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Knowledge and Approximate Knowledge

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Abstract

Traditionally, epistemologists have held that only truth-related factors matter in the question of whether a subject can be said to know a proposition. Various philosophers have recently departed from this doctrine by claiming that the answer to this question also depends on practical concerns. They take this move to be warranted by the fact that people’s knowledge attributions appear sensitive to contextual variation, in particular variation due to differing stakes. This paper proposes an alternative explanation of the aforementioned fact, one that allows us to stick to the orthodoxy. The alternative applies the conceptual spaces approach to the concept of knowledge. With knowledge conceived of spatially, the variability in knowledge attributions follows from recent work on identity, according to which our standards for judging things (including concepts) to be identical are context-dependent. On the proposal to be made, it depends on what is at stake in a context whether it is worth distinguishing between knowing and being at least close to knowing.

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Notes

  1. Bayesian decision theory is sometimes criticized on the grounds that it is highly idealized. But, first, the same is true for virtually any scientific theory. Second, there is a promising ongoing de-idealization program; see in particular Weirich’s work in this vein (e.g., (2004)).

  2. See Unger (1975) and, for a more recent treatment, Davis (2007). Lewis (1979) also observes the context-dependence of standards of precision, but for him these have semantic rather than (merely) pragmatic significance. Lewis (1996) is naturally read as developing this idea into a contextualist semantics of “knows.”

  3. See also Kennedy (2007:24 f) on the relation between standards of precision and what is at stake in a context.

  4. See, e.g., Hetherington (2012), Starmans and Friedman (2012), and Turri (2012). See Nagel et al. (2013) and Starmans and Friedman (2013) for worthwhile discussion.

  5. At least this is so on all of the quantitative measures of inductive and abductive strength that one finds in the literature.

  6. See Oddie (2007) for an overview of the literature and for some examples of measures of truth-closeness. Authors concerned with vagueness have also proposed accounts in which truth admits of degrees. See, for instance, Edgington (1997) and Smith (2008).

  7. As an anonymous referee rightly reminded us, knowledge is generally taken to be factive. Whether this makes knowledge incompatible with a non-maximal degree of truth is not so clear, however. For instance, Edgington (1997) can be read as suggesting that a degree of truth close to the maximum may be enough for qualifying as true in a categorical sense. Also, Cobreros et al.’s (2012) distinction between strict and tolerant truth, where the latter is defined in terms of similarity to classical truth, may help to account for our intuition that knowledge is factive even if knowledge is compatible with a non-maximal degree of truth: knowledge may be factive in the sense that it requires tolerant truth, but no strict truth.

  8. If you believe that it is 323.992 m high, can you know that it is 323.992 m high if it is 323.9924 m high? And so on.

  9. If geometrically representing knowledge requires more than three dimensions, then the question is to be asked in terms of hypercubes, hyperplanes, etc.

  10. We have defined the utilities such that they are always positive. This choice is inconsequential: only the relative utilities matter, since they determine the differences between expected utilities of various actions (i.e., the absolute utilities are on an interval scale rather than a ratio scale).

  11. In the example in the text above, we had that x L  = 2, x H  = 20, and y = 1.

  12. It should be easy to see how this schematic situation fits both the Bank Cases and the Airport Cases. For the Bank Cases, let h 1 be the hypothesis that the bank is open on Saturday, and let \(h_2 = \neg h_1\). Furthermore, let a 1 be the option of going to the bank on Friday; a 2 the option of going to the bank on Saturday; x the utility of going to the bank while it is open; and y the utility of avoiding the long queues on Friday. For the Airport Cases, let h 1 be the hypothesis that the intended flight has a layover in Chicago, with again \(h_2 = \neg h_1\). Let a 1 be the option of contacting the airline and rescheduling the flight if necessary; a 2 the option of taking the intended flight; x the utility of having a layover in Chicago; and y the utility of avoiding the hassle of contacting the airline.

  13. Applied to the Bank Cases: if the agent is completely certain that the bank will be closed on Saturday, she will go there on Friday, which is her only option to achieve her main goal.

  14. Applied to the Bank Cases again: if the agent is completely certain that the bank will be open on Saturday, she will go there on Saturday, which allows her to achieve her main goal while avoiding the queues on Friday.

  15. As an anonymous referee observed, variants of DeRose’s Bank Cases could be used to argue for the context-sensitivity of attributions of certainty. The referee also observed that our decision-theoretic explanation of the context-sensitivity of knowledge attributions would generalize swiftly to an explanation of the context-sensitivity of certainty attributions.

  16. We are greatly indebted to René van Woudenberg and to an anonymous referee for this journal for very helpful comments on previous versions of this paper.

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Authors and Affiliations

  1. Faculty of Philosophy, VU University, Amsterdam, The Netherlands

    Lieven Decock

  2. Faculty of Philosophy, University of Groningen, Groningen, The Netherlands

    Igor Douven & Sylvia Wenmackers

  3. Institute of Philosophy, University of Leuven, Leuven, Belgium

    Christoph Kelp

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  1. Lieven Decock
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  2. Igor Douven
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  4. Sylvia Wenmackers
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Correspondence to Igor Douven.

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Decock, L., Douven, I., Kelp, C. et al. Knowledge and Approximate Knowledge. Erkenn 79 (Suppl 6), 1129–1150 (2014). https://doi.org/10.1007/s10670-013-9544-2

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