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The Utility of Knowledge

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Abstract

Recent epistemology has introduced a new criterion of adequacy for analyses of knowledge: such an analysis, to be adequate, must be compatible with the common view that knowledge is better than true belief. One account which is widely thought to fail this test is reliabilism, according to which, roughly, knowledge is true belief formed by a reliable process. Reliabilism fails, so the argument goes, because of the ‘swamping problem’. In brief, provided a belief is true, we do not care whether or not it was formed by a reliable process. The value of reliability is ‘swamped’ by the value of truth: truth combined with reliability is no better than truth alone. This paper approaches these issues from the perspective of decision theory. It argues that the ‘swamping effect’ involves a sort of information-sensitivity that is well modelled decision-theoretically. It then employs this modelling to investigate a strategy, proposed by Goldman and Olsson, for saving reliabilism from the swamp, the so-called ‘conditional probability solution’. It concludes that the strategy is only partially successful.

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Article 22 July 2014

Jeffrey Sanford Russell, John Hawthorne & Lara Buchak

Notes

  1. For a helpful overview of the topic, see Pritchard (2007); the term ‘extra value of knowledge problem’, often shortened to ‘EVOK’, is from Goldman and Olsson (2009).

  2. The example is originally due to Zagzebski (2003, p. 13).

  3. On signatory value, see Bradley (1998).

  4. For simplicity, I elide the distinction between preferences and value-judgements. If a person may prefer X to Y without thinking X better than Y, the difference seems unimportant here.

  5. I use ‘V’ as in ‘veridical’, instead of ‘T’ as in ‘true’, to save confusion with ‘\(\top\)’, the tautological proposition, on which more below.

  6. So the set of all propositions is \(\mathcal{P}(\mathcal{P}(L)^2), \) where \(\mathcal{P}(X)\) is the power set of X.

  7. Note, since I’ve assumed that the total number of Bea’s beliefs is fixed, this goal, maximising the expected number of true beliefs, is equivalent to the goal of minimising the expected number of false beliefs.

  8. The prior expectation is the expectation conditional on \(\top\).

  9. See e.g. Jeffrey (1983, pp. 81–82).

  10. Given parallel assumptions (i.e. by simply transposing the subscripts ‘1’ and ‘2’), veritism would also imply that u(V 2) < u(K 2).

  11. Cf. Goldman and Olsson (2009, p. 31).

  12. See e.g. Hodges and Lehmann (1970, p. 151.)

References

  • Bradley, B. (1998). Extrinsic value. Philosophical studies, 91, 109–126.

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Acknowledgment

I would like to thank J. Adam Carter and Duncan Pritchard for helpful discussions on the topic of this article.

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Authors and Affiliations

  1. Department of Philosophy, University of Edinburgh, Dugald Stewart Building, 3 Charles Street, Edinburgh, EH8 9AD, UK

    Campbell Brown

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  1. Campbell Brown
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Correspondence to Campbell Brown.

Appendix

Appendix

In this “Appendix” I briefly explain why the expected number of true beliefs conditional on X is equal to

$$ \sum_{i=1}^n p(V_i|X). $$

First, for any set of beliefs A, let E X (A) be the expected number of true beliefs in A conditional on X. Then for sets of beliefs A and B, if \(A \cap B = \emptyset, E_X(A \cup B) = E_X(A) + E_X(B), \) this following from the ‘additive law of expectation’.Footnote 12 So

$$ E_X(L) = \sum_{i=1}^n E_X(\{l_i\}). $$

And \(E_X(\{l_i\}) = p(V_i|X). \) So

$$ E_X(L) = \sum_{i=1}^n p(V_i|X). $$

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Brown, C. The Utility of Knowledge. Erkenn 77, 155–165 (2012). https://doi.org/10.1007/s10670-011-9296-9

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