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Knowledge in the face of conspiracy conditionals


A plausible principle about the felicitous use of indicative conditionals says that there is something strange about asserting an indicative conditional when you know whether its antecedent is true. But in most contexts there is nothing strange at all about asserting indicative conditionals like ‘If Oswald didn’t shoot Kennedy, then someone else did’. This paper argues that the only compelling explanation of these facts requires the resources of contextualism about knowledge.

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  1. 1.

    Given the potential context-sensitivity of the expressions \(\ulcorner \)S\(\urcorner \) and \(\ulcorner \)p\(\urcorner \), this condition isn’t quite right. More accurate would be something like: If \(\ulcorner \)S knows that p\(\urcorner \) is true in one context c, then it is true in every context \(c'\) that assigns the same semantic value to \(\ulcorner \)S\(\urcorner \) and \(\ulcorner \)p\(\urcorner \) as c assigns them. But I will stick with the simpler construal in the main text for the sake of readability.

  2. 2.

    The point would be cleaner but more cumbersome to state if (\(\hbox {P}_1\))–(\(\hbox {P}_3\)) were made tenseless.

  3. 3.

    Some readers may wonder why the consequent of ignorance is stated meta-linguistically. (If you don’t wonder about this, I suggest you skip this footnote.) The reason is this. Assuming ‘knows’ is context-sensitive, there is a question of how to interpret slogans like \(\ulcorner \)If S knows whether p, then S shouldn’t assert ‘If p, q’\(\urcorner \). They can either be interpreted as universal generalizations over all contexts, or they can be interpreted as claims about specific contexts. If they’re interpreted as universal generalizations over all contexts, then the principle we’re working with is:

    In every context c: \(\ulcorner \)If S knows whether p, then S shouldn’t assert ‘If p, q’\(\urcorner \) expresses a truth in c.

    Now suppose \(\ulcorner \)S shouldn’t assert ‘If p, q’\(\urcorner \) is context-insensitive, and thus that it either expresses a truth in every context or a falsehood in every context. Given that \(\ulcorner \)If S knows whether p, then S shouldn’t assert ‘If p, q’\(\urcorner \) expresses a truth in every context (by hypothesis), it follows that if there is a context in which \(\ulcorner \)S knows whether p\(\urcorner \) expresses a truth, then in every context \(\ulcorner \)S shouldn’t assert ‘If p, q’\(\urcorner \) must express a truth. But this is exactly what we’re going to want to deny, for we’re going to see evidence that the appropriateness of the assertion of a indicative conditionals varies across contexts. So if we want to think of the slogan underlying ignorance as a universal generalization over all contexts, we need both its antecedent and consequent to be relativized to contexts. Hence the doubly meta-linguistic statement of the principle.

    Of course there remains the question of why we’re treating the slogan underlying ignorance as a universal generalization over all contexts. Why not instead think the true principle is something like the following?

    If \(\ulcorner \)S knows whether p\(\urcorner \) expresses a truth in S’s context, then S shouldn’t assert ‘If p, q’.

    I lack the space to explain fully why I find this implementation inadequate, but the basic worry is this (see also Worsnip 2017 for similar discussion). In making the facts about the appropriateness of the assertion of S’s assertion of indicative conditional depend invariantly on features of S’s context, we predict that speeches like the following should be acceptable:


    For suppose S is in a context in which she would speak truly in asserting ‘I don’t know whether p’, but that we are in a context in which we would speak truly in asserting ‘S knows perfectly well whether p’ (maybe S in the grip of a skeptical puzzle and we aren’t). Then for all the present version of ignorance is concerned, (2) should be fine. But as we will see shortly, there is good reason to think that speeches like (2) are context-invariantly problematic. So I think the only contextualist-friendly way of interpreting ignorance is as a principle that establishes a penumbral connection between the truth of sentences about knowledge and the truth of sentences about whether certain indicative conditionals are appropriate to assert. As far as I can see, the only principle capable of doing this is ignorance in its doubly meta-linguistic form. (Thanks to an anonymous reviewer for pressing me to say more about this issue.)

