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Why horizontalism


Horizontalism is the thesis that what a speaker asserts in literally and sincerely uttering an indicative sentence is some horizontal proposition of her utterance; diagonalism is the thesis that what a speaker asserts in literally and sincerely uttering an indicative sentence is some diagonal proposition of her utterance. Recent work on assertion has reached no clear consensus favoring either horizontalism or diagonalism. I explore a novel strategy for adjudicating between the two views by considering the advantages and disadvantages which would accrue to a linguistic community as a result of adopting different committal practices—that is, practices of associating utterances with the propositions to which speakers undertake assertoric commitments in uttering them—ultimately concluding that a horizontalist practice has important advantages over its competitors.

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  1. 1.

    Conan Doyle (1902, 189). Devoted fans will, I hope, excuse philosophically motivated alterations of the plot.

  2. 2.

    To say that Holmes asserts a given proposition is not to say that Watson learns that proposition from Holmes’s utterance. The proposition Watson learns from Holmes’s utterance may or may not be the same as the proposition Holmes asserts—I do not wish to take a stand on this issue. For those to whom assertion-talk does not come naturally, the difference between the horizontalist and diagonalist answers can to an extent be appreciated by considering the question of what Holmes tells Watson in [Sherlock], though, again, this question must be distinguished from the question of what Watson comes to believe on the basis of this telling.

  3. 3.

    Indeed, with the exception of what in Sects. 2 and 3 I will call (Nondefective Objective Horizontalism) and (Objective Horizontalism), every way of associating utterances with assertoric contents considered below is one according to which the assertoric content of an utterance can diverge from its grammatically determined content.

  4. 4.

    This is not to say that any two theorists who disagree about the correct answer to the philosopher’s puzzle must agree about the grammar of English. Disagreement about the correct answer to the philosopher’s puzzle could be rooted in disagreement at any of a number of levels: disagreement about the meanings of the context-insensitive lexical items which occur in Holmes’s utterance, for example, or disagreement about how the context of Holmes’s utterance determines the semantic value of the pronoun ‘he’ (that is, disagreement about the correct metasemantics for deictic pronouns in English—see footnote 10 below). The point I wish to register is simply that two theorists might disagree about the correct answer to the philosopher’s puzzle solely in virtue of disagreeing about the correct theory of assertion; that is, that agreement about grammar (construed so as to incorporate both semantics and metasemantics) does not suffice for agreement about the correct answer to the philosopher’s puzzle. This more modest claim is all I need to motivate the discussion which follows. Thanks to an anonymous referee for pressing me to clarify this point.

  5. 5.

    Thanks to an anonymous referee for pressing me to clarify this point.

  6. 6.

    It is sometimes suggested that this is not a platitude, and that Stalnaker rejects the view that assertion is a committal speech act, on the grounds that he occasionally theorizes about non-committal speech acts, such as hypothetical reasoning and plan formation, along with assertion. Though the Stalnakerian framework is useful for modeling these other speech acts, and though Stalnaker himself seldom writes about commitment, it is a misreading of Stalnaker to attribute this view to him. He makes this clear in a number of places. For example: “I should emphasize that I am not claiming that one can define assertion in terms of a context-change rule, since that rule will govern speech acts that fall under a more generic concept. A full characterization of what an assertion is would also involve norms and commitments.” (2014, 89).

  7. 7.

    Thanks to an anonymous referee for pressing me to clarify this point.

  8. 8.

    I thus set aside for the sake of simplicity proposals, like that of Lewis (1980), on which the grammar of language is a function from ordered n-tuples (with n greater than 3) to truth values. Everything I say in what follows is compatible with such proposals, except that the procedures for recovering the horizontal and superdiagonal propositions of an utterance given below must be revised to account for the additional complexity of the underlying grammar.

  9. 9.

    There is a small literature concerning cases in which the passage from utterance to extralinguistic context is unusual, as in the so-called “answering machine paradox” [see, for example, Sidelle (1991) and Predelli (1998)]. We need not be overly concerned about such cases in what follows, however, since it is a criterion of adequacy for any theory of them that it show how, in everyday cases like the ones at issue here, we can move from a given utterance to the context in which it was produced.

