Deductive Cogency, understanding, and acceptance


Deductive Cogency holds that the set of propositions towards which one has, or is prepared to have, a given type of propositional attitude should be consistent and closed under logical consequence. While there are many propositional attitudes that are not subject to this requirement, e.g. hoping and imagining, it is at least prima facie plausible that Deductive Cogency applies to the doxastic attitude involved in propositional knowledge, viz. (outright) belief. However, this thought is undermined by the well-known preface paradox, leading a number of philosophers to conclude that Deductive Cogency has at best a very limited role to play in our epistemic lives. I argue here that Deductive Cogency is still an important epistemic requirement, albeit not as a requirement on belief. Instead, building on a distinction between belief and acceptance introduced by Jonathan Cohen and recent developments in the epistemology of understanding, I propose that Deductive Cogency applies to the attitude of treating propositions as given in the context of attempting to understand a given phenomenon. I then argue that this simultaneously accounts for the plausibility of the considerations in favor of Deductive Cogency and avoids the problematic consequences of the preface paradox.

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  1. 1.

    Unless otherwise specified, I will use ‘belief’ to refer to this binary doxastic attitude, e.g. as opposed to the gradable doxastic attitude variously known as ‘degree of belief’, ‘level of confidence’, or ‘credence’ (See Sect. 2 for discussion).

  2. 2.

    A pro tanto requirement for something is a requirement that might be trumped or outweighed by other conflicting considerations. Importantly, however, the fact that pro tanto requirements may be overridden or outweighed in particular cases does not mean that they do not apply in those cases. In this respect, pro tanto requirements should be contrasted with prima facie requirements, where the latter is something that may merely appear to be a genuine requirement.

  3. 3.

    The usual rationale for weakening DC-B in this way is that people cannot be expected to recognize what deductive consequences follow from a set of propositions, and thus that the original requirement would be too demanding. In my view, this argument confuses the issue of whether a set of propositions is consistent and closed under logical consequence with the issue of whether an agent recognizes that the set has these logical properties. While it would be preposterous to require agents to recognize that a set of propositions they believe or are prepared to believe is consistent and closed under logical consequence, it is quite another thing to require that the set be consistent and closed under logical consequence. Admittedly, agents will then not generally be in a position to recognize whether they themselves obey DC-B, and thus whether their beliefs are indeed epistemically justified, but only very strong forms of epistemic internalism would claim otherwise [e.g. what Pryor (2001, p. 105) calls ‘Access Internalism’].

  4. 4.

    Roughly, the weakening allows agents to satisfy DC-B by failing to recognize, or even deliberately forgetting, logical connections between propositions. For example, someone who believes an inconsistent pair of propositions may satisfy DC-B in virtue of failing to recognize that the propositions are inconsistent. This has the absurd consequence that one may come to have justified beliefs by deliberately forgetting or neglecting to investigate logical connections between propositions.

  5. 5.

    Some philosophers (e.g. Radford 1966; Black 1971; Myers-Schulz and Schwitzgebel 2013) have rejected the consensus that knowing that P involves or entails believing that P. Accordingly, these philosophers may not be able to identify the sort of doxastic attitude that we will be concerned with in this paper as the doxastic attitude involved in knowing that P. However, even these philosophers can identify this attitude as the attitude involved in knowing that P according to the views they argue against, i.e. according to mainstream accounts of knowledge. Thus, for our purposes, it turns out not to matter whether knowledge actually involves belief—all that matters is that belief that P can be identified as the the doxastic attitude that is widely assumed to be involved in knowing that P.

  6. 6.

    I have put ‘explanation’ and ‘explanantia’ in scare quotes to indicate that it is usually taken for granted that explanations require true explanantia (see, e.g., Hempel and Oppenheim 1948, pp. 137–138). For a dissenting view, see Fraassen (1980, pp. 97–101).

  7. 7.

    Additionally, at least one version of the causal account of explanation explicitly requires the use of deductive logic to derive the explanandum from the propositions appealed to in the explanans, viz. Strevens’s (2004, 2008) kairetic account of explanation.

  8. 8.

    This argument is discussed in detail by Kaplan (1981b, 1995, 1996, 2013). See also Pollock (1983).

  9. 9.

    See Foley (1993, pp. 166–173), Weintraub (2001, pp. 446–448), and especially Christensen (2004, pp. 79–96).

  10. 10.

    It is also, misleadingly, sometimes referred to as ‘Bayesianism’—misleadingly because Probabilism does not entail Bayesianism’s core tenet, Bayesian Conditionalization. Bayesian Conditionalization is a diachronic requirement that goes well beyond Probabilism’s purely synchronic requirement that an agent’s credences at a time should satisfy the probability axioms.

  11. 11.

    See, for example, Kaplan (1995, 1996, 2013).

  12. 12.