  4. 4.

    For some arguments in favor of there being a connection between knowledge and assertion along the lines of these norms (though not necessarily in their exact form), see (e.g.) Unger (1975, ch. 6), Williamson (2000, ch. 11), DeRose (2002), Benton (2016), Turri (2016). See also Worsnip (2017) and the citations therein for a sense of the larger debate around knowledge accounts of assertion, with particular attention to its relationship to epistemic contextualism.

  5. 5.

    Given a contextualist account of ‘knows’, this way of making the point is somewhat sloppy with use and mention. But the basic point is just that when someone asserts a conditional like (2) or (3), a natural thought to go through your head will be along the lines of ‘Does that person not know whether they had a bagel for breakfast this morning?’.

  6. 6.

    We will revisit this point in some detail in Sect. 6.

  7. 7.

    Though see the discussion of so-called ‘echoing’ and ‘concessive’ uses of the indicative conditional in Sect. 3. Also see Dorst (2019a) for some evidence to the contrary.

  8. 8.

    A similar line of reasoning suggests that it should be generally impermissible to assert \(\ulcorner \)p or q\(\urcorner \) when either disjunct is known, as well as \(\ulcorner \)If p, q\(\urcorner \) when the consequent q is known. I think these generalizations are basically as good as the one ignorance is meant to capture, but the class of exception cases is messier for them than it is for ignorance.

  9. 9.

    A note about terminology: I distinguish indicative conditionals from counterfactual conditionals wholly in terms of their semantic properties, rather than (e.g.) their syntactic properties. Putting things as roughly as our purposes call for: an indicative conditional is a conditional whose semantics concerns what is happening at a contextually determined set of epistemic possibilities, while a counterfactual conditional is a conditional whose semantics concerns what is happening at a contextually determined set of (sometimes epistemically impossible) metaphysical possibilities. Nothing in this distinction rules out the existence of conditionals with indicative marking (e.g., \(\ulcorner \)If p, q\(\urcorner \)) whose semantics is counterfactual, and likewise conditionals with subjunctive marking (e.g., \(\ulcorner \)If it were/had been that p, it would be/would have been that q\(\urcorner \)) whose semantics is indicative. See, e.g., von Fintel (1999), Khoo (2015) and the citations therein for further discussion.

  10. 10.

    See, e.g., Stalnaker (1975), von Fintel (1999), Gillies (2010), Leahy (2011), Khoo (2015).

  11. 11.

    I get the ‘echoing’ label from Dorr and Hawthorne (2013, pp. 890–891).

  12. 12.

    As an anonymous reviewer points out, one who knows that \(\lnot \)p might want to assert the indicative conditional \(\ulcorner \)If p, q\(\urcorner \) as a way of indicating that if one were to come to believe p, one would also believe q. But one needn’t be in a context in which it would be appropriate to assert \(\ulcorner \lnot \)q; so \(\lnot \)p\(\urcorner \) to do this. The aforementioned test thus only provides a sufficient condition for a conditional’s being used in an echoic manner.

  13. 13.

    There are two other categories of conditionals whose uses are typically non-canonical, but whose discussion I omit from the main text given their failure to pose any clear problem for ignorance: biscuit conditionals and donkey conditionals. Examples of biscuit conditionals include:


    It should be clear that biscuit conditionals are unlike ordinary indicative conditionals, at least on the latter’s standard uses. But regardless of whether or not they are canonical, they are not counterexamples to ignorance. It is just as strange to assert a biscuit when one knows whether its antecedent is true as it is to assert an ordinary indicative when one knows whether its antecedent is true. (See, e.g., DeRose and Grandy (1999) and Predelli (2009) for further discussion of biscuits.) Examples of donkey conditionals include:


    Mysteries abound with donkey conditionals—see, e.g., King and Lewis (2017) for an introduction. I will not pay much attention to them here, as it is not obvious they even count as indicative conditionals in the sense I am interested in (see footnote 9 above). But even if they are genuine indicatives, then as far I can tell they are just echoing conditionals, and so what goes for those goes for these. But even if that’s wrong, it should be clear that the conditionals of interest to this paper (to be introduced in Sect. 4) are relevantly dissimilar to conditionals like (16) and (17).

