2. An argument for Deflationism

In arguing that negative action sentences quantify over events, I seem to be facing an uphill battle. Once we adopt a neo-Davidsonian approach to ordinary action sentences, Deflationism seems to follow naturally. For negative actions are understood in terms of what an agent does not do, rather than in terms of what she does, and so it is natural to think that negative action sentences are the negations of ordinary ones. Moreover, it seems that Davidson’s original argument for treating ordinary action sentences as existential quantifications over events can be turned into an argument for treating negative action sentences as negative-existentials. His argument, you may recall, was that his analysis provides for a simple explanation of the validity of ‘adverb-dropping’ inferences. Consider the following sentences, paired with their neo-Davidsonian analyses:

Obviously, in their English formulations, (3) entails both (4) and (5), and each of these three sentences entails (6). The neo-Davidsonian analyses explain why these entailments hold: when we infer (6) from (4), we simply drop the conjunct ‘In(e, bathroom)’ from within the scope of ‘(∃e)’; when we infer (6) from (5), we drop ‘t = midnight’ from within the scope of ‘[∃t : t < t*]’; and when we infer (4), (5), or (6) from (3), we make one or both of these moves. Thus, each inference is validated by the principle (∃x) (Fx & Gx) ⊢ (∃x) Fx.

But now compare (3)–(6) with the following negative action sentences, analysed as existential quantifications over events:

Obviously, in their English formulations, (7) does not entail (9), for Jones might have omitted to butter toast in the bathroom at midnight, and yet succeeded in buttering toast in the kitchen at midnight, in which case (7) is true while (9) is false. And yet, the neo-Davidsonian analyses validate the inference, by the principle (∃x) (Fx & Gx) ⊢ (∃x) Fx. What’s worse, Deflationism seems to provide an easy explanation of why this inference is invalid. According to Deflationism, (7) and (9) are analysed as negative-existentials:

Note that in (7*) the adverb ‘In(e, bathroom)’ is in the scope of ‘~ (∃e)’; so dropping it to get to (9*) would violate the principle ~ (∃x)(Fx & Gx) ⊬ ~ (∃x) Fx. Thus, the invalidity of this adverb-dropping inference seems to count in favour of Deflationism, and against a more thoroughly neo-Davidsonian approach.

Things are more complicated where (8) and (10) are concerned. Note first that these sentences seem to be ambiguous. On one reading, (8) says that there is some specific time such that Jones omitted to butter toast in the bathroom then. On this reading, (8) intuitively follows from (7), since if Jones omitted to butter toast in the bathroom at midnight, then midnight is a time such that Jones omitted to butter toast in the bathroom then. Similarly, there is a reading of (10) on which it says that there is some specific time such that Jones omitted to butter toast then, and on this reading (10) intuitively follows from (9). The neo-Davidsonian analyses sketched above nicely capture these readings – call them ‘the (a)-readings’ – and the validity of these inferences: we infer (8) from (7), and (10) from (9), simply by dropping ‘t = midnight’ from inside the scope of ‘[∃t : t < t*].’

But there is another reading of (8), on which it says, not that there is some specific time such that Jones omitted to butter toast in the bathroom then, but rather that Jones omitted to butter toast in the bathroom at any time. On this reading, (8) does not follow from (7), since even if Jones omitted to butter toast in the bathroom at midnight, he may still have buttered toast in the bathroom at some other time, in which case (7) is true while this reading of (8) is false. Similarly, there is a reading of (10) on which it says, not that there is some specific time such that Jones omitted to butter toast then, but rather that Jones omitted to butter toast at any time, and on this reading (10) does not follow from (9). The neo-Davidsonian analyses sketched above capture neither these readings – call them ‘the (b)-readings’ – nor the invalidity of these inferences.

The task of the next section is to develop a neo-Davidsonian semantics for negative action sentences which can (i) block the inference from (7) to (9), (ii) capture the (b)-readings of (8) and (10), and (iii) block the inferences from (7) to (8) and from (9) to (10), on those readings.

