¹ Kvanvig, John, The Value of Knowledge and the Pursuit of Understanding (Cambridge: Cambridge University Press, 2003)CrossRefGoogle Scholar.

² This provisional formulation of the assumption is clarified and refined in §1.

³ Williams, Bernard, Descartes: The Project of Pure Enquiry (London: Penguin Books, 1978)Google Scholar. 2005 edition published by Routledge, London.

⁴ One also finds Platonic value problems formulated as normative questions: for example, it is asked why we ought to desire knowledge and not just true belief. Although I will not discuss normative formulations of Platonic value problems further in this paper, I think that we can also explain the tendency to formulate Platonic value problems in normative terms by appealing to the value assumption. To anticipate, if it is assumed that we desire knowledge rather than true belief because knowledge is more valuable than true belief, then it is natural to think that we ought to desire knowledge rather than true belief.

⁵ Millar, Alan, ‘Why Knowledge Matters’ Aristotelian Society Supplementary Volume, 85 (2011), 63–81, 64–65CrossRefGoogle Scholar.

⁶ ‘Through his representation of Socrates in Meno, Plato provides a way of articulating the problem’ (Ibid., 65).

⁷ According to oxforddictionaries.com, the traditional distinction between the verbs ‘enquire’ and ‘inquire’ is that the former describes any case of asking a question, whereas the latter refers exclusively to making formal investigations. Since the kind of enquiry of interest here isn't confined to formal investigations, ‘enquiry’ is the more appropriate term for my purposes.

⁸ Scientists have been able to determine the colours of some dinosaurs by analysing pigments contained in fossilised feathers. For example, Francis Gooding reports that the ‘fuzzy, birdlike Sinosauropteryx was ginger, with white and ginger bands along the length of a long, fluffy tail’. Gooding, Francis, ‘What lives and what dies?’ London Review of Books, 41 (2019), 11–13Google Scholar. Available at: https://www.lrb.co.uk/v41/n01/francisgooding/what-lives-and-what-dies [Accessed 6 Feb. 2019].

⁹ Much more could be said about the sense, if any, in which knowledge is the aim of enquiry, but I will not pursue this issue further here. The crucial point for present purposes is just that Millar formulates his problem both as a problem about the value of knowledge and as a problem about the aim of an activity.

¹⁰ In the present sense of ‘intermediate’, state S is intermediate between true belief and knowledge just in case (i) that one knows p entails one is in S, (ii) that one is in S doesn't entail that one knows p, (iii) that one is in S entails that one truly believes p, but (iv) that one truly believes p doesn't entail that one is in S. For the classic counterexamples to the claim that having a justified true belief that p is sufficient for knowing that p, see Gettier, Edmund, ‘Is Justified True Belief Knowledge?’ Analysis, 23 (1963) 121–123CrossRefGoogle Scholar.

¹¹ Another example of a Platonic value problem in this sense is what Pritchard calls the ‘tertiary value problem’. This is the problem of explaining ‘why knowledge is more valuable than that which falls short of knowledge not merely as a matter of degree but of kind’ (Duncan Pritchard & John Turri, ‘The Value of Knowledge’ The Stanford Encyclopedia of Philosophy (Winter 2017 Edition), Edward N. Zalta (ed.), https://plato.stanford.edu/archives/win2017/entries/knowledgevalue/. I won't discuss the tertiary value problem further here.

¹² Prichard and Turri's formulation of the secondary value problem differs from mine in two respects: (i) it involves the assumption that knowledge has parts, and that these parts include true belief and anything else necessary for knowledge; (ii) on Pritchard and Turri's understanding, the primary value problem falls within the scope of the secondary value problem. These differences are unimportant for present purposes.

¹³ Patrick Bondy, ‘Epistemic Value’, The Internet Encyclopedia of Philosophy, ISSN 2161-0002, https://www.iep.utm.edu/home/about/ [Accessed 6 Feb. 2019].

¹⁴ Once one is armed with the distinction between these different ways of formulating Platonic value problems, it isn't difficult to find other places where philosophers formulate value problems as questions about our desires, preferences or aims. For a particularly clear example of this tendency, see the opening paragraph of Section 1 of Jones, W.E., ‘Why do we value knowledge?’ American Philosophical Quarterly, 34 (1997), 423–440Google Scholar.

¹⁵ Fricker, Miranda, ‘The Value of Knowledge and the Test of Time’ Royal Institute of Philosophy Supplement, 64 (2009), 121–138, 121CrossRefGoogle Scholar.

