., that Heperus=Phosphorus). But this doesn’t imply that the propositions expressed by S1 and S3 aren’t contradictory. And that's enough to unseat No Contradiction.

(Thanks to John DePoe for bringing these issues to my attention in this post on Liar Paradoxes; in the comments, I reproduce some of these ideas)

What it is Like to be a Dualist?


Peter van Inwagen is one of several prominent analytic philosophers who underwent a conversion to Christianity well into his career. He describes what it was like to look back at his past unbelief as follows (this is from his wonderful autobiographical essay, "Quam Dilecta"):

I can remember pretty well one feature of this period that is particularly relevant to my topic: what it was like not to have any religious beliefs. That is, I can remember pretty clearly certain episodes of thought that are possible only for the secular mind, but the memory is not "sympathetic"; it is a sort of looking at the past from the outside. Here is an analogy. Suppose that you now love someone you once hated. You might well be able to remember an episode during which your hatred manifested itself--say, in the writing of a letter in which you said terrible things to that person. You might remember very clearly, for example, hesitating between two turns of phrase, and deciding that one of them was the more likely to wound, and choosing it on that account. But since you now love that person, and (presumably) cannot feel the way you felt when you hated, there is a good sense in which you cannot "remember what it was like" to write the letter. You are looking at your past from outside.

Something similar has happened to me in recent years. Not a religious conversion, but rather a conversion with respect to certain philosophical doctrines.

I once had many intuitions about mind and body, especially of the modal variety. It seemed clearly possible to me that I might exist and my body not. These intuitions pulled me toward substance dualism. But the more I thought about minds and bodies and the more I read about physicalism, the less sway these intuitions had on me.

Nowadays, I can't really muster those intuitions at all. They've vanished. I have nothing profound to say here. But I will remark on the oddness of this state. It feels strange to not clearly remember what it was like to believe the things I once did. All I can say, I suppose, is that it's weird, and that van Inwagen's remarks capture this feeling as well as any.

Conee's Newletter Entry


In the 2006 newsletter for the philosophy department at Rochester, Earl Conee has this to say:

My entries to our department's annual newsletter have been a lot alike. They have reported my having engaged in the usual mix of teaching, research, and service - with no details - and ended with the fact that I contributed the newsletter entry. Traditionalists, in whom anxiety may already have been provoked by these unusual preliminaries, will be relieved to find that my entry this year differs only in this preliminary way. My report is that I have engaged in the usual mix of work activities, culminating in this newsletter entry.