3. The analysis of negative action sentences

The source of the trouble with adverbs is that, in sketching a neo-Davidsonian semantics for negative action sentences, we treated each sentence as containing a single event-variable, bound by a single existential quantifier. This treatment leaves nothing for the adverb ‘in the bathroom’ to modify but that variable, and so it allows that adverb to be validly dropped. This treatment is misguided right from the start, for it suggests that ‘in the bathroom’ functions in (7) and (8) the way it functions in (3) and (4), to give the location of some event in which Jones is involved. But that is not its function, since (7) and (8) can be true even if Jones is not in the bathroom, and so even if he is not involved in any event that occurs there. Rather, it is simply meant to give the relevant place at which there is no event of Jones buttering toast (Clarke Reference Clarke, Aguilar and Buckareff2010, 140). By misrepresenting the role this adverb plays in negative action sentences like (7) and (8), the simple neo-Davidsonian analyses validate invalid inferences.

Fortunately, there is a natural solution to this problem. The phrase ‘omit to butter toast’ is a complex one, constructed from the verbs ‘omit’ and ‘butter toast’. If we adopt a neo-Davidsonian semantics on which verb phrases are treated as introducing event-variables and predicates thereof, then we should not assume that the phrase ‘omit to butter toast’ introduces a single event-variable, of which ‘Omission-to-butter-toast’ is predicated. The more natural proposal is that ‘omit’ and ‘butter toast’ each contribute their own event-variable and event-predicate, that is, that ‘omit’ contributes a variable for omissions while ‘butter toast’ contributes a variable for butterings of toast. If we have these two variables to work with, then we need not predicate ‘in the bathroom’ of the omission-variable, thereby treating that adverb as giving the location of Jones’ omission. Instead, we can predicate it of the buttering-variable, thereby capturing the fact that it gives the location at which there is no buttering-event.

Of course, we cannot simply bind both variables with existential quantifiers, since that would have (7) saying, in part, that there was a buttering of toast by Jones, which is not what we want. Whereas the variable for omissions must be bound by ‘(∃e)’, the variable for butterings must be bound by ‘~ (∃e′).’

If we no longer rely on a single event-variable and the one-place predicate ‘Omission- to-butter-toast’, how are we to relate our two variables to show that Jones’ omission is an omission to butter toast, rather than an omission to do something else? Here I take my inspiration from Michael Smith’s (Reference Smith, Aguilar and Buckareff2010) account of what it is to refrain from doing something. Smith considers Hornsby’s (Reference Hornsby, Hyman and Steward2004) case of an agent, A, who refrains from taking another chocolate. Hornsby thinks that refraining from taking a chocolate is not a matter of the occurrence of an event. Smith disagrees.

Extending Smith’s point, I say that to omit to do something or refrain from doing it, at a certain time, is to ensure – in a sense to be clarified – that one does not do that thing at that time, and that negative action sentences existentially quantify over events in which agents ensure that they do not do certain things at certain times. (Here times may be moments or intervals, and the relevant time is either explicitly mentioned in the sentence, or supplied by context) Schematically, a sentence of the form ‘x omits to φ at t’ or ‘x refrains from φ-ing at t’ can be analysed as:

where ‘Ensure(e, ~ (∃e′) Agent(x, e′) & φ(e′) & At(e, t))’ means that e ensures that the proposition ‘~ (∃e′) Agent(x, e′) & φ(e′) & At(e, t)’ is true.¹¹ Note that the ensuring-event occurs at the same time at which no φ-ing event occurs. This is intuitive: while there is a sense of ‘ensure’ in which Jones can ensure, at an earlier time, that he will not butter toast, it would be odd to describe that earlier behaviour as his omission. To omit to butter toast at t, Jones must ensure at t that he does not do so.¹²

What is it to ensure that one does not φ, in the relevant sense? Smith’s idea seems to be that to ensure that one does not φ at a time is to do something else which is incompatible with φ-ing at that time. But the things we do are not always incompatible with the things we omit to do. Suppose I am preparing a pasta sauce for my dinner. I chop some onions, heat some oil, add the tomatoes, add the tomato paste … I do everything I need to, except add garlic. It is not true that everything I do is incompatible with adding garlic – I could have done so while adding the oil, or while adding the tomatoes – but nonetheless I omit to add garlic.

