An Empirical Solution to the Puzzle of Macbeth’s Dagger

Abstract

In this paper I present an empirical solution to the puzzle of Macbeth’s dagger. The puzzle of Macbeth’s dagger is the question of whether, in having his fatal vision of a dagger, Macbeth sees a dagger. I answer this question by addressing a more general one: the question of whether perceptual verbs are intensional transitive verbs (ITVs). I present seven experiments, each of which tests a collection of perceptual verbs for one of the three features characteristic of ITVs. One of these features is Nonexistence: the failure of sentences involving transitive verbs to entail the existence of their direct objects. The experiments reveal that with respect to all three of these features, “see” behaves much more like a paradigmatically extensional verb than an intensional one. But surprisingly, unlike “see”, “perceive” behaves much more like a paradigmatically intensional verb. This shows that the category of perceptual verbs is not uniform with respect to the features of intensionality; while Macbeth does not see a dagger, he may still perceive one.

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Notes

  1. 1.

    Among the defenders of the view that we can perceive things that do not exist, whether by sight or otherwise, are Moore (1905, 1952), Ayer (1940, 1956), Smythies (1956), Anscombe (1965), Hintikka (1969), Lewis (1983), Harman (1990), Chomsky (1995), Brogaard (2014, 2015) and Bourget (2017, 2019).

  2. 2.

    Defenders of this view include Austin (1962), Dretske (1969), Cartwright (1957), Soames (2003), and Jackson (1977). Additionally, relationalists in the philosophy of perception, such as Brewer (2011), Campbell (2002), Fish (2009) and Logue (2012) often claim that their view can claim semantic orthodoxy, and so seem to endorse the view that direct-object perceptual reports are fully extensional.

  3. 3.

    In what follows, I will use “direct-obect” as a term for the object answering to the NP in the direct-object position of a perceptual ascription. Thus, I take a direct-object noun phrase to be a piece of language, while the direct object is, potentially, an object, if it exists.

  4. 4.

    Perceptual can also be used intransitively, but when they are, they are typically taken to report epistemic notions. See Chisholm (1956) for the original account of the different uses of perceptual verbs, and Johnston (2014) for a detailed account of why the intransitive uses of such verbs are not perceptual. Of course, representationalists in the philosophy of perception often define technical terms for the perceptual propositional attitude, but they acknowledge that these expressions are not present in natural language or folk perceptual psychology.

  5. 5.

    Anscombe (1965) was the first person to generalize the question of Macbeth’s dagger into a question concerning intensionality generally: are our perceptual verbs intensional transitive verbs? She answered the question in the affirmative.

  6. 6.

    For the most part, contributors to the debate have relied on informally evoking readers’ intuitions concerning example sentences, and generalizing from these examples to the entire category of perceptual verbs. For two notable examples, see Anscombe (1965) and Bourget (2017), although there are many others.

  7. 7.

    Importantly, saying that there are two readings of our perceptual verbs, and two readings of the ascriptions in which they figure, does not entail that these verbs have two different senses; perceptual verbs need not be lexically ambiguous. Rather, as we will see, in the manner of intensional transitive verbs more generally, the intensionalist can hold that perceptual verbs give rise to two different scopal readings of the same ascription, and treat the ambiguity as one in semantic structure.

  8. 8.

    Instead, many authors claim that in this case, Macbeth merely seems to see a dagger.

  9. 9.

    There is an approach to intentionality, and the semantics of intensional verbs, that comes very close to the sense-datum theorist’s position. Suppose that Ponce is searching for the fountain of youth. The fountain of youth does not exist. So what is he looking for? One possibility is that he is looking for an abstract object: he is looking for something, but it is not a fountain, and is does not have any properties that would render it concrete. Such a view is often associated with so-called “split readings” of intensional ascriptions, on which the determiner takes wide scope over the verb but leaves its restrictor inside. On such a view, Ponce is looking for something that he thinks is a fountain, but which is actually abstract, in the same way that Macbeth might be seeing a sense-datum that he thinks is a dagger, but turns out not to be.

  10. 10.

    Anscombe (1965) was the first person to recognize this, and to argue explicitly that perceptual verbs are intensional. Anscombe laid out the three traditional features of intensional transitive verbs and argued that perceptual verbs exhibit these features.

  11. 11.

    The restriction to positive quantifiers includes quantified NPs like ‘a dog’, ‘the men who robbed him’, ‘four gorgons’, and ‘infinitely many numbers’, while excluding negative NPs like ‘no dogs’, ‘no one’, ‘at most three gorgons’, etc.

  12. 12.