  10. 10.

    How exactly does a context determine which proposition is grammatically associated with a given sentence? Borrowing terminology from King (2014), let us refer to this question as the question of the metasemantics of context sensitivity. Though in what follows I will sometimes write as if I take for granted an intentionalist metasemantics according to which the propositions grammatically associated with sentences containing demonstratives and deictic pronouns are determined by the referential intentions (and perhaps also gestures) of the speakers who utter them, this is an issue on which I do not wish to take a stand. Because they concern assertoric content rather than semantics, my arguments in what follows are compatible with any plausible metasemantics for context-sensitive vocabulary. Thanks to an anonymous referee for pressing me to clarify this point.

  11. 11.

    In what follows I will assume, along with most others who have written on assertion, that an utterance is associated with at most one assertoric content. For an alternative picture, according to which assertion must be modeled as a relation between utterances and contents rather than as a function from utterances to contents, see Soames (2005).

  12. 12.

    Thanks to an anonymous referee for pressing me to distinguish between this descriptive claim and the corresponding theoretical question.

  13. 13.

    See Sect. 6 for an application of this observation.

  14. 14.

    Note that the claim that the commitment involved in genuine assertion goes beyond the commitment involved in mere intentional communication is consistent with attempts to analyze assertion at least partly in terms of intentional communication. In the Gricean tradition, for example, what a speaker means in performing a communicative act is defined partly in terms of what she thereby intends to communicate, and what a speaker says in producing an utterance (which for our purposes we may understand to be equivalent to what she asserts) is defined partly in terms of what she means in producing that utterance. This sort of view can be reconciled with the intuitive attractiveness of holding that speakers are more strongly committed to what they assert than to what they (for example) conversationally implicate as long as we think that the extra conditions which must be met for a proposition to be said rather than merely meant can be relevant to the level of commitment a speaker undertakes in putting it forward.

  15. 15.

    I will understand the common ground of a conversation at a time to be the set of propositions all interlocutors take for granted for the purposes of the conversation at that time.

  16. 16.

    More precisely, if G is the grammar, s is the sentence uttered, and \(c_{w}\) is the context in which it is uttered in w, the horizontal proposition of the utterance at w is the set of worlds \(w'\) such that \(G(\langle s, c_{w}, w' \rangle ) = 1\).

  17. 17.

    More precisely, if f is the function which maps each utterance/world pair \(\langle u, w \rangle \) to the context \(c_{w}\) in which u is uttered at w, then the superdiagonal proposition of an utterance u of a sentence s is the set of worlds w such that \(G(\langle s, f(\langle u, w \rangle ), w \rangle ) = 1\).

  18. 18.

    The truth-values of the superdiagonal proposition of an utterance at different worlds are always calculated with reference to the grammar G actually in use by the community. A distinct proposition, which we may call the hyperdiagonal, is definable by feeding each world, sentence, and utterance context into the grammar in use by the community in which the utterance is produced at that world. The superdiagonal and hyperdiagonal propositions of an utterance u at a world w may differ in truth-value at worlds where that utterance is produced in a community with a grammar distinct from the grammar of the community in which it is produced at w. Nevertheless, since the distinction between the superdiagonal proposition of an utterance and its hyperdiagonal proposition does not affect the plausibility of any of the arguments in what follows, I will suppress it for the purposes of this article.

  19. 19.

    A conversation is nondefective at a world iff at that world all interlocutors take the same propositions for granted for the purposes of the conversation.

  20. 20.

    If, following Lewis (1975), we think of a community as having coordinated on a grammar just in case it obeys a convention of truthfulness and trust in the deliverances of that grammar, then we must regard facts about whether sentences are taken to express truths in contexts at worlds as explanatorily prior to facts about the grammars of communities. In that case, it may seem to make little sense to assume that a community has coordinated on a grammar and then ask how members of that community use that grammar to assign assertoric contents to utterances.