The solution to this problem is to distinguish the things I do, as I prepare the sauce, from the event that is my doing of them (Hornsby Reference Hornsby1980, 3–5). The objection assumes that my view is that, whenever one omits to φ at t, or refrains from φ-ing at t, one does something else, ψ, such that one could not have both φ-ed and ψ-ed at t. But that is not my view – what ensures that the agent does not φ is not the thing she does, or perhaps the fact that she does that thing, but rather the event that is her particular doing of that thing. Applying this to the original example, while nothing I do is incompatible with adding garlic, the occurrence of my doing of those things is. For, on a plausible view of the individuation of events, the event that is my actual preparation of the sauce has a very narrowly defined essence: it necessarily consists in my moving my body in precisely these ways at these times. Any event in which I move my body in a slightly different way is not my actual preparation of the sauce. Thus, if I were to have moved my body slightly differently, say by using my right hand to stir the sauce instead of my left, then while I might have done all of the same things – chop the onions, heat the oil, add the tomatoes, and so on – the event that is my actual doing of these things would not have occurred. Similarly, if I were to have added the garlic, then I would have had to have moved my body in some way in which I did not actually move it, and so the event which actually occurred would not have occurred.

A second respect in which Smith’s idea needs modification is that ‘incompatible’ suggests a very strong relation of exclusion – i.e. that it is impossible for my doing of what I do to occur, and yet for me to do what I actually omit to do at that time. But that relation is too strong. Consider a case where I am in a departmental meeting at which a vote is called. Votes will be counted by a show of hands, and I refrain from voting by keeping my hands at my sides. Does my behaviour necessitate that I do not vote? No, for the incompatibility of my action and voting is the result, not just of the essential, intrinsic features of my action, but of facts about how people in my department cast their votes, and these facts are contingent – there are possible worlds in which the voting rules are different, and members of the department vote precisely by keeping their hands at their sides. If my actual act of keeping my hands at my sides occurs in one of those worlds, then I will not refrain from voting.

Rather than saying that the ensuring-event is incompatible with φ-ing at t in all worlds, we should restrict our gaze to worlds in which certain relevant facts about the actual world are held fixed. My act of keeping my hands at my sides is incompatible with voting in the sense that, given the actual voting procedures, if that act occurs then I do not cast a vote.

On my view, then, negative action sentences quantify over events in which an agent ensures that she does not do a certain thing at a certain time – that is, they quantify over events whose occurrence is incompatible with the agent doing that thing at that time, given certain relevant facts about the actual world.

This view gives a satisfying treatment to adverbs and block patently invalid adverb-dropping inferences. For instance, instead of (7), we now have (leaving aside the complications discussed in notes 1 and 8):

Here, ‘in the bathroom’ is predicated of the variable for buttering-events, and so it has the function of giving the relevant location at which there is no buttering of toast by Jones. To drop the adverb ‘in the bathroom’ from this sentence is to drop a conjunct from within the scope of ‘~ (∃e′)’, in violation of the principle ~ (∃x) (Fx & Gx) ⊬ ~ (∃x) Fx. Thus, (7**) does not entail (9**):

In addition, this neo-Davidsonian approach, like the simpler one from the previous section, easily captures the (a)-readings of (8) and (10), on which they say that there is some specific time such that Jones omitted to do such-and-such then, and on which they intuitively follow from (7) and (9):

(7**) reports that at some specific time, namely midnight, Jones ensured that he did not butter toast in the bathroom then, and thus it entails (8**a), that at some specific time, Jones ensured that he did not butter toast in the bathroom then. (9**a) entails (10**a) for a similar reason.

But what about the (b)-readings of (8) and (10), on which they say that Jones omitted to do such-and-such at any time? As we saw, the simple neo-Davidsonian analyses from the previous section do not capture these readings. The obvious solution is to replace the existential quantifier over times with a universal one: on their (b)-readings, (8) and (10) say that Jones ensured that he did not do such-and-such at any relevant time.

(The quantifier must be restricted to relevant times, otherwise ‘Jones omitted to butter toast’, for instance, would mean that Jones never buttered toast in his life, which it does not. Fortunately, if omission reports presuppose that the agent was supposed to do the relevant thing, then we have a natural account of how the quantifier in that sentence gets restricted: it ranges only over that interval of time in which Jones was supposed to butter toast.) On this analysis, the inferences from (7) to (8) and from (9) to (10) are invalid, just as we wanted. (7**) reports that at some time, namely midnight, Jones ensured that he did not butter toast in the bathroom then. It does not follow from this that Jones ensured that he did not butter toast in the bathroom at every relevant time, so (7**) does not entail (8**b). The move from (9**) to (10**b) is blocked for similar reasons. Thus, my neo-Davidsonian approach invalidates each of the invalid inferences from Section 2.

