Motion and Change in Aristotle's Physics 5.1

copy Koninklijke Brill NV Leiden 2012 DOI 101163156852812X607298

Phronesis 57 (2012) 63-99 brillnlphro

Motion and Change in Aristotlersquos Physics 5 1

Jacob RosenHumboldt-Universitaumlt zu Berlin Excellence Cluster Topoi

Hannoversche Straszlige 6 10099 Berlin GermanyJacobrosenphilosophiehu-berlinde

AbstractThis paper illustrates how Aristotlersquos topological theses about change in Physics 5-6 can help address metaphysical issues Two distinctions from Physics 5 1 are discussed changing per se versus changing per aliud motion versus change Change from white to black is motion and alteration whereas change from white to not white is neither But is not every change from white to black identical with a change from white to not white Theses from Physics 6 refute the identity Is change from white to black at least accompanied by change from white to not white Perhaps but given further theses from Physics 6 this supposition yields unwelcome consequences Most likely when something changes from white to black it changes merely per aliud not per se from white to not white Genuine change between white and not white is found elsewhere its admission has bearing on Aristotlersquos theory of perception

KeywordsAristotle change motion per se accidental

1 Introduction

For Aristotle the study of nature centers around the study of change1 Aristotle addresses this central topic from various angles in various texts The treatise occupying books 5 and 6 of the Physics offers a study of change from an especially general and abstract standpoint In this treatise Aristo-tle is not directly concerned with such matters as which kinds of thing undergo change or what causes them to change when they do nor with

1) See for example Phys 3 1 200b12-15 For comparison consider that the axioms in Newtonrsquos Principia Mathematica are titled lsquoleges motusrsquo laws of motion

64 J Rosen Phronesis 57 (2012) 63-99

the ontological question what change is (whether it is activity or other-ness or non-being or so forth) His aim here is to articulate the structural or topological features which any change must have For example he establishes that every change occupies not an instant but an interval of time and that changes (as well as spatial magnitudes and times) are con-tinuous He argues further that whatever is continuous is atomless all of its parts have further proper parts and thus in particular it has no point-like parts These and related theses have large metaphysical and empirical consequences they figure for example in the cosmological arguments of Physics 8 and in Aristotlersquos general theory of the generation and perishing of composite entities2

A further reason for interest in the treatise is that Aristotlersquos claims about change there may shed light on his understanding of certain other types of occurrence occurrences whose status as changes is (surprisingly) denied or whose relation to change is controversial For example Aristotle sug-gests that coming into contact and losing contact are not changes3 and perhaps one reason is that these transitions do not have the temporal struc-ture required of change in Physics 5-6 A more important example is Aris-totlersquos treatment of perception where his views about the role of alteration and change is under vigorous debate I believe that Physics 5-6 offers clues that can help move the debate forward there is not space here to justify this hope in detail but along the way I will offer a small example to illus-trate the point

This paper will focus on two distinctions made at the opening of Aristotlersquos treatise in Physics 5 1 first a distinction between changing4 per se and changing per aliud and second a distinction among changes (μεταβολαί) between those that are motions (κινήσεις) and those that are not motions The first is a special case of a ubiquitous and ever-

2) In GC 1 2 Aristotle explains that the atomless structure of bodies makes a crucial differ-ence to the proper account of their generation perishing and alteration Contemporary philosophers also have argued from the actual or possible existence of so-called lsquoatomless gunkrsquo to major theses about the metaphysics of composite entities See for example Theo-dore Sider lsquoVan Inwagen and the Possibility of Gunkrsquo Analysis 53 (1993) 285-289 Dean Zimmerman lsquoTheories of Masses and Problems of Constitutionrsquo Phil Review 104 (1995) 53-110 Jonathan Schaffer lsquoIs There a Fundamental Levelrsquo Noucircs 37 (2003) 498-513) DC 1 11 280b6-9 26-84) In this paper the verbs lsquochangersquo and lsquomoversquo are always used in their intransitive sense to undergo change or undergo motion