    But one can maintain that something like conventions of truthfulness and trust suffice to determine the grammar of a community without conceding the incoherence of questions about committal practices. Suppose, for example, that the grammar on which a community has coordinated is determined by the linguistic behavior of its members in a restricted class of situations where the common ground between interlocutors is minimal and there is no ignorance about the contexts in which utterances are produced. While it would then arguably be incoherent to suppose that the community adopts a committal practice which conflicts in some sense with its linguistic behavior in this class of situations, we can coherently imagine that it might adopt various committal practices which differ with respect to assertions taking place in less ideal situations. Indeed, this is exactly where most of the committal practices discussed here do differ. Thanks to John Hawthorne for pressing this objection.

  21. 21.

    Special cases include, for example, utterances of sentences like ‘That is non-self-identical’, which express necessary falsehoods however the context sensitivity of their lexical items is resolved.

  22. 22.

    Thanks to an anonymous referee for pressing me to clarify this point.

  23. 23.

    Of course, in cases where there is ignorance about what property is denoted by a predicate, or about the Kaplanian character of a context-sensitive expression, there will be uncertainty about which superdiagonal proposition is expressed. For example, an utterance of ‘ophthalmologists are eye doctors’ in English expresses a necessarily true superdiagonal but a contingent hyperdiagonal. So there is some reason to distinguish between speaker- and audience-centered versions superdiagonalism. Nevertheless, since we have assumed that interlocutors have coordinated on a grammar, and since the speaker- and audience-centered versions of (Superdiagonalism) are subject to many of the same criticisms as (Superdiagonalism), I omit further discussion of them in what follows.

  24. 24.

    It may seem that I have neglected to mention two important further options: first, that a speaker is committed to the conjunction of the propositions newly entailed by the context set when it is updated with the superdiagonal proposition of her utterance; second, that a speaker’s assertoric commitment is determined by some disjunctive rule (for example, Stalnaker’s (1978) proposal that one asserts the horizontal proposition of one’s utterance in some circumstances and a diagonal proposition in others). The first of these options is, however, illusory. Given that the conjunction of the superdiagonal and the context set will itself be newly entailed by the context set after updating, and given that it is the strongest such proposition, what seems at first to be a further option is in reality equivalent to (Nondefective Contextual Diagonalism). The possibility of a disjunctive committal practice with be discussed in Sect. 9 below.

  25. 25.

    I do not wish to deny that (in some sense) the speaker in this case takes the possible-worlds proposition that Catherine is a national treasure to be the horizontal proposition of her utterance; my point is that she does not take this proposition /rather than the proposition that Diana is a national treasure/ to be the horizontal proposition of her utterance, because she does not distinguish between the two propositions. Thanks to John Hawthorne and Jeff King for helpful discussion of this case.

  26. 26.

    Of course, even on (Objective Horizontalism), Smith could argue that he should be excused for having claimed that Jones was an embezzler, given that he had evidence that he was pointing at Schmones. But this is a different sort of defense: one in which Smith concedes that he has undertaken a commitment to the horizontal proposition of his utterance.

  27. 27.

    A question remains about why, in a less fanciful version of [Definite] (that is, one in which there are no complexities involving Schmones), Smith’s speech about claiming that the person I was talking to is an embezzler rather than that Jones is an embezzler seems less convincing. My suggestion here is that this is because we take Smith to know that the person I am talking to is an embezzler just in case Jones is an embezzler, and we also assume that this biconditional is in the common ground. Given these two assumptions (and a plausible closure principle for knowledge), Smith is plausibly blameless for having asserted that the person you are talking to is an embezzler if and only if he is in a position to blamelessly assert that Jones is an embezzler—he meets the evidential standard for asserting one just in case he meets the evidential standard for asserting the other, and so on. Since, given the common ground, he also communicates the same propositions regardless of what he asserts, there is a sense in which it is beside the point for him to argue that he claimed one but not the other: if he would have deserved criticism for asserting that Jones is an embezzler, he actually deserves criticism for asserting that the person I was talking to is an embezzler. This is perhaps a second sense in which Smith’s commitment to the proposition that Jones is an embezzler is stronger than the commitment usually associated with hinting or implicating, though not one which will be of much comfort to the friend of (Superdiagonalism), since speakers often lack the kind of knowledge it requires, as when they are mistaken about, or suspend judgment concerning, which propositions are materially equivalent to the assertoric contents of their utterances.

