Acts and Embodiment

The theory of embodiment is used in providing an account of the identity of acts and in providing solutions to various puzzles concerning acts.

I wish in this paper to consider how the theory of embodiment outlined in some earlier papers of Fine (1982Fine ( , 1999Fine ( , 2006 can be applied to questions concerning the identity of acts. This will involve going over some old ground. But I also hope to elaborate on what I previously said and to relate it to some of the more recent literature on the topic. 1 I distinguish the question 'what is it to act?' from the question 'what is an act?' ( §1). My focus is almost entirely on the second question. I propose a pluralist position on the identity of acts (under which the act of shooting and the act of killing are not one and the same) and, although I do not provide a full defense of pluralism, I do argue that one of the principal arguments proposed in favor of the opposing monist position is not sound and can be seen, under proper consideration, to favor the pluralist position ( §2). I outline the theory of embodiment that I have developed in other work ( §3) and then use the theory to explain what the distinct acts posited by the pluralist might plausibly be taken to be ( §4). I use the resulting application of the theory to deal with some vexed questions concerning when an act occurs, the essential properties of an act, what it is to perform one act by performing another, and the relationship between acts and activities ( §5). I know of no other view, monist or pluralist, that is able to deal so satisfactorily with these questions and this, to my mind, along with the plausibility of the corresponding view for material things, provides strong abductive evidence in its favor ( §5). §1 TWO QUESTIONS We may distinguish two questions from within the theory of action. The first -and, from the perspective of action theory, more important -question is 'what is it to act?'. What, for example, is it to raise my arm or, more generally, what is it for A to φ, where A is a doer (such as a person) and to φ is to do something (such as raise one's arm)?
The second -and, from the perspective of action theory -less important question is 'what is an act?'. What, for example, is the (token) act of raising my arm or, more generally, what is the (token) act of A's φ-ing, for any doer A and doing φ?
I hope it is clear that these are distinct questions. I hope it is also clear that their answers will be largely, if not wholly, independent of one another. 2 Consider the analogy with knowledge. We might ask 'what is it to know that p?'. But we might also ask what is knowledge, i.e. a case of knowing? To the first question, we might answer 'to know that p is to truly and justifiably believe that p' and, to the second question, we might answer 'knowledge is a belief had in circumstances in which one knows what one believes'. But the answer to the first question in no way dictates the answer to the second question or the second to the first.
The first of our questions is conceptual; it is concerned with the concept of acting, of what it is to act. The second question is ontological; it is concerned, not with the concept of acting but with the objects that are the acts. In both cases we wish to understand the nature of something -but it is something predicative in the first case and something objectual in the second case (cf. Correia 2006).
Discussion of the two questions are often run together. Thus in Davidson (1971), one finds a view both about what it is to act (in terms of a bodily movement having a certain kind of cause) and about what acts are (bodily movements). But my concern in what follows will be exclusively with the ontological question; and, indeed, I will try as far as possible to make my discussion of this question independent of any particular view one might adopt on the conceptual question.
In considering the ontological question, it is important to use locutions that clearly and unambiguously designate acts. It has been common in the philosophical literature to designate 1 This paper was originally intended for a volume that never saw the light of day. I wish to thank Alec Hinshelwood for referring me to some of the recent literature on action theory, to thank Adam Przepiórkowski for some helpful comments and referring me to some of the related literature in linguistics, and to thank the referees of earlier versions of the paper for very helpful comments.

2
Cf Fine (1982: 101-2). Ginet (2012: 70), voices a similar sentiment. Metaphysics DOI: 10.5334/met.98 acts by means of gerund expressions such as 'Smith's shooting the gun' or 'Smith's shooting of the gun'. But it is not altogether clear what such expressions designate or, if they do designate, that they are unambiguously used to designate acts. 3 Suppose that Bill and Sue get married and, to save time (they are New Yorkers), they simultaneously say 'I do', thereby tying the knot. Now one might very well think that the phrases 'Bill's marrying Sue', 'Sue's marrying Bill' designate -or, at least, can be used to designate -the very same thing, the event perhaps of the two getting married. 4 But Bill's act of marrying Sue is clearly different from Sue's act of marrying Bill, since the agent of the first is Bill, not Sue, and the agent of the second is Sue, not Bill. But this then means that it cannot be the case, on the proposed view, both that the expression 'Bill's marrying Sue' designates Bill's act of marrying Sue and that 'Sue's marrying Bill' designates Sue's act of marrying Bill ; and this might lead one to think, more generally, that the gerund expressions designate -or, at least, can be used to designate -events that are not the same as any particular act.

Fine
In order to avoid any possible ambiguity or unclarity on this score, it would be preferable to avoid the use of such bare gerund expressions in designating to acts. What I would like to propose instead is that we make use of such locutions as 'Smith's act of shooting' or 'the act of Smith's shooting', in which the reference to a (token) act is made explicit. If any expressions designate acts, then these surely do and there can be no ambiguity in their designating acts rather than something else. §2 PLURALISM The question we face is: what is an act? But there is a preliminary question whose answer very much shapes our answer to this question. Suppose Smith shoots a gun and thereby kills Jones. There is then Smith's act of shooting the gun and Smith's act of killing Jones. Are these acts identical or not?