J Rosen Phronesis 57 (2012) 63-99 65

troublesome distinction ndash that between per se and per aliud ndash which Aris-totle also invokes in connection with causation knowledge sameness and various other topics Aristotlersquos use of it here raises the usual difficulties in addition to some more special issues in the metaphysics of actions and events We will not have space to discuss the issues and difficulties in full but I will try to clarify them enough to make it plausible that Aristotlersquos distinction is coherent and principled So much is necessary for my pur-poses because I will draw on this first distinction in explaining and defend-ing the second that between motions and non-motions

This latter distinction as we will see amounts to the following A change is a motion if it proceeds (per se) either between contrary endpoints such as white and black or between endpoints that lie along a range bounded by contraries for example dark grey and light grey A change is not a motion if its endpoints are neither contraries nor intermediates but rather contradic-tories for example white and not white The distinction implies that there may be changes of quality which are not motions and since alteration is a species of motion are not alterations We may call such changes qualitative generations and perishings

The distinction between motion and non-motion is open to an obvious objection Many changes seem equally describable as changes between contrary endpoints such as white and black and as changes between con-tradictory endpoints such as white and not white Does it not follow that these changes both are motions and are not motions We will consider how best to counter this objection drawing first on the distinction between per se and per aliud and second on some topological theses from Physics 6 First I will suggest that when something changes (per se) from white to black it changes only per aliud from white to not white On a second approach we will suppose for the sake of argument that whatever changes (per se) from white to black also changes (per se) from white to not white but then it can be shown at least for typical cases that the two changes cannot be identical We will also see that the supposed existence of the latter change places unwelcome constraints on the temporal structure of the former change

2 Change per se vs change per aliud

Whenever change occurs there is a subject that changes a starting point from which the subject changes and an endpoint to which it changes


Typically many different descriptions will apply to a changing subject it might fit both the description lsquothe chameleonrsquo and the description lsquoLudwigrsquos petrsquo for example Furthermore many different properties will be gained and lost by the subject while changing and many different descrip-tions will apply to each of these properties When it changes a chameleon might acquire both the property yellow and the more determinate property canary yellow and this latter might correctly be described both as lsquocanary yellowrsquo and as lsquoLudwigrsquos favorite colorrsquo All these many different descrip-tions can be combined in various ways so as to produce many true sen-tences lsquothe chameleon changes from green to canary yellowrsquo lsquothe chameleon changes from green to yellowrsquo lsquoLudwigrsquos pet changes from Ludwigrsquos most hated color to Ludwigrsquos favorite colorrsquo and so forth

For Aristotle there is a difference of status among these sentences Cer-tain descriptions of the changing subject and of that from which and to which it changes are favored over others Under less favored descriptions Aristotle will say that the subject changes in a given way merely lsquoper aliud rsquo (κατrsquo ἄλλο) ndash more specifically either that it changes lsquoaccidentallyrsquo or that it changes lsquopartwisersquo (κατὰ συμβεβηκός κατὰ μέρος) Under more favored descriptions he will say that the subject changes lsquoper sersquo (καθrsquo αὑτό)

Aristotle discusses the difference between changing per aliud and chang-ing per se in the first half of Physics 5 1 His discussion is divided into two main parts First he focuses on different ways of describing the subject of change Later he turns to the different ways of describing the starting point and endpoint of change

21 The subject of change

Of all that changes (a) some changes accidentally [ ] (b) some is said to change (full stop) because something of it changes [ ] (c) but there is something that moves neither accidentally nor because something else which is of it does but by being itself the primary thing that moves And this is what is per se moveable (Physics 5 1 224a21-9)5

In the first lines of the chapter Aristotle distinguishes between changing (a) accidentally (b) partwise and (c) primarily or per se all in connection with different ways of specifying the subject of change (The shift from lsquochangersquo to lsquomoversquo in (c) does not appear to be significant Later in the

5) All translations are my own


chapter Aristotle will distinguish between changing and moving but for now he seems to treat them as equivalent) He provides examples of chang-ing accidentally and partwise occupying the two ellipses in the above quo-tation Here is his example of changing accidentally

For example when we say that the musical walks because that of which being musical is an attribute walks (Physics 5 1 224a22-3)

Aristotle does not specify what sort of entity it is that has being musical as an attribute but we may assume that it is a man Presumably Aristotle would say that the man walks per se Since the man is musical and the man walks it follows that a musical entity walks However Aristotle tells us the musical entity walks accidentally