    This is especially implausible if the value of the threshold t can vary, e.g. depending on one’s context or the stakes involved (a common assumption among proponents of the Lockean Thesis).

  13. 13.

    Notice that (2) is simply the negation of (1).

  14. 14.

    Similar points are often made using the lottery paradox (Kyburg 1961). However, I focus on the preface paradox here since lottery cases raise a number of issues orthogonal to our current concerns, e.g. whether purely statistical or chance-based evidence can justify one in believing a proposition (see, e.g., Nelkin 2000).

  15. 15.

    Kaplan (1996, p. 15) adopts an orthodox Bayesian view of levels of confidence in terms of betting dispositions, on which an agent’s level of confidence in a proposition P is r just in case the agent places a monetary value equal to \(\$r\) on a bet that pays \(\$1\) if P is true and \(\$0\) if P is false.

  16. 16.

    Kaplan (1995, 1996) presents the following theory of belief in the context of defending DC-B:

    You count as believing P just if, were your sole aim to assert the truth (as it pertains to P), and your only options were to assert that P, assert that \(\lnot P\) or make neither assertion, you would prefer to assert that P (Kaplan 1996, p. 109).

    It’s worth noting that in Kaplan’s most recent work on this topic, he suggests that ‘belief’ is not univocal and thus that the above definition captures only one sense of belief (Kaplan 2013, p. 13). Importantly, however, it is this sense of belief that Kaplan claims is subject to Deductive Cogency.

  17. 17.

    I am assuming here, as is standard, that there is a close connection between one’s level of confidence in P and one’s willingness to bet on P.

  18. 18.

    One might think that the intuitive connection between belief and levels of confidence is undermined by Hawthorne, Rothschild, and Spectre’s argument that belief is ‘weak’ in the sense that it is “compatible with having relatively little confidence” in the believed proposition (Hawthorne et al. 2016, p. 1393). However, on closer inspection, even they require that the believed proposition “be above some contextually determined threshold of likeliness” (Hawthorne et al. 2016, p. 1400). Since DC-B is incompatible with any confidence-threshold for belief, even proponents of the thesis that belief is ‘weak’ will be forced to reject DC-B.

  19. 19.

    As was famously argued by Williams (1973).

  20. 20.

    See, for example, Cohen (1986), DeRose (1992), Lewis (1996), Neta (2002), and the exchange between Cohen (2005) and Conee (2005).

  21. 21.

    A memorable illustration of this is provided by Andy Clark and David Chalmers’s “The extended mind” (1998), in which the following footnote was attached to the author’s names: “Authors are listed in the order of degree of belief in the central thesis” (Clark and Chalmers 1998, 7).

  22. 22.

    Thanks to an anonymous reviewer for pressing me to clarify the nature of acceptance in this respect.

  23. 23.

    Cohen (1992, pp. 27–33) himself suggests that acceptance is subject to something like Deductive Cogency, but the thesis Cohen defends is much stronger (and correspondingly less plausible) than the thesis defended here. For one thing, Cohen claims that acceptance is not only subject to the normative requirement that what one accepts should be consistent and closed under logical consequence, but he further makes the metaphysical claim that acceptance of (knowingly) inconsistent propositions is impossible and that the acceptance of a set of propositions involves accepting their logical consequences. No claim of the latter (metaphysical) sort is made here. Furthermore, Cohen suggests that Deductive Cogency applies to acceptance in any context, whereas I argue in this section that we must restrict the contexts in which acceptance would be subject to Deductive Cogency. This is an important difference since the solution to the preface paradox that I propose below is, as a result, not available to Cohen. Instead, Cohen is forced into a Kaplan-style response to the preface paradox on which an author cannot rationally assert in the preface of her book that she has made a mistake in the body of the book (see Cohen 1992, p. 36).

  24. 24.

    Others have argued that understanding and explanation are not so closely related, and that various non-explanatory abilities are also involved in understanding (see, e.g., de Regt and Dieks 2005; Lipton 2009; Hills 2016; de Regt and Gijsbers 2016; Dellsén 2016a), although most if not all authors argue that explanation is involved in understanding in some way or another (for a possible exception, see Wilkenfeld 2013).

  25. 25.

    This example is modelled after the one discussed by Dellsén (2016b, pp. 11–13).

  26. 26.

    Again, this is not to deny that understanding and belief often go together. The point here is not that understanding is incompatible with belief, but that understanding is compatible with lack of belief, at least in principle.

  27. 27.

    ‘Noetic’ from the Greek word ‘nous’, which is often translated into English as ‘understanding’.

  28. 28.

    Elgin (2004) defines a somewhat similar notion of ‘cognitive acceptance’ with reference to understanding: “To cognitively accept that p, is to take it that p’s divergence from truth, if any, does not matter cognitively”, where a consideration is cognitive in her sense “to the extent that it figures in an understanding of how things are” (Elgin 2004, p. 120). However, this definition relies on Elgin’s claim that genuine understanding can be based on falsehoods (Elgin 2004, 2009), which is highly contentious (see, e.g. Kvanvig 2009a; Wilkenfeld 2015).