In addition to solving the problem of adverbs, this analysis allows us to identify negative actions with ordinary, positive events, rather than treating them as thoroughly negative entities, like absences. For me to refrain from voting, for instance, is for me to (intentionally) be the agent of some event which ensures that I do not vote at that time, and so we can say that my refrainment just is whatever event plays that ensuring-role. As we have seen, an event of me keeping my hands at my sides can play that role, and so we can identify my refrainment with that event. Generalizing, every negative action can be identified with a positive event whose occurrence is incompatible with the agent doing a certain thing, at the time that event occurs.¹³

I noted in Section 1 that, on one opposing view, a negative action is identical to a positive event only if the latter is a positive action which the agent performs in order not to do a certain thing. My view differs from this one in two important respects.

First, I do not assume Deflationism. This is an advantage for two reasons. First, as I will argue in Section 4, Deflationism is false. Second, Deflationism threatens to make the identification of a negative action with a positive one incoherent. On my view, ‘Jones omitted to butter toast’ quantifies over omission-events, and so the phrase ‘Jones’ omission to butter toast’ can be used to denote the event quantified over – ‘Jones’ omission to butter toast’ stands to ‘Jones omitted to butter toast’ as ‘Jones’ buttering of toast’ stands to ‘Jones buttered toast’. On the opposing view, by contrast, ‘Jones omitted to butter toast’ is a negative-existential; it does not quantify over omission-events. It is therefore unclear how ‘Jones’ omission to butter toast’ can have the function of denoting an event.¹⁴ But if that phrase does not denote an event, then it makes no sense to say that we may identify the event it denotes with a positive action.

One might reply that ‘Jones omitted to butter toast’ expresses a negative-existential proposition only in cases where Jones’ omission is a basic one – if his omission is not basic, then that sentence existentially quantifies over omission-events, and so we may identify his omission with a positive action (Vermazen Reference Vermazen, Vermazen and Hintikka1985, 99 n.14). But given that we may utter that sentence without knowing whether Jones’ omission was basic, this looks miraculous. It would be an astonishing coincidence if that sentence just happened to quantify over omission-events only when such events existed.

The second difference is that, because my notion of ‘ensuring’ makes no appeal to intention – to ensure that one does not φ at t is not to do anything in order not to φ at t – my view allows even basic negative actions to be identified with positive events. The event which ensures that x does not φ at t need not be a positive action. Thus, my view allows event-based theories of agency to accommodate basic negative actions, while the opposing view does not.¹⁵

4. Seeing negative actions

I now turn to the task of showing that my approach to negative action sentences is not only workable, but preferable to Deflationism. Consider the following pair of sentences, in which action phrases occur alongside perceptual locutions:

These sentences have two interesting features. First, the names ‘Brutus’ and ‘Caesar’ occur in a transparent context in (11a), but they occur in an opaque context in (11b). If (11a) is true and Brutus is the tallest person in the room, then it follows that I see the tallest person in the room stab Caesar. But if (11b) is true and Brutus is the tallest person in the room, then it does not follow that I see that the tallest person in the room is stabbing Caesar. For seeing that p is a way of knowing that p (Williamson Reference Williamson2000, 33–41) – it is, roughly, knowing that p by virtue of visual perception – and I may not know that Brutus is the tallest person in the room. (Of course, not all uses of ‘see that’ express perceptual knowledge, but I am only concerned with such uses here.)

Second, neither one of (11a) and (11b) entails the other. In a case where I see Brutus stab Caesar but do not recognize either of them, (11a) is true but (11b) is false. A more complex scenario can be constructed where (11b) is true but (11a) is false. Seeing that p is true does not generally require seeing the objects and properties involved in the truth of p – e.g. I can see that my wife is home by seeing her shoes in the front hallway, even though her shoes being in the hallway is no part of the fact that my wife is home (since that same fact could obtain even if her shoes were in the closet, or out for repairs). So, it seems, (11b) can be true even in a case where I cannot see either Brutus or Caesar. Suppose that Brutus has a variety of weapons laid out on a table. Unable to watch the assassination, I avert my eyes. If I look at the table, and see that out of all of Brutus’ weapons only the knife is missing, I can come to know by what I see that Brutus is stabbing Caesar. Hence, it seems to me, I can see that Brutus is stabbing Caesar, in this case, without actually seeing him do it.

