In defence of single-premise closure
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It’s often thought that the phenomenon of risk aggregation poses a problem for multi-premise closure but not for single-premise closure (either with respect to knowledge or with respect to justified belief). But recently, Lasonen-Aarnio and Schechter have challenged this thought. Lasonen-Aarnio argues that, insofar as risk aggregation poses a problem for multi-premise closure, it poses a similar problem for single-premise closure. For she thinks that, there being such a thing as deductive risk, risk may aggregate over a single premise and the deduction itself. Schechter argues that single-premise closure succumbs to risk aggregation outright. For he thinks that there could be a long sequence of competent single-premise deductions such that, even though we are justified in believing the initial premise of the sequence, intutively, we are not justified in believing the final conclusion. This intuition, Schechter thinks, vitiates single-premise closure. In this paper, I defend single-premise closure against the arguments offered by Lasonen-Aarnio and Schechter.
KeywordsSingle-premise closure Multi-premise closure Deduction Knowledge Justification Reasoning
Thanks to an anonymous reviewer and to the audience at the 2015 Australasian Association of Philosophy Conference for valuable comments. I’ve also benefitted from discussion with Michael Pelczar, Ben Blumson, and the honours students in my epistemology class in 2015. Thanks, in particular, to Bernadette Chin for feedback on a draft of the paper.
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