If they are identical then there is no further question to be answered as to how they are related. Moreover, if we go on to say that Smith's act of shooting the gun is identical to a certain movement of his body, then the question of the nature of acts (or, at least, of bodily acts) can be subsumed under the question of the nature of bodily movements. If, on the other hand, the acts are not identical, then we owe an explanation of how they are related. We also owe an explanation of how all these different acts can co-exist. For there is a clear sense in which if Smith shoots the gun then there is nothing more that he must do in order to kill Jones. But if there is nothing more that he must do then how, all the same, does he get to do more?
Monists such as Davidson (1971) and Anscombe (1957) claim that the acts are identical; pluralists such as Goldman (1970) deny that they are identical. I am a committed pluralist and have attempted to argue for the doctrine, though largely in regard to material things, in a number of previous papers. 5 However, it is not my aim here either to repeat his arguments or to review the extensive literature on the topic. I merely wish to point out that the standard monist response to the pluralist does not in fact work, even in those cases which might appear to be most favorable to the monist's position. 6 The pluralist may initially be tempted to argue that Smith's act of shooting is not identical to Smith's act of killing since the one, we may suppose, is intentional while the other is not. To this the obvious monist response is that the predicate 'intentional' is intensional. Whether an act is intentional may depend not only on the act that is designated but also on how it is described. So there is but a single act here, intentional under the description shooting (since Smith intended to shoot) but not intentional under the description killing (since Smith did not intend to kill). 3 See Bach (1980: 119 fn. 2) and, for a more recent discussion of the syntax and semantics of ing-expressions see Grimm & McNally (2015). 4 Goldman (1974: 14) and Ginet (2012: 51) appeal to similar examples, though to somewhat different ends.

6
This follows up on a theme from Fine (1982) and is further developed in §5 of Fine (2003). Fine Metaphysics DOI: 10.5334/met.98 At this stage in the argument, most pluralists would be willing to concede the monist's point (they might even agree that 'intentional' is intensional) and would attempt to replicate an argument of this sort with predicates whose extensionality is not in doubt. But in actual fact, the monist's response is not even plausible in this particular case.
The monist no doubt has familiar intensional predicates like 'look for' in mind. Thus the police may be looking for the murderer, not the mayor, even though the murderer is the mayor, since they are searching for this one person under the description murderer, not mayor. Strictly speaking, the sentence 'the police are looking for the mayor' has two readings: under the more natural 'de dicto' or narrow scope reading, it means that they are looking for the person who is the mayor under that very description; and under the less natural 'de re' or wide scope reading, it means they are looking for the person who is in fact the mayor, though not necessarily under that description. And this is, in general, how intensional predicates work. When a description occurs within their scope, the resulting sentence may either have a de re or a de dicto reading. 7 But this is not how it is for 'intentional'. I have been talking about Smith's act of killing Jones. Consider the sentence 'The act I was talking about was intentional'. Then this can only have a de re meaning, to the effect that the act of killing was intentional; it cannot mean that the act was intentional under the description of my talking about it. Consider now the sentence 'Smith's act of killing was intentional'. Presumably, the monist will take the locution 'Smith's act of killing Jones' to be equivalent to some such description as 'the act that caused Jones' death'. 8 So, again, the sentence should have two readings. But it can only have one reading -in this case, the de dicto reading to the effect that the act was intentional under the description of being a killing. 9 It therefore looks as if there are two ways of specifying an act, one merely descriptive of the act, telling us how the act is (as in 'the act I was talking about') and the other definitive of the act, telling us what the act is (as in 'the act of killing'). When the first is used, the resulting sentence is only capable of a de re reading and, when the second is used, the resulting sentence is only capable of a de dicto reading. In neither case, do we have -or normally have -an ambiguous reading, as one would expect under the usual forms of intensionality.
Why, then, might it be correct to say that the act of shooting was intentional but not the act of killing? The most plausible explanation, it seems to me, is not that we have some hitherto undreamt of form of intensionality (that is insensitive to some of the different ways in which the act might be described) but that the difference in how the act is defined (as a shooting or a killing, say) will lead to a difference in what the act is.
It might be thought that there are examples on the other side that show the intention-predicate to be straightforwardly intensional. For I might say that Smith's act of killing Jones was intentional but not Smith's act of killing the mayor (since Smith did not intend to kill the mayor even though Jones is the mayor). But the scope ambiguity in this case is plausibly attributed, not to the predicate 'intentional', but to the operator 'the act of'. For in the context 'the act of Smith's killing -', 'the mayor' can have either narrow or wide scope, and it is the scope ambiguity of 'the mayor' in the narrower rather than the broader context that accounts for the two readings.
It is ironic that Davidson explains the adverbial modification of action verbs in terms of adjectival modification, since the two function rather differently. Adverbs characteristically serve to define an act. Thus 'Smith's act of singing loudly' defines the act as loud and the act can only properly be said to be intentional if Smith intended to sing loudly. Adjectives, by contrast, can be used either 7 Perhaps both readings also arise for extensional predicates, but they will not lead to any difference in truth value as long the description designates.