  14. 14.

    I should note that it would work just as well for our purposes if the primary conversational norm were “Assert the strongest relevant thing you know to be true and can expect your audience to believe you know to be true”. In that case concessive uses of the indicative conditional would plausibly count as canonical, as their use would be responsive to the norm’s second conjunct. But dialectically speaking this would just be a reshuffling of labels. As we will see in Sect. 5, the uses of indicative conditionals that are of central interest to this paper are not invariably concessive uses, and so whether those uses count as canonical or non-canonical is irrelevant to the truth of ignorance (and, by extension, the truth of invariatism about knowledge).

  15. 15.

    The only exception I know of is Gillies (2004, p. 585), who mentions it once and then does not return to the issue.

  16. 16.

    One philosophical case I find particularly sharp draws on some recent papers (cited below) on epistemic puzzles concerning unobserved tosses of fair coins. Suppose you know a fair coin is about to be flipped 1000 times. Supposing the distribution of heads/tails in fact ends up being relatively normal, do you know prior to the coin’s being flipped that it won’t land heads all 1000 times? There are persuasive arguments suggesting that the moderate invariantist must say ‘Yes’—see, e.g., Bacon (2014, §1) and Dorr et al. (2014). Supposing these arguments are sound, it follows that these indicatives are conspiracy conditionals:

  17. 17.

    It is to be implicit through this section that unless stated otherwise we are restricting attention to canonical uses of the indicative conditional.

  18. 18.

    Since it is possible to shift contexts mid-sentence, we should expect it to be possible to hear good readings of (31)–(33). But this is no threat to coordination, for there are also good readings of sentences like (34) and (35):

  19. 19.

    The vague characterization just given suffices for present purposes, but see, e.g., Stalnaker (1999, 2002) and the citations therein for explication.

  20. 20.

    It’s not at all clear it works for (36)–(37), but the objection I’m about to make to its treatment of (2) will get at the same fundamental problem in a simpler way.

  21. 21.

    Supposing we want the difference between Gettiered and non-Gettiered subjects to count as “purely epistemic” (which I take to be the presumptive view), facts about the etiology of S’s belief and perhaps the hostility of her environment will probably have to factor in too. But for our purposes it is safe to ignore these compilcations.

  22. 22.

    For just a small sampling of the literature on this phenomenon, with a particular focus on work that offers ordinary language evidence in favor of alternatives to moderate and skeptical invariantism, see, e.g., Austin (1946), Cohen (1986), Lewis (1996), Cohen (1999), DeRose (1992, 1995, 2002), Hawthorne (2004), Schaffer (2005b, 2007), Stanley (2005), Schaffer and Szabo (2014).

  23. 23.

    The literature here is truly massive. See, e.g., Rysiew (2001), Fantl and McGrath (2002, 2009), Hawthorne (2004, §4.2), Bach (2005), Schaffer (2005a), Williamson (2005), Stanley (2005), Adler (2006), McGrath (2007), Nagel (2008, 2010b), May et al. (2010), Reed (2010), Weatherson (2012), Buckwalter and Schaffer (2015), and Roeber (2018). Note that many of these authors—in particular those who defend subject-sensitive accounts of knowledge—build certain aspects of X into the semantics of ‘knows’ itself. As we will see in Sect. 8, whether X goes into one’s semantics or one’s error theory makes no difference to the problem posed by conspiracy conditionals.