If we take a neo-Davidsonian tack and analyse ‘Brutus stabs Caesar’ as quantifying over stabbing-events, then we can explain these two features (Parsons Reference Parsons1990, 15–17). First, we analyse ‘Brutus stabs Caesar’ as¹⁶:

(12) reports the occurrence of an event, a stabbing of Caesar by Brutus. Given this analysis, we can treat (11a) as reporting that I see this event:

By contrast with (11a), (11b) reports that I have a certain attitude, seeing that, to the proposition that Caesar is stabbing Brutus. We can thus give it the much simpler analysis:

where ‘See’ is a two-place predicate which relates individuals to propositions, ¹⁷ the relation of seeing that such-and-such is true, and ‘p’ denotes the proposition that Brutus is stabbing Caesar. (I leave aside the difficult issue of how to analyse the progressive ‘stabbing’ in a neo-Davidsonian framework.)

This semantics explains the transparency of (11a) and the opacity of (11b). In (11a), ‘Brutus’ and ‘Caesar’ are components of the description of an object seen – namely, the event of Brutus stabbing Caesar – and, in general, co-referring names and descriptions can be substituted salva veritate in reports of object-perception. If ‘I see Tibbles’ is true, then so is ‘I see the youngest of my cats’, provided Tibbles satisfies that description. By contrast, (11b) reports a de dicto propositional attitude; the description of the event as a stabbing of Caesar by Brutus occurs within the embedded proposition, and descriptions occurring within the scope of a propositional attitude operator generally occur in an opaque context. It also explains the independence of (11a) and (11b). (11a) says that I see an event satisfying a certain description, which does not entail that I see that there is such an event. (11b) fails to entail (11a) for a similar reason. Seeing that p is coming to know p by way of visual perception, so (11b) reports perceptual knowledge. But (11b) does not require that what allows me to know that Brutus is stabbing Caesar is perception of the actual stabbing.

Now compare (11a) and (11b) to these sentence-pairs:

Each of these sentences is well-formed, and the resulting pairs are syntactically similar to the pair of (11a) and (11b). Furthermore, each pair exhibits the features of (11a) and (11b) which drew our attention in the previous section. The names ‘Randy’ and ‘Theresa’ occur in transparent contexts in (13a) and (14a), but they occur in opaque contexts in (13b) and (14b). And the (a)-sentences and the (b)-sentences do not entail one another. The (a)-sentences obviously do not entail the (b)-sentences, since I can see Randy omit to pick up milk, or Theresa refrain from smiling, without realizing that it is Randy or Theresa that I am seeing. To see that (13b) does not entail (13a), suppose that I am hiding in the milk cooler at the grocery store, and that the milk cartons are arranged on a conveyor, so if Randy takes one from the front the rest of them will slide down to fill in the gap. I cannot see Randy from my vantage point, but I will be able to see if he picks up milk by watching the cartons on the conveyor. Finally, suppose that I can hear Randy whistling as he walks around the store, and I hear him walk past the milk. By watching the milk cartons I see that none of them are removed, and hence I see that Randy is omitting to pick up milk. But since I do not see Randy himself, I do not actually see him omit to pick up milk. To see that (14b) does not entail (14a), suppose I am walking behind Theresa, so I cannot see her face. Suppose also that I know that Theresa has a peculiar habit of rubbing the back of her head when she smiles. Now Bill comes walking in our direction. It seems that by watching her arms and/or the back of her head, I can know whether or not Theresa is smiling at Bill. If she does not rub the back of her head, I can thereby see that she is successfully refraining from smiling at him. But because I cannot see her face, I do not actually see her refrain from smiling.

A neo-Davidsonian analysis of negative action sentences, on which they quantify over omissions and refrainments, explains these features. First, we analyse ‘Randy omits to pick up milk’ and ‘Theresa refrains from smiling, ’ schematically, as:

Since (15) reports the existence of an event of Randy omitting to pick up milk, we can analyse (13a) as reporting that I see that event, and likewise for (16) and (14a):

By contrast, (13b) and (14b) report that I have a certain attitude towards the propositions expressed by (15) and (16), respectively.

The explanation of the semantic features of (13a)–(14b) works just as before. (13a) and (14a) are reports of object-perception, and since ‘Randy’ and ‘Theresa’ are parts of the descriptions of the objects seen – namely, Randy’s omission and Theresa’s refrainment, respectively – they occur in a transparent context. By contrast, in (13b) and (14b) these names occur inside the scope of a propositional attitude operator, and so they are in an opaque context. Further, because (13a) and (14a) simply report that I see an event satisfying a certain description, they do not entail that I see that there is such an event. And while (13b) and (14b) do report perceptual knowledge that there is such an event, they entail nothing about what it is I see which gives me that knowledge.