8
Cf. Davidson (1971: 229), "To describe an event as a killing is to describe it as an event (here an action) that caused a death". Metaphysics DOI: 10.5334/met.98 to define or to describe an act. Thus 'Smith's loud act of singing' can be used either to describe or to define the act as loud and so the act can properly be said to be intentional even if Smith did not intend to sing loudly. This therefore suggests that there is something fundamentally misguided in treating all of the various forms of adverbial modification as merely different ways of describing a given act.

§3 THE THEORY OF EMBODIMENT
The pluralist faces a problem: what are these different acts -the shooting, the killing etc., and how are they related?
I wish to answer these questions by appeal to the theory of embodiment. I shall here provide the briefest of expositions, emphasizing the points of special interest, since I have given a fuller exposition elsewhere.
The theory has two parts: a theory of rigid embodiment, which deals with objects whose constitution or matter is rigid; and a theory of variable embodiment, which deals with objects whose constitution or matter can vary. For now, we shall simply be interested in the theory of rigid embodiment.
Rigid embodiments can be monadic or polyadic, depending upon whether their matter is singular or plural. For the purpose of explaining individual actions, we can confine our attention to monadic embodiments, although, for the purpose of explaining group actions, we might also wish to appeal to polyadic embodiments (whose plural 'matter' is the acts of the different agents).
The basic idea behind rigid embodiment is that an object and a property or description of the object can come together to form a new object -an object which results, so to speak, from imposing the property upon the given object. 10 We might call an object obtained in this way a qua object and, where b is the given object and φ the property, we might designate it as 'b qua φ' or as 'b under the description φ', and notate it as 'b/φ'. Thus if b is Socrates and φ is being a philosopher, the new object will be Socrates under the description of being a philosopher, while if b is Smith's act of shooting and φ is being a killing then the new object will be Smith's act of shooting under the description of being a killing.
Given a qua object b qua φ, we call b its basis and φ its gloss. It is essential to our understanding of a qua object that it is not identical -or, at least, not generally identical -to its basis. Socrates qua philosopher is not simply Socrates. It is rather some sort of amalgam of the basis and the gloss in which the gloss preserves its predicative role and somehow serves to modify or qualify the basis. Qua objects are governed by certain principles, the most important of which for our purposes are listed below. 11 It is understood that these principles should hold of necessity and hold of any possible objects: º Existence A qua object b/φ exists if and only if b exists and possesses φ.
º Identity Two qua objects are the same iff their bases and glosses are the same.
º Inheritance Given that a qua object exists, it will have exactly the same ordinary properties as its basis.
º Part Both b and φ are parts of b/φ.
º Foundation There is no sequence of objects a 1 , a 2 , a 3 , … , with a 2 the basis for a 1 , a 3 the basis for a 2 , and so on ad infinitum.
A few comments on these principles: Fine Metaphysics DOI: 10.5334/met.98 (1) Identity justifies us in talking of the basis or the gloss of a qua object, for if the qua object a = b/φ, then b and φ must be unique. The principle leaves open when two properties φ and ψ are the same and different views might, of course, be had on this question.
(2) Inheritance does not have unrestricted application to all properties whatever. A qua object b/φ will be a qua object, for example, even though b may not itself be a qua object. The intuitive idea is that Inheritance should only hold when the application of the property to an object does not depend upon its status as a qua object. Although it is hard to be more precise, we certainly will want Inheritance to apply to all locational properties. Thus given that the basis has a location in space (time), it will follow that: Location Given that the qua object exists, its temporal (spatial) location is the same as the temporal (spatial) location of its basis.
(3) According to Part, both the basis and the gloss will be part of the qua object. This means that if the gloss itself has parts then they will also be part of the qua object though, presumably, not in the same way as the basis.
(4) Rigidity is a modal principle. There is a corresponding essentialist principle to the effect that if a is the qua object b/φ then it is essentially the qua object b/φ. Thus according to the essentialist principle, it will lie in the very nature of a qua object to be the qua object that it is.
(5) According to Foundation, any sequence of objects a 1 , a 2 , a 3 , … , with each a k+1 a basis for a k , must eventually terminate in an object a n which is not a qua object. Moreover, given Identity, any such sequence will be unique. Thus each qua object a will be uniquely of the form (… ((c/φ 1 )/φ 2 )… /φ n ) for some c that is not itself a qua object. We might in this case call c the ultimate basis or core of a (as opposed to the immediate basis b of b/φ).
Acts may be summed or compounded. Consider, for example, the act of simultaneously turning my head and scratching my nose. This is the sum or compound of the act of turning my head and the act of scratching my nose. In this case, the component acts occur at the same time and are of the same agent. But we might also sum acts of the same agent which occur at different times, thereby obtaining a sequential act, and we may also sum acts of different agents, thereby obtaining a group act (though in a very thin sense of the term).
In order to accommodate acts of this sort, we should allow the objects of our theory to be summed. Thus given objects a 1 , a 2 , a 3 , … , we allow there to be an object a = a 1 ⊔ a 2 ⊔ a 3 ⊔ … that is the sum or compound of a 1 , a 2 , a 3 , … . In such a case, a 1 , a 2 , a 3 , … will be parts of a. However, the sense of part is somewhat different from the sense in which the gloss φ or its parts are a part of the qua object b/φ, and we shall talk of component parts, or components, a 1 , a 2 , a 3 , … in the case of a sum and of an aspectual part in the case of a gloss.