His example of changing partwise is as follows

The body becomes healthy because the eye or the chest does and these are parts of the whole body (Physics 5 1 224a25-6)

Here change is attributed to a whole body although strictly speaking only a part of that body is changing in the relevant way The term lsquopartwisersquo (κατὰ μέρος) may be added in order to signal this qualification the body becomes healthy partwise

The notion of a thingrsquos changing partwise is I think reasonably unprob-lematic and intuitive Pre-philosophically we all know more or less what the relation is between a part and a whole and we all know more or less how to decide whether all of a thing is changing or whether only some part of the thing is changing Worries could doubtless be raised about these issues and Aristotlersquos notion of changing partwise thereby called into ques-tion but prima facie and in its outlines the notion seems clear enough

The case of changing accidentally on the other hand is much more dif-ficult There are at least two serious problems of interpretation either of which may lead us to doubt whether Aristotlersquos distinction is coherent and contentful The first problem (referring it to our example) concerns the relation between the musical entity and the man On the one hand it is reasonable to think that there is a relation of identity that a single item both belongs to the kind man and enjoys the property musical lsquoThe manrsquo and lsquothe musical entityrsquo are two descriptions of this self-same item Some of Aristotlersquos ways of speaking suggest that he held this very reasonable view of the matter On the other hand he sometimes speaks in ways which


suggest a different view on which the man and the musical entity are two different items although in some sense they coincide This latter view is suggested among others by the apparent fact that Aristotle attributes properties to the one which he denies of the other At least he would assent to the pair of claims lsquothe man walks per sersquo and lsquothe musical entity does not walk per sersquo as well as to the claims lsquothe musical entity walks acci-dentallyrsquo and lsquothe man does not walk accidentallyrsquo So is the musical entity identical with the man or not Is there one item or two

A schooled Aristotelian will answer unperturbed in a way there is one and in a way there are two the musical entity is one in number with the man but the musical entity is not one in being (or in account or in kind) with the man That does indeed correspond closely to what Aristotle says6 Unfortunately many philosophers including myself will not be sure what it means How must we imagine the world as being if we are to imagine that it is true It would be helpful to have a direct answer to the question of identity For I can easily imagine a situation in which the musical entity is identical with the man and I think I can conceive a situation in which the musical entity is coincident but not identical with the man but I can-not conceive or imagine a situation in which the musical entity both is and is not identical with the man Qualifying phrases such as lsquoin numberrsquo and lsquoin beingrsquo do not help me here One may fear that Aristotlersquos talk of lsquoacci-dentallyrsquo and lsquoper sersquo rests on an incoherent combination of commitments to identity and non-identity

It is debated whether Aristotle had the concept of identity which we today employ7 I intend here to remain neutral on that question My ques-tion is how may we imagine the world as being if we want to imagine that things are as Aristotle says they are Or how can we describe a model in which Aristotlersquos claims are true In discussing this question in describing worlds or models we are entitled to employ concepts we possess without immediate regard to whether or not Aristotle possessed them Perhaps it will turn out in the end that because Aristotlersquos metaphysical conceptions

6) For example in Phys 1 7 Aristotle says that the subject of a change ndash thinking of such pairs of descriptions as lsquothe manrsquo and lsquothe unmusicalrsquo ndash is typically one in number but two in kind (εἴδει) (190b23-4) and again that the subject of change is not one in kind or in account (εἴδει or λόγῳ) (190a15-17) See also Phys 3 3 202b8-167) Nicholas White for example tells a story on which Aristotle first had a decent under-standing of the concept but then lost his grip in the face of various puzzles and paradoxes Nicholas White lsquoAristotle on Sameness and Onenessrsquo Phil Review 80 (1971) 177-197


are so radically different from ours the concept of identity has no applica-tion within the world as he believes it to be Perhaps on the special way in which Aristotle used nouns lsquoSocrates is identical with the musicianrsquo makes as little sense as lsquoSocrates is andrsquo This would be an interesting and exciting result but it would require explanation and defense meeting very high standards and to my knowledge no commentator has attempted the task At this stage of our inquiry it is reasonable to assume that Aristotlersquos world did contain self-identical objects and that his normal use of nouns like lsquomanrsquo and lsquomusicianrsquo was such that they denote self-identical objects It is then also legitimate to worry whether in the world as he believed it to be the musician is identical or non-identical with the man or whether he incoherently requires that it be both

