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Rationality and Inconsistent Beliefs

Powerful Essays
Many believe that there is something inherently irrational about accepting each element

of an inconsistent set of propositions. However, arguments for this doctrine seem lacking

other than those that appeal to the principle that the set of propositions that one rationally

accepts is (or should be) closed under logical consequences, or those that note that error

is made inevitable when one accepts an inconsistent set. After explaining why the

preceding sorts of arguments do not succeed, I consider a novel attempt by Keith Lehrer

to undermine the chief argument in favor of the claim that it can sometimes be rational to

accept inconsistent sets. For reasons that will be described, Lehrer’s argument fails.

I. Inconsistency and Deductive Closure

One cannot accept both that it is rational to accept inconsistent sets, and that the set of

propositions that one rationally accepts is closed under logical consequences. Together

these two propositions imply that it is rational to knowingly accept a logically

contradictory statement. But clearly it is not rational to knowingly accept a contradiction.

Thus, we must give up the principle that our rational acceptances are closed under logical

consequences, or else deny that it is ever rational to accept an inconsistent set. This

dilemma is sometimes appealed to as a premise in an argument for the claim that it is

irrational to accept each element of an inconsistent set. According to this argument, since

our rational acceptances are closed under logical consequences, it must be irrational to

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accept inconsistent sets. Versions of this argument have recently been offered by Ryan

(1996) and Evnine (1999).

The preceding sort of argum...

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conjunction is at least as informative as its least informative conjunct will permit us to

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construct an inconsistent set whose elements are both highly informative, and highly

probable. Moreover, any acceptable theory of informativeness will have the consequence

that a conjunction is always at least as informative as its least informative conjunct.

Works Cited

Evnine, Simon. (1999) ‘Believing Conjunctions’, Synthese 118, 210-227.

Lehrer, Keith. (1974): ‘Belief and Error’, in Gram, M.S., and Klemke, E.D., the

Ontological Turn, University of Iowa Press, 216-229.

Lehrer, Keith. (1990): ‘Reason and Consistency’, in his Metamind, Clarendon Press,

148-166.

Pollock, John. (1995) Cognitive Carpentry, MIT Press.

Ryan, Sharon. (1996) ‘The Epistemic Virtues of Consistency’, Synthese 109, 121-141.