  29. 29.

    It’s worth noting that the first three clarifications of DC-B in Sect. 2 apply to DC-NA as well. Let me especially emphasize that DC-NA should, like DC-B, also be understood as a normative epistemic requirement on perfectly rational agents—or, alternatively, as a pro tanto epistemic requirement that would, all other things being equal, improve an agent’s epistemic status. Of course, such a requirement may easily be outweighed by other non-epistemic considerations, or indeed turn out to be impossible to satisfy due to one’s cognitive limitations. Accordingly, there will be many situations in which agents should arguably violate DC-NA all things considered.

  30. 30.

    Those who resist my arguments for taking understanding not to involve belief might wonder whether a requirement similar to DC-NA would hold for the belief that they claim is involved in understanding. To see what this proposal amounts to, let us define “noetic belief” as the belief that would be involved in understanding, such that one noetically believes P relative to some target phenomenon X just in case one’s belief that P figures in one’s explanations of aspects of X. This allows us to define a Deductive Cogency requirement for noetic belief:

    • Deductive Cogency for Noetic Belief (DC-NB): The set of propositions one noetically believes or is prepared to noetically believe, relative to some target phenomenon X, should be consistent and closed under logical consequence.

    However, it should be clear that DC-NB is problematic for a similar reason as DC-B itself. Suppose that understanding some very complex phenomenon X involves noetically believing a large number of independent propositions \(P_1,\ldots ,P_n\). By DC-NB, then, any agent who understands X should (be prepared to) noetically believe the conjunction of these propositions, \((P_1 \wedge \ldots \wedge P_n)\). Since this conjunction can be arbitrarily improbable given a high enough number n of propositions, we have that DC-NB conflicts with any probabilistic restriction on (noetic) belief. This is highly implausible for the same reasons as given in response to Kaplan at the end of Sect. 3.2.

  31. 31.

    Kvanvig elaborates on this in a later piece:

    When the question is whether one knows, the issues that are foremost in our minds are issues about evidence, reliability, reasons for belief, and, perhaps most importantly, non-accidentality regarding the connection between our grounds for belief and the truth of the belief. When the question is whether one has understanding, the issues that are foremost in our minds are issues about the extent of our grasp of the structural relationships (e.g. logical, probabilistic, and explanatory relationships) between the central items of information regarding which the question of understanding arises. (Kvanvig 2009b, p. 97)

  32. 32.

    Similar views are expressed by Cooper (1994), Zagzebski (2001), Pritchard (2009), Grimm (2011), and Bengson (2015).

  33. 33.

    In particular, one might wonder whether Deductive Cogency applies to acceptance in other intellectual contexts beyond those in which one’s aim is to understanding something, and I have no argument for there being no contexts of that kind. This idea does not conflict with DC-NA, which does not in any way deny that other types of propositional attitudes may also be subject to Deductive Cogency.

  34. 34.

    A well-known proponent of this view is Jeffrey (1956, 1968, 1970). See also Maher (1986) for a particularly lucid defense of the view.

  35. 35.

    This brings to mind the widely discussed incompatibility of Quantum Mechanics (QM) and General Relativity (GR). Physicists seem happy to accept each theory in the context of explaining, respectively, purely quantum phenomena (e.g. the emission spectrum of hydrogen atoms) and purely relativistic phenomena (e.g. the formation of black holes). This practice accords with DC-NA in so far as the quantum and relativistic phenomena are genuinely distinct phenomena. However, this cannot be the end of the story since physicists clearly view the incompatibility of QM and GR as a reason to seek a new, unified theory to replace them both, e.g. String Theory. Interestingly, DC-NA accounts for that fact as well, since there are many phenomena that physicists would like to understand that cannot be described as either ‘purely quantum’ or ‘purely relativisitic’, e.g. the ‘smoothness’ of space-time (GR assumes that space is continuous, while QM requires it to be discrete). In so far as physicists are interested in understanding ‘mixed’ phenomena of this kind, DC-NA requires that they seek compatible or unified theories to which they can appeal in their explanations.


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I am grateful for very helpful written comments on earlier drafts of this paper from Christoph Baumberger, Michael Stuart, and two anonymous referees for this journal. For constructive verbal feedback, I would like to thank the audiences at the 2016 Meeting of the European Epistemology Network and the 2016 Joint Sessions of the Aristotelian and Mind Societies.

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Dellsén, F. Deductive Cogency, understanding, and acceptance. Synthese 195, 3121–3141 (2018).

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  • Deductive consistency
  • Deductive closure
  • The preface paradox
  • Belief versus acceptance
  • Epistemology of understanding