As it turns out most or all of the relevant pronouncements in Aristotle appear to admit of consistent interpretation either on the assumption of identity or on the assumption of non-identity8 Provided you make a choice and stick to it and with some luck and ingenuity in this or that passage it seems that you can avoid incoherence Many scholars have plumped for non-identity and a handful of proposals have been made in recent decades as to the nature of the coincidence relation holding between such items as men and musical entities9

My own heart lies with an identity interpretation If we take this approach we must hold that contexts such as lsquo walks per sersquo and lsquo walks accidentallyrsquo are intensional contexts contexts such that coreferential terms can yield sentences with different truth values when they are inserted in place of the ellipsis To see why this might be so consider for comparison the phrases lsquoas suchrsquo and lsquonot as suchrsquo lsquoI admire the man as suchrsquo means that I admire the man as a man and lsquoI admire the musician as suchrsquo means that I admire the musician as a musician It is easy to imagine that one and the same entity is an admirable man but a poor musician and that in consonance with this fact I admire him as a man without admir-ing him as a musician The musician is identical with the man lsquoI admire

8) A large claim which there is not space here to fully justify For a sketch of how a non-identity interpretation might look see the papers cited in n 9 below For the identity approach see nn 10 and 11 below and the text to which they are attached9) Alan Code lsquoAristotlersquos Response to Quinersquos Objections to Modal Logicrsquo Journal of Phil-osophical Logic 5 (1976) 159-186 Frank Lewis lsquoAccidental Sameness in Aristotlersquo Phil Studies 42 (1982) 1-36 Garreth Matthews lsquoAccidental Unitiesrsquo in Schofield and Nuss-baum (eds) Language and Logos Cambridge (1982) 223-240


the man as suchrsquo is true and lsquoI admire the musician as suchrsquo is false lsquoI admire as suchrsquo is therefore an intensional context Next consider the context lsquo walks as suchrsquo lsquoThe man walks as suchrsquo means that the man walks as a man and lsquothe musical entity walks as suchrsquo means that the musi-cal entity walks as a musical entity Walking is different from being admired and it isnrsquot obvious what it means to walk as this or that Still it is to be hoped that some meaning can be found or bestowed If so we can see why contexts such as lsquo walks as suchrsquo and lsquo walks not as suchrsquo would be intensional

Now the phrases lsquoper sersquo and lsquoaccidentallyrsquo have a close affinity with the phrases lsquoas suchrsquo and lsquonot as suchrsquo respectively10 For this reason it is plau-sible that lsquo walks per sersquo and lsquo walks accidentallyrsquo are likewise inten-sional contexts It matters not just which item is being talked about but also how that item is described11

For the purposes of this paperrsquos argument it is not necessary to choose between an identity and a coincidence interpetation my aim is only to outline the prospects for developing some consistent interpetation or other However since it is nearly impossible to write clear English and stay neu-tral I will speak as if the identity interpretation is the correct one In the case of changing partwise we posit two items related as part to whole for example the eye and the body In the case of changing accidentally by contrast I assume that only one item is in question and we must distin-guish between different descriptions of it Under the description lsquomanrsquo the item walks per se under the description lsquomusical entityrsquo this same item walks accidentally

10) Aristotle sometimes explains a lsquoper sersquo or lsquoaccidentallyrsquo claim by means of the word lsquoᾗrsquo which could be translated by lsquoinsofar asrsquo or lsquoquarsquo For example at Phys 2 3 195a5-7 being a cause of a statue lsquonot accidentallyrsquo is explained as being a cause of it lsquoinsofar as it is a statuersquo For some other examples see Phys 1 8 191b22 2 1 192b17-23 3 5 204a14-17 4 3 210b13-18 DA 3 6 430b1611) What should we say about oneness in number and oneness in being An initial proposal lsquo is one in number with ndashndashndashrsquo is an extensional context and x is one in number with y just in case x is identical with y lsquo is one in being with ndashndashndashrsquo is an intensional context when definite descriptions are substituted for lsquo rsquo and lsquondashndashndashrsquo a truth results just in case the descriptions refer by way of the same kind or property More would need to be said to cover cases involving quantification (as at SE 24 179a37-9 Phys 3 3 202b14-16) pronouns and proper names