    For instance, Forbes (2006) uses one mechanism to account for Nonexistence and Nonspecificity, and another to account for Opacity. The tendency to treat Opacity as distinct from the other two properties originated with Fodor (1970), who held that Nonspecificity and Opacity can vary independently, and four different readings are available, one corresponding to each of combination of the presence and absence of each of the properties. For subsequent responses to and defenses of Fodor, see Keshet (2008, 2011) and Szabó (2010, 2011).

  13. 13.

    Participants in this study, and all of the studies presented here, were recruited using Amazon’s Mechanical Turk. Participants in Experiment 1 were English speakers, 54.7% male, average age 34.5, with 45% having at least a bachelor’s degree. However, one limitation of the study was that, while English fluency was a requirement to participate, it was not possible to verify that speakers were native speakers of English. This may have had some effect on the results, although since the sample size was relatively large for a study of this kind, there is reason to think that the results are still detecting a genuine pattern in English usage.

  14. 14.

    It is important that each pair of questions within each vignette is minimal: they differ only in the verb they involve. Thus, absent interaction effects, any differences in participant responses can be attributed to differences in meaning between the verbs. Thus, pointing out that certain noun phrases are more apt to lead to intensional or extensional readings does not account for the core data, which concern the differences between perceptual verbs and paradigmatically intensional and extensional verbs.

  15. 15.

    The results were analyzed using a 5 (verb: touch vs. see vs. perceive vs. sense vs. search) \(\times \) 3 (vignette: elf vs. panda vs. extra-terrestrial) mixed ANOVA. As expected, there was a significant effect of verb, \(F(4,796) = 215.34, p < .001\), but no significant effect of vignette, \(F(2,199) = .661, p = .518\), and no significant interaction, \(F(8,796) = .862, p = .549\). To explore the differences between the verbs, I compared the verbs pairwise, correcting for multiple comparisons with Bonferroni’s adjustment. Unsurprisingly, participants gave higher ratings for “search” (\(M = 5.47, SD = 2.26\)) than for “touch” (\(M = 1.34, SD = .985\)), \(p < .001\). Ratings for “perceive” (\(M = 3.89, SD = 2.27\)) were significantly higher than the ratings for “touch”, \(p < .001\), and significantly lower than those for “search”, \(p < 001\). The ratings for “sees” (\(M = 1.94, SD = 1.73\)) and “sense” (\(M = 2.28, SD = 1.78\)) also differed significantly from both “touch” and “search”, in both cases with \(p < .001\).

  16. 16.

    I am grateful to an anonymous referee for Erkenntnis for suggesting this follow-up variation on the experiment.

  17. 17.

    Participants were English speakers, 56.5% of whom were male, average age 29.8, with 79.8% having at least a bachelor’s degree.

  18. 18.

    The results were analyzed using a 5 (verb: touch vs. see vs. perceive vs. sense vs. search) \(\times \) 3 (vignette: elf vs. panda vs. extra-terrestrial) mixed ANOVA. As expected, there was a significant effect of verb, \(F(4,840) = 36.64, p < .001\), but no significant effect of vignette, \(F(2,210) = .496, p = .610\), and no significant interaction, \(F(8,840) = .671, p = .718\). To explore the differences between the verbs, I compared the verbs pairwise, correcting for multiple comparisons with Bonferroni’s adjustment. Unsurprisingly, participants gave higher ratings for “searched for” (\(M = 5.47, SD = 1.341\)) than for “touched” (\(M = 4.15, SD = 2.186\)), \(p < .001\). Ratings for “perceived” (\(M = 5.16, SD = 1.603\)) were significantly higher than the ratings for “touch”, \(p < .001\), and significantly lower than those for “search”, \(p = .049\). The ratings for “saw” (\(M = 4.41, SD = 2.087\)) differed significantly from “touched” (\(p = .001\)) and “searched for” (\(p < .001\)), as did the rating for “sensed”(\(M = 4.81, SD = 1.826\)), in both cases with \(p < .001\).

  19. 19.

    Although “perceived” and “searched for” differed only with \(p = .049\).

  20. 20.

    Participants were English speakers, 58.7% male, average age 33.3, with 67.5% of participants having at least a bachelor’s degree.

  21. 21.