The operation ⊔ of summation is governed by some standard principles, which can be found in any standard text on mereology. However, there are also two important principles governing its interaction with the operation/of glossing: Separation Suppose that a 1 , a 2 , a 3 , … are all the qua objects which are components of a. Then a is the sum of a 1 , a 2 , a 3 , … with a unique object aʹ (possibly null) that has none of a 1 , a 2 , a 3 , … as a component part; According to Separation, we may separate out the qua objects which are component parts of any given object, leaving a unique 'remainder' that has no qua objects as its component parts. If we think of qua objects and sums of qua objects and other objects as being successively generated, then it is hard to see how this principle might fail. According to Distribution, we may distribute the operation of glossing across conjunction (though conjunction on the objects then converts to summation). 12 20 Fine Metaphysics DOI: 10.5334/met.98 §4 ACTS AS EMBODIMENTS I now wish to apply the theory of embodiment to the nature of acts -first, in this section, connecting the ontology of qua objects with the ontology of acts and then, in the next section, connecting the behavior of qua objects with the behavior of acts. In applying the theory in this way, I can perhaps be seen to have provided something analogous to a scientific model. There is, on the one hand, a theoretical domain of qua objects, as given by the theory of embodiment. There is, on the other hand, a pre-theoretical domain of acts and events as given, so to speak, by our ordinary judgement or 'observation'. We then attempt to correlate the objects and properties in the pre-theoretical domain with the objects and properties of the theoretical domain in such a way that the observed behavior of the objects of the pre-theoretical domain can be understood in terms of the predicted behavior of the objects with which they have been correlated. Ideally, the pre-theoretical and theoretical domains and the connection between them would be described with complete precision, though we are far from having done anything so complete or precise.
In applying the theory, we face a critical question. Suppose we take Smith's act of killing to be a qua object. It will then be of the form (… ((c/φ 1 )/φ 2 )…/φ n ) for some core object c that is not itself a qua object. The question then is: what is the core c? We may plausibly suppose that each of the intermediate qua objects (c/φ 1 ), (c/φ 1 )/φ 2 …, (… ((c/φ 1 )/φ 2 )…/φ n−1 ) is also an act. Thus in the case of Smith's act of killing, its immediate basis is perhaps Smith's act of shooting, the immediate basis of this act is then perhaps his pulling the trigger, and so on. But what of c itself? 13 There are perhaps two main answers to this question, corresponding to the two leading monist positions. 14 According to the first, the core c is something like an act of trying or willing, so that it is acts 'all the way down'. However, c might well be taken in this case to be a mental, rather than a bodily, act and, unlike other acts, it will not itself be a qua object. According to the second answer, the core c is the movement of a body. Whether c is itself an act is not so clear. Although many monists might take it to be so, it is perhaps most plausibly taken in the present context not to be an act but some kind of 'act-neutral' event. Acts would then issue from bodily movements by placing them under a suitable gloss. One might, however, also take c itself to be an act. In this case, it will again be acts all the way down but with a bodily, rather than a mental, act as the core.
From the present point of view, monists who take acts to be volitions or bodily movements may have got something right. For they may have correctly identified the core of any act even though they have incorrectly identified each act with its core.
In Fine (1982), I had proposed taking the core of any bodily act to be a bodily movement. I am now more inclined to think of it as something mental, like an act of trying or willing; and this is what I shall assume in what follows. 15 However, much, though not all, of what I say can be modified so as to accommodate alternative views as to what the core might be.
There are some related questions concerning the gloss. One question concerns the identity of the glosses which can occur in an act. Suppose that c is an act of willing. Then for which glosses φ 1 , φ 2 , … , φ n is (… ((c/φ 1 )/φ 2 )…/φ n ) an act? I myself am inclined to adopt a permissive attitude under which any modification of c will result in an act, although one can envisage adopting less permissive views under which the glosses should be reasonably determinate, for example, or relate specifically to the circumstances or consequences of the act. 13 In considering this and some other questions, I have ignored the complications that arise from the existence of compound acts. The notion of core here is somewhat reminiscent of Ginet's notion of an ultimate core (Ginet 2012:51), though he provides no real account of what it is or of how it might give rise to a 'layered structure'.
14 As found in Davidson (1971) and the earlier work of Hornsby (1980), for example, although Hornsby takes a bodily movement, in the relevant sense, also to be a trying.
15 The mental pluralist faces some of the same difficulties as the mental monist; there is, for example, a question for both of them as to whether acts can be observed (Hyman 2015: 57). I believe that these difficulties can be metand, indeed, have been largely met in the work of Hornsby and others. I might also note note that Hyman's view on the identity of acts (2015: §3.2) could be seen to be a very special case of the present view, in which the result of an act is incorporated into the gloss. But this is not the place to discuss such questions. Another question concerns, not the existence of acts, but our reference to acts. Suppose we provide an ordinary specification of an act (such as 'Smith's act of killing Jones'). Then to which act, given that it is a qua object, will we be referring? What is the relationship between the specification of the act and the constitution of the qua object?