There remains a second problem of interpretation What does it take for something to change per se rather than accidentally under a given descrip-tion Why is it that the man walks per se and the musical entity walks accidentally rather than the other way around It is important that there be some principled way of answering this question if the distinction between per se and per aliud is to have content Aristotle himself does not provide any explicit systematic answer However we can derive some help from the following remark

And this [sc what moves per se] is what is per se moveable This is different according to different kinds of motion for example alterable and within alteration healable or heatable are different (Physics 5 1 224a28-30)

Aristotle draws a connection here between changing in a given way per se and being capable per se of changing in that way This may seem trivial ndash it is obvious that whatever does something is capable of doing that thing ndash but nevertheless the remark has significant implications This is because here in the sublunary realm capacities for change commonly belong to things essentially whereas the changes themselves do not It is not essential to or definitional of a man that he be walking (he exists also while he is still) but perhaps it is essential to him that he be capable of walking After all Aristotle holds that a nature is a principle of change and rest and he closely associates a thingrsquos nature with its essence and definition12 Given this natural kinds will have included in their definitions the capacity to undergo certain sorts of change As a result many things have a descrip-tion (namely one assigning it to a natural kind) under which it is essen-tially capable of changing in certain ways Being essentially capable of change surely entails being per se capable of change13 So then given Aris-totlersquos remark connecting change per se with changeability per se we are led to the following proposal

PER SE subject If a description identifies something as belonging to a kind whose definition includes the capacity to change in a certain way and if the thing is changing in that way then under this description the thing is changing in that way per se

12) Phys 2 1 192b21-3 193b3-713) Cf Post An 1 4 73a34-5


Let me illustrate with the example of the walking man According to the proposal the man walks per se if the man walks and the definition of man includes the capacity to walk Now Aristotle never commits himself to a definition of man but he often mentions lsquobiped animalrsquo as a candidate This would fit into a classificatory scheme sometimes employed in Aristo-tlersquos biological works in which animals are differentiated according to their primary mode of locomotion flying swimming walking or creeping Walking animals are referred to as lsquofootedrsquo or lsquoland animalsrsquo and are sub-divided according to number of feet into biped quadruped and so on Thus the definition lsquobiped animalrsquo identifies man as a species of footed and hence walking animal In some sense of lsquoincludersquo then the definition of man includes the capacity to walk Hence the man is essentially capable of walking and on the occasions on which he actually walks the man walks per se

I propose this as a sufficient condition for undergoing a given change per se not as a necessary condition There may be sorts of change which no kind of thing is essentially capable of undergoing For example to my knowledge Aristotle never suggests that the capacity to change color belongs to any essence or definition We should not infer that nothing ever changes color per se In such cases we must look for other strategies for identifying the per se subject of change One suggestion would be that a change from one property to another belongs per se to something under those descriptions under which the properties themselves belong per se to the thing For example since bodily surfaces are colored per se it is reason-able to think that bodily surfaces change color per se

22 The endpoint of change

After discussing the subject of change Aristotle goes on to consider the starting point and endpoint of change14 In parallel with the subject Aris-totle explains here too it turns out that under some specifications of an endpoint a thing changes into this endpoint per se while under other descriptions of the endpoint the thing changes into it only accidentally or partwise Aristotle explains as follows

14) In between he also addresses the agent of change but his discussion of this is not impor-tant for present purposes


In the endpoints too there is the accidental and the partwise ndash in sum the per aliud ndash and there is the primary and not per aliud For example something that turns white changes accidentally into what is being thought of because being thought of is an attribute of the color and it changes into color because white is a part of color (similarly into Europe because Athens is a part of Europe) whereas it changes into the white color per se (Physics 5 1 224b16-22)