  28. 28.

    Especially committed proponents of (Superdiagonalism) may maintain that, even if what I have claimed so far is true, there must be some other notion of commitment which will serve their purposes. The burden is on them, however, to develop a theory of the relevant notion of commitment. In the absence of such a theory, it is difficult to resist the conclusion that a superdiagonalist committal practice struggles with respect to utility.

  29. 29.

    In treating the English optative construction as a force marker, I assume that it does not interact compositionally with its prejacent to change which proposition is expressed; that is, I assume that the proposition which the grammar assigns to \(\phi \) is the same as the proposition which the grammar assigns to \(\ulcorner \)Would that \(\phi ! \urcorner \), the difference between the two being entirely a matter of what speech act is conventionally performed by uttering them. I consider this assumption plausible. Nevertheless, even if theoretical considerations ultimately suggest that it is false, it suffices for my purposes to note, first, that there may be other languages in which optative constructions are genuine force markers in the sense described, and, second, that a community could introduce some construction which worked in the suggested way. The argument would then be that the introduction of such a construction would be useful only for a community with a horizontalist committal practice, and that it is an advantage for a committal practice to be easily extensible in this way.

  30. 30.

    What if, according to the speaker, every world is such that there is a world which is better than it? Then instead of speaking of “all of the best possible worlds,” we can require that every world w be such that (i) there is a better world w′ at which the assertoric content of \(\phi \) is true, and (ii) every world better than w′ is such that the assertoric content of \(\phi \) is true. (Cf. Kratzer 2012, 40.)

  31. 31.

    There is a question about whether all the worlds which are subjectively best for Devin are ones at which she utters “He is here”; if not, then the relevant superdiagonal proposition will fail to be defined over the set of best worlds, yielding once again the prediction that sentences of the form \(\ulcorner \)Would that \(\phi !\urcorner \) may almost never be produced felicitously.

  32. 32.

    Indeed, this observation follows from the more general point that, on (Superdiagonalism), the assertoric content of an utterance is sensitive only to the sentence uttered and not to the extralinguistic context in which it is uttered: an utterance of a given sentence always counts as assertion of the same proposition, regardless of context. This is not to say that (Superdiagonalism) is incompatible with grammatical context sensitivity—the total pattern of the dependence of grammatical content on extralinguistic context is what determines the superdiagonal proposition associated with a given utterance, so that metasemantic differences in the underlying grammar correspond to the assignment of different superdiagonal propositions to utterances.

  33. 33.

    This is not to say that they assign contents to all utterances at all worlds where those utterances exist—we saw in Sect. 4 that this is not the case.

  34. 34.

    John Hawthorne points out that it seems in spirit of (Stalnakerian Disjunctivism) to allow for a certain kind of extension even when there fails to be a unique proposition which it is common ground is the horizontal proposition expressed by an utterance. For example, an utterance of a conjunction could be such that both conjuncts contain context-sensitive expressions, but it is common ground that the expression in the first conjunct takes a certain value, whereas the value taken by the expression in the second differs across the context set. In such a case, it seems in the spirit of (Stalnakerian Disjunctivism) to say that the assertoric content of the utterance is defined at worlds outside the context set, and that it is at least as strong as the first conjunct. We may, however, safely ignore this complication in what follows.


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Thanks are due to Elisabeth Camp, Jeffrey C. King, Ernie Lepore, Paul Pietroski, Jeffrey Sanford Russell, and two anonymous referees for helpful comments on various drafts of this paper. I am especially indebted to Andy Egan and John Hawthorne for their detailed and extensive feedback on multiple early drafts.

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Correspondence to Cameron Domenico Kirk-Giannini.

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Kirk-Giannini, C.D. Why horizontalism. Philos Stud 177, 2881–2905 (2020).

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  • Pragmatics
  • Speech act theory
  • Assertion