The answer will depend, of course, on how we specify the act. As we have already observed, some aspects of a specification will be merely descriptive of the act ('the act I was talking about') whilst others will be definitive of the act ('the act of killing'). The role of the descriptive aspects would appear to be relatively unproblematic since we may plausibly assume that, for any specification α of an act, there will be a purely definitive specification β that picks out the very same act (we might think of β as a 'canonical' specification of this act).
But what of the definitive aspects? They presumably tell us something about the gloss. But what exactly? Consider again 'Smith's act of killing' and let us suppose that it refers to a qua object of the form b/φ. Then what is φ?
There are a number of answers that might plausibly be given. My own view is that, depending upon the context, there may be some indeterminacy in what we should take the act to be. It could, for example, be the mere act of killing someone (as when Smith shoots indiscriminately into a crowd) or the act of killing a particular person (as when Smith aims his gun on Jones). In the first case, the gloss will be the property of being a killing while, in the second case, it will be the property of being a killing of Jones. Thus the gloss will itself have a kind of core and the various acts will result from some more or less specific elaboration of the core. Something similar may hold of the intermediate glosses φ 1 , φ 2 , … , φ n−1 though, in this case, I am inclined to think that the glosses should be taken to be relatively specific and determinate.
If, on this view, we ask whether Smith's act of killing is the same as his act of killing Jones, then no determinate answer can be given since, on one way of construing the respective specifications, they will refer to the same act while, on another way of construing them, they will refer to different acts. We may thereby steer a middle course between the extreme fine-grained view of act identity found in Goldman (1970) and the more moderate fine-grained view found in Thomson (1971b) and Ginet (2012).
A further question concerns the relationship between what one might call 'vertical' and 'horizontal' glossing. Suppose that ψ is a property of a qua object a of the form b/φ. Then there are two ways in which we may form a qua object from ψ and a. Under vertical glossing, we form the 'layered' qua object a/ψ (= (b/φ)/ψ) in the usual way. But under horizontal glossing, we form the 'leveled' qua object b/(φ ∧ ψ) (which is plausibly the same as b/(ψ ∧ φ)). Thus, in the one case, we impose the property ψ upon the qua object b/φ and go one step up in the hierarchy of qua objects, and, in the other case, we impose the property ψ within the qua object b/φ and stay at the same level in the hierarchy.
Given that the property ψ is involved in the formation of a qua object corresponding to the specification of an act, the question therefore arises as to whether the qua object is obtained through a vertical or horizontal form of glossing. Consider, for example, the act of singing and suppose it to be a qua object of the form b/φ. Then is the act of singing in the rain a qua object of the form (b/φ)/ψ, where ψ is being in the rain, or is it a qua object of the form b/(φ ∧ ψ)?
There are a number of rough tests to determine which it should be. One is whether we can properly say that the one act is simply done by means of the other (more on by later). Thus the act of singing loudly in the rain is not simply done by singing loudly and, likewise, the act of singing loudly is not simply done by singing. On the other hand, the act of killing is simply done by shooting.
Another test is whether we can regard the act as a compound of two other acts, corresponding to φ and ψ. For given the Distribution principle above, the qua object b/(φ ∧ ψ) which results from horizontal glossing will also be identical to the compound act (b/φ) ⊔ (b/ψ). Thus the act of singing loudly in the rain may plausibly be taken to be the compound of an act (b/φ) of singing loudly and the act (b/ψ) of singing in the rain (where the underlying singing is the same). On the other hand, the act of killing (which we may take to be of the form (b/φ)/ψ) cannot very well be regarded as the compound of the act b/φ of a shooting and the act b/ψ of killing. We therefore see that there are a number of questions that need to be taken into account in considering how the specification of an act correlates with a qua object. We must somehow distinguish between the descriptive and definitive aspects of the specification; we need to be able to identify a core; we need to ascertain how determinate or specific the gloss should be; and we need to be able to tell whether a potential gloss should be configured horizontally or vertically.
One very general feature of our account is that we cannot, as a rule, read off the constitution of a qua object from the specification of the act but must also take the circumstances into account. Thus I might specify an act as a killing, but only the circumstances can tell me whether its basis should be a shooting, say, or a stabbing.
Although both we and the world will contribute to determining what the act should be, it is not altogether clear what their respective contributions are or how they come together. We might say, at a high level of abstraction, that the Mind imposes an order or template on the world and the world then determines how the order or template is realized. Thus we will tend to think of the acts as classified into kinds (a killing, an uttering, a sitting) just as we think of material things as classified into kinds; we will tend to think of them as constituted 'vertically' by their causal ancestry (a killing by a shooting, for example) just as we tend to think of material things are constituted by their natural division into parts; and we will tend to think of the acts as constituted 'horizontally' by the circumstances in which they are taken to occur. 16 Reference is then to what in the world best satisfies the specification and conforms to the order.
However, the classification and constitution of objects seems much less clear in the case of acts (and events more generally) than in the case of material things; and it would appear to be a large and difficult question to set out in convincing detail the order or template through which they are determined. 17

§5 THE APPLICATION OF EMBODIMENT THEORY TO ACTS
The present section considers how we might understand the behavior of acts in terms of the embodiments with which they are correlated, and it constitutes the heart of the paper. I shall consider four topics in allthe timing of acts, their essential properties, the by-relation, and activitiesalthough there are a number of other important topics that I might also have considered.