  24. 24.

    In the case of first-personal knowledge ascriptions \(A = S\).

  25. 25.

    Nagel (2010b) offers an extended criticism of Hawthorne and Williamson’s use of the availability heuristic in their error theories. Her preferred account appeals to the phenomenon of ‘epistemic egocentricism’, whereby people fail to suppress privileged information (i.e. what they know or are concerned with) in evaluating the judgments of others. The complaints about Williamson and Hawthorne’s error theories will apply just as much to hers.

  26. 26.

    To borrow from an example of Hawthorne’s (2004, p. 64), just because I’m watching The Matrix doesn’t mean it will be appropriate to assert something like:

  27. 27.

    See footnote 16.

  28. 28.

    Note too that even if we had a view on which the mere consideration of possibilities of error (whether vividly or not) could be enough to cloud our judgments about knowledge—and mind you this would put a lot of strain on the “error” part of the error theory—I doubt that even this is always involved in the circumstances in which ordinary speakers assert conspiracy conditionals. For example: if after asserting (44) you were to ask me ‘How might you acquire enough money for an African safari?’ I could well reply ‘I have absolutely no idea. It may well be impossible. But if I somehow manage to do it I’m going to go on one’. It is hard to see such speeches as being in keeping with the kinds of ideas suggested by Williamson, Hawthorne, and Lewis.

  29. 29.

    Thanks to an anonymous reviewer for pressing me to consider this response.

  30. 30.

    Although we don’t know much about mechanism Y, we do know from the previous section that Y \(\ne \) X—i.e., combinations of facts about stakes and salience.

  31. 31.

    The facts about S’s environment can count as purely epistemic factor too, but obviously those are not what shift in accordance with our judgments about the assertability of conspiracy conditionals.

  32. 32.

    Cf. Nagel (2010a), who defends a similar line on behalf of the moderate invariantist in response to challenges from our judgments about knowledge ascriptions in high-stakes situations.

  33. 33.

    For further evidence that it is implausible that speakers who assert conspiracy conditionals in the canonical way fail to have beliefs about the truth of those conditionals’ antecedents, see, e.g., Hawthorne et al. (2016), Dorst (2019b), Rothschild (2020).

  34. 34.

    For more on full belief see, e.g., Hintikka (1962), Stalnaker (1984), Williamson (2000), Buchak (2014), Greco (2015).

  35. 35.

    See, e.g., Radford (1966), Stanley (2008), Beddor (2020).

  36. 36.

    As I will use the label ‘sensitive invariantism’, one who believes knowledge is subject to “pragmatic encroachment” (and isn’t a contextualist) is a sensitive invariantist. See Kim (2017) for a helpful overview.

  37. 37.

    See, e.g., issues related to “semantic blindness” discussed by Schiffer (1996), Williamson (2005), Greenough and Kindermann (2017).

  38. 38.

    Of course it is open to the sensitive invariantist to modify her account of the non-epistemic factors to which knowledge is sensitive. Perhaps she can claim that the presence of Y factors (introduced in Sect. 8), like the presence of X factors, destroys knowledge. What are the Y factors? Again, it’s not all together clear. But so long as there is some identifiable psychological feature responsible for S’s taking herself to be in a position to canonically assert a conspiracy conditional, then it’s always a theoretical option to take the absence of that psychological feature to be a non-epistemic precondition on knowledge.