Such considerations don’t suffice to show that a neo-Davidsonian semantics for negative action sentences is correct, since a deflationist might be able to account for the features of (13a)–(14b) on her own terms. The deflationist faces no serious obstacles in analysing the (b)-sentences. She can agree that they are reports of propositional attitudes, and simply insist that the relevant propositions get negative-existential analyses. The trouble comes with the (a)-sentences. The deflationist must try to get the benefits of treating these sentences as reports of object-perception, without treating them as reporting that I see certain events, namely Randy’s omission and Theresa’s refrainment. But then, what sort of object do these sentences report me as seeing?

It might seem obvious what a deflationist should say: the (a)-sentences report that I see absences. But this answer faces two problems. First, it requires a commitment to realism about absences, which most philosophers, deflationists included, would rather avoid. Second, this answer gets the truth-conditions for the (a)-sentences wrong. If absences can be seen then they must apparently be located in space and time, and anyone who sees an absence must have perceptual access to that spatiotemporal location. Now, intuitively, an absence of Fs is located at the relevant place where there are no Fs, so if Randy’s omission to pick up milk is an absence, it must be located at the relevant place where there is no event of his picking up milk, and for me to see this absence I must have perceptual access to that location. But this line of reasoning suggests that (13a) is true in cases where it is intuitively false. Recall that, in order to see Randy omit to pick up milk, I must see Randy (that, after all, is why I cannot see him omit to pick up milk when I am hiding in the milk cooler). Now suppose that I am waiting for Randy at the grocery store, but this time I am not hiding in the milk cooler, but out on the main floor with a clear view of the milk shelf. It seems that I am in a very good position to see the absence of events in which Randy picks up milk – if that absence is located at the grocery store, it is surely located more specifically at or around the milk shelf. But now suppose further that Randy is not in the grocery store. It seems that, precisely because I cannot see Randy, I cannot see him omit to pick up milk – although I can see that he is omitting to pick up milk. This is a case where (13a) should be false, but, because I apparently have a clear view of the absence, the deflationist proposal counts it as true.

Likewise, this answer counts (13a) as false when it is intuitively true. Modify the above case so that, instead of waiting for Randy at the grocery store, I am sitting in the passenger seat of his car as he drives home. It seems that, precisely because I can see Randy, I can see him omit to pick up milk. But because I am nowhere near the grocery store, I cannot see the absence of picking-up milk events at the grocery store. Thus, the deflationist proposal counts (13a) false when it should be true.

A second answer that a deflationist might give is that (13a) and (14a) report that I see the relevant person, at the time that they omit/refrain:

This semantics captures the fact that I must see Randy in order to see him omit to pick up milk. It also places ‘Randy’ and ‘Theresa’ in transparent contexts, and it explains the logical independence of the (a)- and (b)-sentences, since I can see Randy while he omits to pick up milk without seeing that he is omitting to pick up milk, and vice versa.

Unfortunately, this proposal still gets the truth-conditions of the (a)-sentences wrong, because while seeing the relevant agents is necessary for their truth, it is not sufficient. Recall the example where I am walking behind Theresa and cannot see her refrain from smiling, but can know by looking at her arms and the back of her head that she is refraining from smiling. This is a case where (14a) should be false. But (14a*) comes out true in this case, since as Theresa refrains from smiling, I see her by virtue of seeing the back of her. So (14a*) cannot provide the right analysis of (14a). Similarly, (13a*) cannot be right analysis of (13a). Suppose I am hiding from Randy in the milk cooler, as before, but this time suppose that my view of him is not completely obstructed, and I have a clear view of him from his knees down to his feet. It is clear that, in this case, I can see Randy. But it is equally clear that I cannot see him omit to pick up milk. Even if I see that the milk cartons remain undisturbed, and hence can see that he is omitting to pick up milk, I do not actually see him do this. Thus (13a*) can be true while (13a) is false.