    Experiment 3—like, as we will see, Experiments 5 and 7—involved a broader range of perceptual verbs. The goal of testing this broader range was first to locate “perceive” and “sense” within this broader category. Doing so allows us to compare “see” and “perceive” to other perceptual verbs, in the hope of gleaning additional insights. But studying a broader range of perceptual verbs also has intrinsic interest for those interested in sensory modalities other than vision. Additionally, Experiments 3, 5, and 7 differed from the other studies in that they made use of “have a sensation of” as opposed to “sense”. The reason for this change is that “sense” has a strong cognitive, non-perceptual interpretation, which dominates its perceptual use. Of course, other perceptual verbs likewise have cognitive readings, but the goal of switching from “sense” to “have a sensation of” was to restrict attention to sensations, which are only present in conscious perceptual states.

  22. 22.

    After being presented with the instructions, participants were presented with the questions all at once, but in a random order. The instructions and examples remained on the screen.

  23. 23.

    The results were analyzed using a 9 (verb: see vs. hear vs. smell vs. touch vs. feel vs. perceive vs. have a sensation of vs. search for vs. kick) \(\times \) 4 (vignette: dragon vs. panda vs. extra-terrestrial vs. dodo) mixed ANOVA. As expected, there was a significant effect of verb, \(F(8,1720) = 147.44, p < .001\), but no significant effect of vignette, \(F(3,215) = .387, p = .762\), and a significant interaction, \(F(24,1720) = 1.57, p = .04\). To explore the differences between the verbs, I compared the verbs pairwise, correcting for multiple comparisons with Bonferroni’s adjustment. As expected, the highest mean was for “searched for” (\(M = 6.02, SD = 1.52\)) while the lowest was for kick (\(M = 2.44, SD = 2.04\)). Ratings for “perceived” (\(M = 4.74, SD = 2.01\)) were significantly higher than the ratings for “kick”, \(p < .001\), “touch” (\(M = 2.60, SD = 2.168)\), \(p < .001\), and “have a sensation of” (\(M = 4.15, SD = 2.19\)), \(p = .003\), and significantly lower than those for “search for” (\(p < .001\)). The ratings for “see” (\(M = 2.92, SD = 2.20\)) differed significantly from “kicked” (\(p < .001\)) and “searched for” (\(p < .001\)), but not from “hear” (\(M = 2.89, SD = 2.215\)), \(p = 1.000\)), “smell” (\(M = 2.66, SD = 2.16\)), \(p = .140\)) or “feel” (\(M = 2.71, SD = 2.20\)), \(p = 1.000\).

  24. 24.

    Participants were English speakers, 46.9% male, average age 32.3, with 65.2% having at least a bachelor’s degree.

  25. 25.

    Experiments 2 and 3 differed slightly from Experiment 1 in that they made use of the paradigmatically intensional verb + preposition combination “look for”, as opposed to “search for”.

  26. 26.

    The results were analyzed using a 5 (verb: touch vs. see vs. perceive vs. sense vs. search) \(\times \) 3 (vignette: dog vs. car vs. mouse) mixed ANOVA. As expected, there was a significant effect of verb, \(F(4,876) = 28.26, p < .001\), but no significant effect of vignette, \(F(2,219) = .907, p = .518\), and no significant interaction, \(F(8,876) = .862, p = .952\). To explore the differences between the verbs, I compared the verbs pairwise, correcting for multiple comparisons with Bonferroni’s adjustment. Unsurprisingly, participants gave higher ratings for “search” (\(M = 5.47, SD = 1.75\)) than for “touch” (\(M = 4.17, SD = 2.29\)), \(p < .001\). Ratings for “perceive” (\(M = 5.04, SD = 1.87\)) were significantly higher than the ratings for “touch”, \(p < .001\), but did not differ significantly from those for “search”, \(p = .084\). The ratings “sense” (\(M = 5.14, SD = 1.78\)) also differed significantly from “touch”, \(p < .001\) “search”, but did not differ from “search”, \(p = .249\). Contrarily, the average rating for “sees” did not differ from that of “touch”, \(p = 1.000\), but did differ significantly from “search”, \(p < .001\).

  27. 27.

    The behavior of “sense” is somewhat strange, given that nonexistence and nonspecificity are often explained by the same mechanism (see, for instance, Forbes (2006)). However, there are some existence-entailing verbs that do not require specificity. These verbs have an “incorporated” semantics: indefinites in their object positions take obligatory narrow scope, and are nonspecific, but are existence-entailing. Examples of such constructions are incorporated VPs such as “mouse-caught” or “salmon-ate”. The incorporated status of the nominal gives it a nonspecific interpretation, but the extensionality of the verb entails that there must be something that was caught or eaten. See Dayal (2003, 2011) and van Geenhoven (1998) for further discussion. The connection between intensional transitive verbs and semantic incorporation is discussed at length by van Geenhoven and McNally (2005).

