Believing Conjunctions

• Published in: Synthese (Dordrecht) 1999-01, Vol.118 (2), p.201-227
• Main Author: Evnine, Simon J.
• Format: Article
• Language: English
• Subjects: Astronomical objects; Belief; Conjunctions; Contradictories; Epistemology; Epistemology. Philosophy of science. Theory of knowledge; Essays; Lotteries; Paradoxes; Philosophy; Priests; Rationality; Reason; Spiritual belief systems; Truth
• ISSN: 0039-7857; 1573-0964
• DOI: 10.1023/A:1005114419965

Without evaluating them all here, let me just state my own preferred response.12 I believe that the problem comes in the initial move, the claim that it is rational to have the belief that ticket n will not win, for all n. This move is defended by Foley who says, in effect, that by increasing the number of tickets used in the example, we can raise the probability that a given ticket will not win to a point where it is greater than the probability that any given empirical belief is true. [...]in a lottery with 20 million tickets, the probability that ticket n will not win, for any n, is 20 million to 1, much better odds than we would give to an uncontroversial example of what might be a rational belief under certain circumstances, such as that your car is not being stolen from your garage at this very moment.This argument presupposes an acceptance rule that makes a beliefs rationality contingent only on the probability of its truth.13 But this ignoresBELIEVING CONJUNCTIONS 207the impact of the existence of other beliefs, except as they factor in to the probability calculations for the given belief. Since for any exponential function and any polynomial function, there will come an argument past which the value of the exponential function will exceed that of the polynomial function, algorithms the execution time of which increases exponentially are considered inherently inefficient.20 Checking for consistency between different beliefs is a task for which the execution time increases exponentially as a function of the number of beliefs being checked. The kinds of cases which James thought called for this bold policy would include just the kinds of areas where we are likely to be tempted by hypothesizing subsystems of belief religious faith, being in love, and so on. Since Cliffords principle requires the rational influence on each belief of all other relevant beliefs, James denial of it can be seen as a claim that people should, in some cases, isolate beliefs from the rational influence of other beliefs that may be relevant as forms of evidence. [...]it is possible to say that a closure condition in an RTBA is a priori implausible.24 That a conjunctive belief requires some mental act of bringing together the two conjuncts is argued for by Armstrong 1973, p. 107.25 See Routley and Routley 1975, pp. 21015 and Stalnaker 1984, pp. 824.26 The approaches to belief evinced in Davidson 1984, Dennett 1987, and Stalnaker 1984 would all be conducive to seeing (Conj) in t