In order to see someone while they perform a negative action, it suffices to see some part(s) of that person. But in order to see someone perform a negative action, it does not suffice to see just any part(s) of that person. Rather, there are certain parts that I must see. If I can see Theresa’s face, and in particular her mouth and cheeks, then I can see her refrain from smiling, but if I am walking behind her and unable to see her mouth or cheeks, then I cannot see her refrain from smiling. Likewise, if I can see Randy’s arms, then I can see him omit to pick up milk, but if I am hiding in the cooler and unable to see anything above his knees, I cannot.

Note that the same point holds for positive actions. It is not sufficient, for (11a) to be true, that I see Brutus at the time that he stabs Caesar; if my view is obscured so that I cannot see anything above Brutus’ knees, then although I see Brutus as he stabs Caesar, I do not actually see him stab Caesar. This suggests that a similar explanation for the insufficiency applies to both positive and negative actions.

In the case of positive actions, the natural explanation why seeing someone while they φ does not suffice for seeing them φ appeals to the idea that actions are events: seeing someone while they φ is not generally sufficient for seeing the event of their φ-ing. For instance, in the scenario where I cannot see anything above Brutus’ knees, I see Brutus but I do not see the event that is his stabbing Caesar. For that event does not involve all parts of Brutus’ body, but only those parts that he actually uses to do the stabbing. Since he does not use his legs to do the stabbing, they are not involved in the event, and so seeing them does not allow me to see that event.

If negative actions are events – and in particular, events of the sort I claimed they are in the previous section – we can give a parallel explanation why the truth of (13a*) and (14a*) does not suffice for the truth of (13a) and (14a). When Theresa refrains from smiling, she does something her doing of which ensures that she does not smile at that time, and it seems that only her mouth and cheeks are involved in this ensuring-event. After all, smiling is something Theresa would do with her mouth and cheeks: in order to smile, she must move the muscles in and around her mouth in certain ways; it does not matter what she does with any other parts of her body, so none of those parts are involved in an act of smiling. Thus, in order to ensure that she does not smile, she must do something with her mouth and cheeks, her doing of which is incompatible with smiling. Since that doing is her refrainment, I must see her mouth and cheeks in order to see her refrain from smiling.

Likewise, when Randy omits to pick up milk, he does something his doing of which ensures that he does not pick up milk at that time, and it seems that only his arms are involved in this ensuring-event. After all, picking up milk is something Randy would do with his arms: in order to pick up milk, he must move at least one of his arms in a certain way; it does not matter what he does with any other parts of his body, so none of those parts is involved in an act of picking up milk. Thus, in order to ensure that he does not pick up milk, he must do something with his arms, his doing of which is incompatible with picking up milk. Since that doing is his omission, I must see his arms in order to see him omit to pick up milk.

So, not only do (13a*) and (14a*) get the truth-conditions of (13a) and (14a) wrong, but the natural explanation of why they do so is that negative actions are events. My account gets the truth-conditions right, and moreover gets them right for the right reason.

We have increasingly compelling reasons to think that (13a) and (14a) report that I see an event of some kind. In particular, we have good reason to think they report me as seeing an event which ensures that the agent does not do the relevant thing. As a last-ditch effort to account for the semantic features of these sentences, a deflationist might try to accept that conclusion while denying that the event I see is a negative action, thereby denying the need to construe simpler negative action sentences as quantifying over events. In making this move, the deflationist adopts my own semantics for (13a) and (14a), but she maintains that ‘Randy omits to pick up milk’ and ‘Theresa refrains from smiling’ have negative-existential form and that (13b) and (14b) report an attitude towards these negative-existential propositions.

It is precisely this combination of commitments – that the (a)-sentences quantify over ensuring-events while simpler negative action sentences do not – that generates the first problem for this proposal, namely, that it cannot give a satisfactory account of how the meanings of (13a) and (14a) are constructed from their parts.

Consider again (11a), ‘I see Brutus stab Caesar’, and (12), ‘Brutus stabs Caesar’. As we saw, a compelling analysis of (11a) treats it as quantifying over (at least one) event which is a stabbing of Caesar by Brutus. I left it as an intuitive point that we can achieve this analysis by likewise treating (12) as quantifying over such events, but in fact the neo-Davidsonian analysis of (11a) strongly constrains us to give this analysis of (12), in order to give an account of how the meaning of (11a) is constructed from the meanings of its parts. In particular, we must say which word or phrase in that sentence accounts for the presence of the event-variable for stabbings of Caesar by Brutus. We obviously cannot treat the word ‘see’ or the phrase ‘I see’ as contributing this event-variable, since not every sentence that reports a seeing, or a seeing by me, quantifies over such events – the sentence ‘I see the Statue of Liberty’ does not, for example. By analysing (12) as an existential quantification over stabbings of Caesar by Brutus, we can treat the phrase ‘Brutus stab Caesar’ in (11a) as contributing that variable. Thus, a neo-Davidsonian analysis of (11a) constrains us to give a neo-Davidsonian analysis of (12).