THE TIMING OF ACTS
Smith shoots Jones on Tuesday and Jones dies from the wounds the next day. When did Smith's act of killing occur?
This has been a much vexed question. 18 But the answer seems to be obvious. The act occurred when Smith pulled the trigger, neither before nor after. Moreover, this answer seems to be supported by an utterly compelling principle. I do not know about esse est percipi in the case of material things, but surely esse est agendi in the case of actsto occur is to be done, or performed: and hence an act can occur only when it is being performed. 19 But Smith might not be doing anything after he pulls the trigger, perhaps he immediately drops dead. This should make no difference to when the act of killing occurs and, since he is not performing any acts after pulling the trigger, the act of killing can no longer occur. Fine Metaphysics DOI: 10.5334/met.98 There are a couple of reasons why some philosophers may have been reluctant to accept this seemingly obvious conclusion. One is that it has not been in accord with their theoretical leanings. Thus if one takes an act to be something like a causing (Hyman 2015;Thomson 1977) then it is not plausible to suppose that the causing occurs at the same time as the cause. Another is that the question has not been clearly framed as one about acts. Thus it may be thought to be unclear when Smith killed Jones. It may even be thought to be unclear when Smith's killing of Jones took place. But neither is clearly or unequivocally about Smith's act of killing Jones. Nor does it really help, in my opinion, to talk of Smith's action of killing Jones. For 'action' unlike 'act' can be used more broadly for agentive happenings (as when 'Action!' is called on a movie set). But if we frame the question as one explicitly about the act of killing, then it seems clearor, at least, much clearer what the answer should be.
But there is another, more serious, reason for rejecting the result, which is that it is inconsistent with some other, seemingly compelling, principles. For it may well be thought that: if event e cannot occur without event f occurring then e occurs whenever f occurs.
But Smith's act of killing Jones cannot occur without Jones' death occurring and so Smith's act occurs when the death occurs and not just when he is pulling the trigger. Or again, it may be thought that: if event f is a part of event e then e occurs whenever f occurs.
But Smith's act of killing Jones is surely partly constituted by Jones' death, it has his death as a part, and so, for this reason too, Smith's act will occur when the death occurs. Although I have stated two justifying principles, the first is plausibly taken to derive from the second, for it will be because the death is a part of the act of the killing that the act of killing cannot occur without the death. The second principle may also have the advantage of relying on mereological rather than de re modal judgements.
It therefore looks as if we are in a typical philosophical predicament. However, the theory of embodiment can be used to account both for the original intuition that the act of killing occurs only at the earlier time and for why we are misled into thinking that it also occurs at the later time. For the act a of killing will be a qua object of the form (… ((c/φ 1 )/φ 2 )…/φ n ) and so, by repeated applications of Inheritance (or, more specifically, of Location), the act will occur when its core occurs. But granted that the core is either a bodily movement or a volitional act, it will only occur at the earlier time.
Now the death of Jones may plausibly be taken to be part of the qua object. For the immediate gloss φ n is a part of the qua object (by Part). But φ n may plausibly taken to be, or to have as a part, the property of being the cause of the death d of Jones. Thus d is a part of the gloss and hence a part of the qua object. However, it is an aspectual rather than a component part; and the previous principle that an event occurs whenever any of its parts occur is only plausible for component parts, not for aspectual parts. Thus the error in thinking that the act of killing occurs at the later time arises from the failure to distinguish between the different ways in which one event may be part of another; and the theory of embodiment makes clear how these different relations of part might come into play in determining when the act occurs. 20 A monist is obliged, by her very position, to accept that the act of killing can only occur at the earlier time. It has often been thought that the pluralist cannot accept such a view since the different acts will bring different future events in their train; and, if this is right, then it would appear to be a very real mark against their position. But we see that by construing acts as qua objects, we can accept the monist's view on the timing of an act without accepting their monism.
20 Something similar may be said in the case of perception. I see a star which has since long gone. When did my perception of the star occur? By treating the perception as a suitable qua object, we can say 'now' even though the occurrence of the perception requires the occurrence of an event in the distant past. And something similar may also be said, of course, in regard to spatial location.

THE ESSENTIAL PROPERTIES OF ACTS
Smith's act of shooting the gun was a killing and Smith's act of killing Jones was also a killing. But there appears to be a difference in how each of them is a killing. Smith's act of shooting was only accidentally a killing; if Smith had not been in the way, then that very act of shooting would not have been a killing. On the other hand, Smith's act of killing is essentially a killing, not only in the modal sense that it is necessary that that very act is a killing (or, at least, a killing if it exists), but also in the sense that it is a killing by its very nature, that this is (in part) what it is.
Of course, a monist will reject these modal and essentialist intuitions since they require one to hold that the acts of shooting and of killing are not the same. I myself find the intuitions very compelling and am inclined to think that it is largely for doctrinaire reasons that they have not been accepted. But even if they are accepted, we pluralists still owe an explanation of why the two acts should differ in this way.