    Call this view extra-sensitive invariantism. Although I don’t have a knockdown argument against it, I think there are at least two reasons to be reluctant to adopt it. First, extra-sensitive invariantism seems to me mysterious in a way that traditional forms of sensitive invariantism are not. Given the intuitive connections between knowledge, action, and deliberation, it’s not so surprising that non-epistemic factors like what’s at stake for S or what possibilities are salient to S could make a difference to what S knows. After all, reflection on what’s at stake given p or on the various ways in which p could be false does tend to have the effect of making one’s epistemic position with respect to p seem worse. But those who assert conspiracy conditionals in the canonical needn’t have pessimistic thoughts on the strength of their evidence with respect to conditional’s antecedent. (I take it that something like this is partially what explains Sect. 7’s observation that there is a difference in discourse initial assertability of conspiracy conditionals and skeptical knowledge ascriptions.) This makes the claim that Y factors are knowledge-destroying feel especially ad hoc. Second, if we (the audience) are in a context in which we take \(\ulcorner \)S knows whether p\(\urcorner \) to express a truth and we hear S assert \(\ulcorner \)If p, q\(\urcorner \) in the canonical way, we won’t always come to believe that \(\ulcorner \)S knows whether p\(\urcorner \) expresses a falsehood. Sometimes our reaction will be to think or say something like \(\ulcorner \)Why is S saying ‘If p, q’? She knows whether p!\(\urcorner \). Indeed, this is the kind of reaction that back in Sect. 2 I claimed we might have to a person’s asserting (2 ‘If I had a bagel for breakfast this morning, then I went out for brunch with Jim.’). If extra-sensitive invariantism is correct, however, such a reaction rests on a mistake. For if S is sincerely asserting \(\ulcorner \)If p, q\(\urcorner \) in the canonical way, then the Y factors must be present for S with respect to p. Given extra-sensitive invariantism, this entails that in no context does \(\ulcorner \)S knows whether p\(\urcorner \) express a truth. This is surely a cost to the view. (Thanks to an anonymous reviewer for pressing me to address this proposal.)

  39. 39.

    This isn’t to say that the story is perfectly tidy. As an anonymous reviewer points out, speeches like the following seem infelicitous:


    Given ignorance and a contextualist theory of ‘knows’ this is something of a surprise. Supposing the speech occurs in a single context, the first sentence is felicitously assertable (in the canonical way) only if the second sentence is true. So why should it sound bad?

    I don’t know the answer to this question. But I also don’t think it’s the epistemic contextualist’s job to answer it. The strangeness of (47) seems to be part of a more general pattern. For example: just about every mainstream theory of knowledge should agree that there are situations in which \(\ulcorner \)S doesn’t know whether it will rain tomorrow\(\urcorner \) expresses a truth. Yet to my ears (48) seems just as bad in S’s mouth as (47) does:


    Likewise, it’s not hard to find contexts in which in asserting a sentence like ‘Everyone is here’, one expresses the true proposition that everyone in the philosophy department is here. Yet it sounds very strange to say something like:


    But again, in any context in which the first sentence expresses a truth (given the circumstances of the world), the second must express a truth too. My hunch is that whatever explains the badness of speeches like (48) and (49) will also explain the badness of (47), but clearly further investigation is needed.

  40. 40.

    Ichikawa (2011) makes a similar point in defense of Lewis’s (1996) theory of ‘knows’.

  41. 41.

    For representative examples see, e.g., Heller (1995), Lewis (1996), Cohen (1998), Rieber (1998), Neta (2002), DeRose (2009).

  42. 42.

    Thanks to an anonymous reviewer for pressing this concern.

  43. 43.

    Although I exclude the sensitive and skeptical invariantists from the current discussion, similar lessons can be drawn for the four-party debate.


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Correspondence to Ben Holguín.

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Thanks to Kyle Blumberg, Cian Dorr, Jeremy Goodman, Harvey Lederman, Jake Nebel, Jim Pryor, Rose Ryan-Flinn, Trevor Teitel, and Jake Zuehl for helpful discussion of previous drafts. Thanks also to three anonymous reviewers for significantly improving the paper with their detailed and substantive comments.

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Holguín, B. Knowledge in the face of conspiracy conditionals. Linguist and Philos 44, 737–771 (2021).

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  • Knowledge
  • Contextualism
  • Indicative conditionals
  • Implicatures
  • Skepticism
  • Pragmatic encroachment