Finite Minds and Open Minds

Abstract

One of the most persistent complaints about Peter Klein’s infinitism involves the finite mind objection: given that we are finite, how can we ever handle an infinite series of reasons? Klein’s answer has been that we need not actually produce an infinite series; it is enough that such a series be available to us. In this chapter, a different reply is presented through the reconstruction of epistemic justification as a trade-off. In acting as responsible agents, we are striking a balance between the number of reasons that we can handle and the level of precision that we want our beliefs to have. If we are unable or unwilling to manage a large number of reasons, then we have to pay the price in terms of justificatory inexactitude and thereby of accepting relatively untrustworthy beliefs. As well as being intuitively attractive, this idea of a trade-off is warranted by the mathematics of epistemic justification, understood as involving probabilistic relations.