¹⁶ Note that even if there is an ‘intuition’ that knowledge is more valuable than true belief-involving states falling short of knowledge that is independent of the value assumption, it remains significant that contrastive claims about the value of knowledge can be motivated by the value assumption, because the value assumption underpins certain objections to philosophical theories of the value of knowledge. For further discussion of this point, see Barney Walker, ‘Knowledge first, stability and value’ Synthese (2019a) https://doi.org/10.1007/s11229-019-02313-7.

¹⁷ An anonymous reviewer has queried whether my claim that Platonic value problems are based on the value assumption is intended to apply to all discussions of those problems, or only to those which formulate Platonic value problems as problems about our desires, preferences or aims. Let me be emphatically clear that I mean to make the former, stronger claim: in my view, even discussions that make no mention of issues about our desires, preferences and aims rest on the value assumption, because there is no reason to think that knowledge is more valuable than true belief independently of the value assumption. Some readers will be chary of this stronger claim, but such readers should still acknowledge the importance of distinguishing questions about our desires, preferences and aims from questions about value: even if Platonic value problems arise independently of the value assumption, it shouldn't be taken for granted that questions about the desires, preferences and aims of enquirers are to be answered by appealing to claims about the comparative value of knowledge.

¹⁸ An observation not all philosophers would accept. For example, some deny that enquiry aims at truth. For discussion, see Hookway, Christopher, ‘Fallibilism and the Aim of Inquiry’ Aristotelian Society Supplementary Volume, 81 (2007), 1–22CrossRefGoogle Scholar.

¹⁹ Williams's explanation occurs in chapter two of Descartes: The Project of Pure Enquiry, at pp. 37–45 of the original Penguin edition and at pp. 23–31 of the more recent Routledge edition. For ease of reference I give page references to both editions, starting with the older Penguin edition.

²⁰ ‘Granted that he [i.e. A] wants to arrive, and that he knows that he must arrive by enquiry, then he wants his enquiries to be reliable’ (40/26).

²¹ Note that Williams takes his question about enquiry – why does an enquirer who wants the truth want to know? – to be distinct from, and independent of, the Meno problem (38/24). He doesn't recognise the connection between Platonic value problems and questions about enquiry I defended in §§1–2. For this reason, his conception of the significance of his argument is quite different from the one assigned to it by the present discussion.

²² A point made by Raz, Joseph, ‘The Myth of Instrumental Rationality’ Journal of Ethics &Social Philosophy, 1 (2005), 2–28Google Scholar.

²³ The example of the espresso and the coffee machine is from Zagzebski, Linda, ‘The Search for the Source of Epistemic Good’ Metaphilosophy 34 (2003), 12–28CrossRefGoogle Scholar. Zagzebski used the example to make the point that just as a good coffee isn't improved for having been made by a reliable machine, so a true belief isn't improved for having been produced by a reliable belief-forming process – i.e. a belief-forming process that ‘reliably’ produces true beliefs. Thus, reliabilist theories of knowledge appear unable to solve the Meno problem. Since Williams's argument is concerned with the aim of enquiry, and not with the value of knowledge, Zagzebski's point is irrelevant to his argument. However, as I show, a variation on her example can be used to illustrate a point that undermines his argument. (Thanks to an anonymous referee for raising the issue of the relation of Zagzebski's point to Williams's argument.)

²⁴ Thanks to an anonymous referee for raising this point.

²⁵ One would have thought that the kinds of means an enquirer ‘must’ use to arrive at true beliefs will depend on the circumstances. If there is no knowledge-producing way of arriving at the truth on some question, but the benefits of having a true belief on that question are big and the costs of having a false belief are small, then it is plausible that a rational enquirer would be permitted – perhaps even obliged – to attempt to arrive at a true belief on that question using methods that don't suffice for knowledge.

²⁶ For an explanation of what would be odd about merely wanting a true belief about the answer to a question, see Barney Walker, ‘Enquiry, Supposition and Judgement’ (2019b) (unpublished manuscript). Central to my explanation is the idea that there is a kind of belief that one has only if one takes oneself to know, and that this is the kind of belief an enquirer is (minimally) interested in. Merely wanting to acquire a true belief of this kind would be odd because one would not have got what one wanted until one took oneself to know the truth.

²⁷ Again, see Barney Walker, ‘Enquiry, Supposition and Judgement’ (2019b) (unpublished manuscript).

²⁸ For very helpful comments, I would like to thank Tom Crowther, Hemdat Lerman, and Guy Longworth. Thanks also to two anonymous referees for critical suggestions that have clarified and sharpened my argument. Most of all, I am indebted to my PhD supervisor, Matt Soteriou, whose insights pervade the paper.