  28. 28.

    Participants were English speakers, 59.2% male, average age 33, with 66.8% having at least a bachelor’s degree.

  29. 29.

    After being presented with the instructions, participants were presented with the questions all at once, but in a random order. The instructions and examples remained on the screen.

  30. 30.

    The results were analyzed using a 9 (verb: see vs. hear vs. smell vs. touch vs. feel vs. perceive vs. have a sensation of vs. search for vs. kick) \(\times \) 3 (vignette: pig vs. cow vs. chicken) mixed ANOVA. As expected, there was a significant effect of verb, \(F(8,1688) = 59.14, p < .001\), but no significant effect of vignette, \(F(2,211) = .898, p = .409\), and no significant interaction, \(F(16,1688) = .617, p = .873\). To explore the differences between the verbs, I compared the verbs pairwise, correcting for multiple comparisons with Bonferroni’s adjustment. As expected, the highest mean was for “searched for” (\(M = 5.57, SD = 1.87\)) while the lowest was for kick (\(M = 2.98, SD = 2.362\)). Ratings for “perceived” (\(M = 5.04, SD = 2.02\)) were significantly higher than the ratings for “kick” (\(p < .001\)) and “touch” (\(M = 3.2, SD = p < .001\)), significantly lower than those for “search for”, \(p < .001\), but did not differ statistically from “hear” (\(M = 4.62, SD = 2.342\)), \(p = 1.000\), “smell” (\(M = 4.93, SD = 2.178\)), \(p = 1.000\), or “have a sensation of” (\(M = 4.7, SD = 2.105\)), \(p = 1.000\). The ratings for “see” (\(M = 3.31, SD = 2.33\)) differed significantly from “kicked” (\(p < .001\)) and “searched for” (\(p < .001\)), but not from “touch” (\(M = 3.2, SD = 2.436\)), \(p = 1.000\), “feel” (\(M = 3.03, SD = 2.296\)), \(p = 1.000\), or “kick”, \(p = 5.17\).

  31. 31.

    Participants were English speakers, 54.7% male, average age 33.4, with 67.1% having at least a bachelor’s degree.

  32. 32.

    The results were analyzed using a 5 (verb: touch vs. see vs. perceive vs. sense vs. look for) \(\times \) 3 (vignette: spy vs. butler vs. wife) mixed ANOVA. As expected, there was a significant effect of verb, \(F(4,784) = 21.55, p < .001\). Somewhat strangely, there was also an effect of vignette, \(F(2,196) = 7.699, p = .001\), although there was no significant interaction, \(F(8,784) = 1.294, p = .243\). One of the vignettes had overall lower scores, perhaps due to the fact that one set of descriptions used perceptually available properties: the Spy vignette made use of an NP “the shortest spy”, one component of which—“height”—was perceptually available, in contrast to the other NPs. However, in this study, there was also variation between vignettes in the kinds of NPs used. Perhaps the combination of a proper name “Ortcutt” and a definite description “the shortest spy” combined to yield noticeably lower scores for that vignette. To explore the differences between the verbs, I compared the verbs pairwise, correcting for multiple comparisons with Bonferroni’s adjustment. Unsurprisingly, participants gave higher ratings for “search” (\(M = 4.41, SD = 2.17\)) than for “touch” (\(M = 3.27, SD = 2.2\)), \(p < .001\). Ratings for “perceive” (\(M = 4.5, SD = 2.09\)) were significantly higher than the ratings for “touch”, \(p < .001\), but did not differ significantly from those for “look for”, \(p = 1.000\). The ratings for “sense” (\(M = 5.14, SD = 1.78\)) also differed significantly from “touch”, \(p < .001\), but did not differ from “search”, again with \(p = 1.000\). The ratings for “see” (\(M = 3.92, SD = 2.26\)) differed significantly from those for “touch”, \(p < .001\), but did not differ significantly from “search”, \(p = .094\).

  33. 33.

    However, even if perceptual verbs have a reading that requires recognition, they also have one that does not. This makes it perfectly felicitous to say things such as “I saw John’s new invention, but had no idea what I was looking at”. The higher scores for Opacity simply make it plausible that there is such a recognition-requiring reading.

  34. 34.

    Participants were English speakers, 57.8% male, average age 34, with 64.7% having at least a bachelor’s degree.

  35. 35.

    After being presented with the instructions, participants were presented with the questions all at once, but in a random order. The instructions and examples remained on the screen.

  36. 36.