I believe that the present theory is well suited to this task. Let us take an act to be a killing if it causes the death of someone (though nothing will turn on whether this is exactly right). Consider now Smith's act a of killing Jones. We may take this to be a qua object of the form b/φ, where the basis b is Smith's act of shooting the gun, let us say, and where the gloss φ is a property whose instantiation by an event requires that it be a killing, i.e. that it cause the death of someone. By Existence, it follows that, necessarily, the act of killing a exists only if the act of shooting possesses φ and hence only if it is a killing. But granted that being a killing is an ordinary property, it will be necessary that the act a of killing exists only if it is a killing.
Consider next Smith's act aʹ of shooting Jones and take it to be a qua object of the form bʹ/ψ, where the basis bʹ, let us say, is Smith's act of pulling the trigger. We may suppose that this act is a killing, i.e. that it causes the death of someone, and, granted that being a killing in this sense is an ordinary property, it follows by Inheritance that Smith's act aʹ of shooting is also a killing. However, in a scenario in which the act bʹ of pulling the trigger is not a killing, the act aʹ of shooting will likewise not be a killing.
We have so far only dealt with the modal difference between the act of killing and the act of shooting. But there would also appear to be an essentialist difference, with the act of killing essentially being a killing and the act of shooting only accidentally being a killing. In discussing this difference, we need to distinguish two senses in which an act can be a killing. It can be a killing in the descriptive sense we have already explained. But it can also be a killing in the sense of being an act that is correctly classified as a killing; and, within the theory of embodiment, we can understand this in terms of its being a qua object whose gloss contains the property of being a killing in the descriptive sense as a part. Thus the first provides a way of describing an act while the second provides a way of classifying an act, of saying what kind of act it is. 21 Granted that a qua object is by its very nature the qua object that it is, it will follow that Smith's act of killing will by its very nature be a killing in the classificatory sense (while Smith's act of shooting will, of course, not be). Moreover, given the principles governing qua objects, the act being a killing in the classificatory sense will explain why it is a killing in the descriptive sense (given that it exists) and it may even be argued that the act of killing is essentially an act of killing in the descriptive sense, though not in the same direct way in which it is an act of killing in the classificatory sense. 22

GETTING BY
One can do one thing by doing another. Smith killed Jones by shooting him. As so expressed, 'by' does not clearly signify a relation between acts. But there appears to be a corresponding relation 21 I have drawn a similar distinction within the realm of material things between the descriptive property of being spherical and the classificatory or sortal property of being a sphere (Fine 2008: 113-4). In this case, unlike the present case, the distinction is grammatically marked.
22 There is a subtle difference in the two cases. The act of killing, I believe, is essentially an act of killing in the classificatory sense regardless of whether it exists while it is only essentially an act of killing in the descriptive sense if it exists. I suspect that the failure to distinguish between the descriptive and classificatory uses of a given predicate has been responsible for a great deal of confusion . Fine Metaphysics DOI: 10.5334/met.98 between acts. For we can say that Smith performed the act of killing Jones by performing the act of shooting Jones or, if we want to avoid the appearance of appealing to some kind of dummy relation between the agent and the act, we can say that the one act -of Smith's killing Jonesoccurred by way of the other act -of Smith's shooting Jones.
Of course, the monist will deny that we have thereby obtained a genuinely extensional predicate of acts, one that is true of two acts regardless of how they are described. For Smith performed the act of killing Jones by performing the act of shooting Jones but did not perform the act of killing Jones by performing the act of killing Jones; and so, if 'by' was a genuinely extensional predicate, Smith's act of killing would not be the same as Smith's act of shooting. I myself have no such qualms and, indeed, would be willing to argue for the extensionality of 'by' in much the same way as I argued for the extensionality of 'intentional'. But even if the predicate is extensional, the pluralist still owes us an explanation of the relation that it expresses.
It should be mentioned, in the first place, that there appear to be a number of different senses in which one can talk of one act being performed or done by way of another (Baier 1971(Baier , 1972. We can get at the relevant sense by insisting that the one act must be constitutively, rather than causally or in some other way, responsible for the other, so that it is by virtue of performing the one act that one performs the other. Thus Smith's act of shooting Jones will in this way be constitutive of his act of killing Jones; and it is interesting that a similar notion of constitution seems to be in play when we talk of one material thing constituting another (as with the clay constituting the statue).
The by-relation is normally taken to be a binary relation, holding between one act and another. But there is also a corresponding multi-grade relation, holding between one act and several acts. For when one act a is the compound a 1 ⊔ a 2 ⊔ … of other acts, we can say that the compound act a is performed by means of the component acts a 1 , a 2 , … . So, for example, when the compound act is the act of turning my head and scratching my nose, we can say that it is performed by means of the respective acts of turning my head and scratching my nose. 23 Given the one-to-many relation, there is a possible ambiguity in the one-one relation. For do we want to allow that a is performed by means of a 1 just because it is performed by means of a 1 , a 2 , … ? Do we want to say, for example, that the act of turning my head and scratching my nose is performed by means of the act of turning my head? I will stipulate that we will not extend the one-one relation in this way. Thus 'by' means wholly or simply by.
I now wish to provide a definition of the by-relation between acts (for which I shall use the term 'BY') within the theory of embodiment. The definition will be inductive; it will consist of rules by which the instances of the by-relation might be generated. However, in stating these rules, it will be somewhat simpler to suppose that the by-relation is reflexive. The irreflexive relation between a and a 1 , a 2 , … can then be defined by requiring that the act a stands in the reflexive by-relation to acts a 1 , a 2 , … which are distinct from a.