The same reasoning applies to (13a) and (14a), on one hand, and (15) and (16), on the other. (13a), ‘I see Randy omit to pick up milk’, is analysed as quantifying over (at least one) event which is an ensuring, by Randy, that he does not pick up milk, and so we must say which word or phrase in that sentence accounts for the presence of the variable for such events. We obviously cannot treat the word ‘see’ or the phrase ‘I see’ as contributing this event-variable, since not every sentence that reports a seeing, or a seeing by me, quantifies over such events. By analysing (15), ‘Randy omits to pick up milk’, as an existential quantification over ensurings, we can treat the phrase ‘Randy omit to pick up milk’ in (13a) as contributing that variable. Similar remarks apply to (14a) and (16). Thus, if we accept a neo-Davidsonian analysis of (13a) and (14a), compositionality constrains us to give a neo-Davidsonian analysis of (15) and (16). The deflationist proposal under consideration violates this constraint by accepting my analysis of (13a) and (14a) as existential quantifications over ensurings, while denying that the simpler negative action sentences (15) and (16) quantify over such events.

The second problem with this deflationist proposal is that, while it can get the truth-conditions of the (a)-sentences correct by piggybacking on my account, it makes those truth-conditions mysterious. If, as the deflationist insists, the fact that Randy omits to pick up milk is not a matter of the occurrence of an event, then why should the fact that I see him omit to pick up milk be a matter of my seeing an event?

The deflationist might try for an epistemological explanation. Seeing x φ is distinct from knowing, on the basis of perception, that x is φ-ing. Nonetheless, it seems that seeing x φ often puts one in a position to know that x is φ-ing. So, the deflationist might say, seeing Randy omit to pick up milk is being in a position to know that he is so omitting, and to be in this position by virtue of seeing Randy. And the obvious way to achieve this is by seeing those parts of Randy’s body that would be involved in an act of picking up milk, were he to perform such an action.

Unfortunately for the deflationist, seeing those parts of x that would be involved in a φ-ing event is generally neither necessary nor sufficient even for being in a position to know on the basis of visual perception of x that x is not φ-ing. My original case in which (14b) is true but (14a) is false shows that it is not necessary: neither Theresa’s arms nor the back of her head would be involved if she were smiling, but I am still in a position to know that she is not smiling by seeing these parts of her body – indeed, I actually know this.

To see that it is not sufficient, consider a case in which I am on the main floor of the grocery store with a clear view of the milk shelf, but that this time Randy has actually come to the store. I see Randy stop in front of a shelf holding both cartons of milk and cartons of cream, but that I am far enough away that I cannot distinguish between the two kinds of carton. I can see both of Randy’s arms, and hence can see the parts of his body that would be involved in an act of picking up milk, were he to perform one. I see Randy grab a carton, put it in his basket, and walk on. If Randy has just omitted to pick up milk, then I have just seen him do so. And yet I am not in a position to know, on the basis of perception, whether or not Randy has picked up milk. Thus, unlike my neo-Davidsonian account, the proposal does not provide a satisfying explanation of the truth-conditions of (13a) and (14a).

I have considered three ways in which a deflationist might account for the semantic features of (13a)–(14b) without taking negative action sentences to quantify over omissions and refrainments. From a semantic perspective, my view outmatches any of these deflationist proposals. Thus, taking a neo-Davidsonian approach to negative action sentences is not just one way of accounting for the data. It is also the best way.

Notes on contributor

Jonathan D. Payton is a PhD student in the Department of Philosophy at the University of Toronto. His interests are in the philosophy of action, general metaphysics, and topics at their intersection. At the time of writing, he is preparing to defend his dissertation, ‘The Metaphysics of Negative Action’, which was funded by a Joseph-Armand Bombardier Doctoral Scholarship from the Social Sciences and Humanities Research Council of Canada.

Funding

This work was supported by Joseph-Armand Bombardier Doctoral Scholarship, awarded by the Social Sciences and Humanities Research Council of Canada [767-2013-1375].