    The results were analyzed using a 9 (verb: see vs. hear vs. smell vs. touch vs. feel vs. perceive vs. have a sensation of vs. search for vs. kick) \(\times \) 3 (vignette: spy vs. butler vs. novelist) mixed ANOVA. As expected, there was a significant effect of verb, \(F(8,1680) = 52.93, p < .001\), but no significant effect of vignette, \(F(2,210) = .646, p = .525\), and no significant interaction, \(F(16,1680) = 1.52, p = .084\). To explore the differences between the verbs, I compared the verbs pairwise, correcting for multiple comparisons with Bonferroni’s adjustment. As expected, the highest mean was for “search for” (\(M = 4.87, SD = 2.01\)) while the lowest was for kick (\(M = 2.81, SD = 2.185\)). Ratings for “perceived” (\(M = 4.82, SD = 2.05\)) were significantly higher than the ratings for “kick”, \(p < .001\), but did not differ statistically from the ratings for “search for” (\(p = 1.000\)) or “have a sensation of” (\(M = 4.51, SD = 2.05\)\(p = .665)\). The ratings for “see” (\(M = 3.31, SD = 2.33\)) were significantly higher than “kick” (\(p < .001\)) and “touch” (\(M = 2.91, SD = 2.168)\)), \(p = .001\), significantly lower than “searched for” (\(p < .001\)), but did not differ statistically from “hear” (\(M = 3.48, SD = 2.215\)), \(p = 1.000\), “smell” (\(M = 3.3, SD = 2.160\)), \(p = 1.000\) or “feel” (\(M = 3.33, SD = 2.20\)), \(p = 1.000\).

  37. 37.

    This argument is closely related to the argument, given in the next section, that the notional readings of perceptual verbs are not due to pragmatic factors.

  38. 38.

    One might object as follows: what accounts for the difference between “sees” and “perceives” is that “perceives” has a cognitive or epistemic use which is not existence entailing. For instance, one can perceive that John was in distress, or perceive the wisdom in someone’s statement. However, “see” likewise has cognitive and epistemic uses: one can see that John is in distress, and see the wisdom in someone’s statement. Thus there is no difference available. But further, when these verbs are used transitively, it is the perceptual reading that is dominant—it is extremely difficult to hear “John perceives a unicorn” as cognitive or epistemic, unless by “cognitive” or “epistemic” one simply means “has a reading that is not existence-entailing.” Cognitive and epistemic readings are much more salient when the verbs take “that”-clauses as complements.

  39. 39.

    There are a number of pragmatic views of how such propositions might be conveyed. One might, for instance, treat them as expressed via loose talk, or pragmatic halos, or via conversational implicatures.

  40. 40.

    This alternative explanation was suggested to me independently by Zoltán Gendler Szabó and an anonymous reviewer for Erkenntnis. Thanks to both of them for raising this possibility.

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Acknowledgements

A special thanks to Daniel Stoljar, Joshua Knobe, Zoltán Gendler Szabó, and two anonymous referees for Erkenntnis for helpful comments on earlier drafts of this manuscript. Thanks also to audiences at the Australian National University, the 2018 Wellington Empirical Philosophy Workshop, and the 2018 meeting of the Australasian Association of Philosophy

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Appendix: Histograms

Appendix: Histograms

Below are the histograms for each verb in Experiments 1, 4, and 6, fifteen in total. Each histogram graphically illustrates the frequency with which each verb received a particular response: for each rating on the Likert scale, 1–7, the histogram shows how many participants chose that score when asked if a particular verb exhibited a particular feature. In all of the studies, higher scores indicate more intensionality. Thus, the further to the right the scores are distributed, the more intensional the verb was with respect to that feature. Each column corresponds to one of the studies, while each row corresponds to one of the verbs. Column (a) gives the histograms for each verb in the Nonexistence study, column (b) the histograms for Nonspecificity, and column (c) presents Opacity (Figs. 8, 9, 10, 11, 12).

Fig. 8
figure8

Histograms for “touch”: a nonexistence, b nonspecificity, and c opacity

Fig. 9
figure9

Histograms for “see”: a nonexistence, b nnspecificity, and c opacity

Fig. 10
figure10

Histograms for “perceive”: a nonexistence, b nonspecificity, and c opacity

Fig. 11
figure11

Histograms for “sense”: a nonexistence, b nonspecificity, and c opacity

Fig. 12
figure12

Histograms for “search for” in a Nonexistence, and “look for” in b nonspecificity, and c opacity

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D’Ambrosio, J. An Empirical Solution to the Puzzle of Macbeth’s Dagger. Erkenn (2020). https://doi.org/10.1007/s10670-020-00253-0

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