There are two 'structural' rules: Vertical Constitution tells us that any act stands in the by-relation to its basis; it is the only rule that involves a drop in the 'level' of the act. Mereological Constitution tells us that any compound act stands in the by-relation to its components. Logical Constitution tells us that an act with a conjunctive gloss stands in the by-relation to the acts with the conjunct glosses and that an act with a disjunctive gloss stands in the by-relation to any act with one of the disjunct glosses (as in: John's act of serving tea or coffee was done by means of his act of serving tea). We should note that, given Distribution above, Mereological Constitution will be equivalent to Conjunctive Constitution; and so either rule might have been dropped.
There are other rules that might have been included under Logical Constitution. We might, for example, have allowed that b/∃xφ(x) BY b/φ(d) (as in Smith's act of killing someone was done by means of his act of killing Jones). More generally, when ψ 1 , ψ 2 , … ground φ then b/φ will stand in the by-relation to b/ψ 1 , a/ψ 2 , … . We therefore see, through the structural and logical rules, that there is a close relationship between the by-relation and the notion of ground; and just as, in the case of ground, we can say that one thing is the case in virtue of other things that are the case so, in the case of the by-relation, we can say that the one act is done in virtue of other acts that are done. Goldman (1977) and Thomson (1977) have also attempted to characterize the by-relation. But their characterization is very different in kind from my own. For they employ counterfactual or causal notions whereas my definition is purely structural. In defining the by-relation, I simply appeal to the structure of the acts in question, as given by their analysis as compounds or qua objects. This suggests that when an act a is done by means of other acts a 1 , a 2 , …, it is essential to a that it is done by means of a 1 , a 2 , …, given that a 1 , a 2 , … exist, since these other acts can simply be 'read off' from a; and it shows that the definition has nothing special to do with acts but will have general application to all qua objects whatever. However, it should be noted that our own structural analysis of the by-relation does not rule out the kind of counterfactual and causal connections to which Goldman and Thomson appeal. When an act of killing, for example, is taken to be an act of shooting under the description of causing a certain death, then it may be taken to be true that the act of killing would not have occurred if the act of shooting had not occurred. It is just that the general form of analysis of the by-relation does not itself involve any particular causal or counterfactual connections.

ACTIVITIES
I should like to conclude by briefly considering the application of the theory of variable embodiments to activities.
Suppose we have a principle φ for picking out different objects at different times. Then according to the theory of variable embodiments, we suppose that there is a new object, the variable embodiment /φ/ of φ, which at each time is embodied or manifested in the object picked out by φ. Variable embodiments are governed by certain principles (Fine 1999) and, in particular, a variable embodiment /φ/ is taken to exist at those times at which the principle φ is defined, i.e. picks out an object.
If φ is a principle which picks out the respective objects e 1 , e 2 , … at the various times t 1 , t 2 , … at which it is defined, then it is important to distinguish between the variable object /φ/ and the compound object e = e 1 ⊔ e 2 ⊔ … . For one thing, e i is a temporary part (at t i ) of /φ/, while it is a timeless part of e. For another thing, e i , as a general rule, is only contingently a part of /φ/, for φ may possibly pick out another object at t i , while it is necessarily a part of e (given that e exists).
It is also important to take note of the distinction between existence (or complete presence) and location. 24 A variable embodiment /φ/ will exist at each time at which φ is defined, not located at 24 See Fine (2006), where further differences between the two notions are explored. Fine Metaphysics DOI: 10.5334/met.98 each of those times; and this will be so even if the object picked out by φ at a time is located at that time. This then leads to a further difference between the variable embodiment /φ/ and the compound e = e 1 ⊔ e 2 ⊔ … for, when e 1 , e 2 , … are located in time, e will be located at the times at which the e 1 , e 2 , … are located while /φ/ will exist at those times (or, rather, exist at those times at which φ is defined).
Activities are to acts as processes are to events. Intuitively, an event or act is something that happens or occurs while a process or activity is something that is going on or occurring (Stout 1997). Thus there is the act of taking a step and the activity of taking a stroll, which is constituted over time by numerous acts of taking a step. The activity -the stroll -could, of course, be cut short, or go on longer, or follow a different route.
I should like to suggest that an activity be identified with a variable embodiment whose manifestations are particular acts. 25 Thus in the case of a stroll, there is some principle φ which picks out the different acts which might constitute the stroll; and the stroll itself will be the variable embodiment /φ/. We can in this way explain why an activity, as opposed to a sequence of acts, is completely present at each time at which it is going on and why the acts which constitute it can be different from what they actually are.
Let me conclude with a general comment. It has been suggested to me that the present pluralist view of acts as embodiments might merely be regarded as a 'notational variant' of the monist view, with the description by which the monist describes his act being folded into that act. But even if there were some sort of parallelism in the two approaches, the monist would, by the pluralist's lights, still be making serious mistakes about the ontology of acts and the language by which they are described. And the parallelism only goes so far. As is clear from the previous discussion, there are subtleties in the pluralist view -as with the layering or compounding of acts -that have no clear counterpart within the monist framework.