Aristotlersquos remarks here are telescopic but they can be understood in close analogy with his discussion of the subject of change First the accidental case In the example of the walking man we began with the truth lsquothe man walks per sersquo Then we selected an attribute of the man musicality and used it to construct an alternative description of him lsquothe musical entityrsquo This yielded the truth lsquothe musical entity walks accidentallyrsquo By analogy in the present example we may begin with the truth lsquothe subject changes into the color white per sersquo Then we select an attribute of the color white ndash let us suppose that it is being thought of by someone ndash and use it to construct an alternative description of the color white namely lsquowhat is being thought of rsquo This yields the truth lsquothe subject changes into what is being thought of accidentallyrsquo

Earlier Aristotle focused on ways of describing the subject of change Under descriptions which pick it out merely as the bearer of an arbitrary attribute the subject changes accidentally and not per se Now Aristotle focuses on ways of describing the endpoint of change Under descriptions which pick it out merely as the bearer of an arbitrary attribute the end-point is changed into accidentally and not per se

Second the partwise case In the example of the eye we began with the truth lsquothe eye becomes healthy per sersquo Then we selected a larger whole of which the eye is part namely the body This yielded the truth lsquothe body becomes healthy partwisersquo By analogy in the first of the present examples we begin with the truth lsquothe subject changes into the color white per sersquo Then we select a larger whole of which the color white is part namely color We may wonder whether white is part of color in quite the same sense as that in which an eye is part of a body but let us grant that it is part in at least some sense Then we arrive at the truth lsquothe subject changes into color partwisersquo Aristotle also gives a second example We begin with the truth lsquothe subject moves into Athens per sersquo select something of which Athens is part namely Europe and arrive at the truth lsquothe subject moves into Europe partwisersquo


Earlier Aristotle focused on part-whole relations among the subjects of change If the primary subject of change is a proper part of S then S changes partwise and not per se Now he focuses on part-whole relations among endpoints of change If the primary endpoint of change is a proper part of B then B is changed into partwise and not per se

Aristotlersquos claims concerning the endpoint of change lead to similar questions as those we encountered for the subject of change What is the relation between white and color and what is the relation between white and what is being thought of How is it decided that the subject changes into color partwise rather than per se and how is it decided that the subject changes into what is being thought of accidentally rather than per se

The answer to the first question is for partwise change comparatively straightforward The relation between white and color is perhaps not the same as that between eye and body but there is at least an intuitive anal-ogy Similarly for the relation between Athens and Europe Broadly we can say that when some item is changed into partwise then the primary end-point of change will stand to this item in the relation of species to genus or determinate to determinable or contained place to containing place

For accidental change the answer to the first question is not straightfor-ward Just as it was unclear whether or not for Aristotle the musical entity is identical with the man so now it is unclear whether or not for Aristotle what is being thought of is identical with the color white On the one hand since Aristotle tells us that the color white is being thought of it is reasonable to think that the color white is (that is is identical with) what is being thought of On the other hand it looks as if Aristotle attributes properties to the one which he denies of the other the first and not the second is changed into per se the second and not the first is changed into accidentally This suggests that what is being thought of is not identical with the color white

Scholars who took a non-identity approach to the man and the musical entity might be expected to do the same in the present case If so they should say that the color white and what is being thought of are two coin-cident but nevertheless different items Note however that in this case the items in question are properties rather than objects A theory of coin-cidence applying to the latter will not necessarily also apply to the former15

15) The accounts of coincidence offered by Code Lewis and Matthews (cf n 9) do not provide room for coincident properties given that properties are neither space-time worms


As before I will favor an identity interpretation in this paper lsquoThe sub-ject changes into per sersquo and lsquothe subject changes into accidentallyrsquo will be taken to be intensional contexts Thus although the terms lsquothe color whitersquo and lsquowhat is being thought of rsquo yield different truth values when substituted into these contexts they refer to the same item We might say that this item is changed into as the color white but not as what is being thought of Admittedly it is not obvious what it means to be changed into as this or that this brings us to our second question

The second question was what does it take for something to change into a given endpoint under a given description per se rather than partwise or accidentally The answer to this question is not clear neither in connec-tion with partwise nor in connection with accidental change For example Aristotle said that someone moves into Europe partwise because Athens is part of Europe But would he also say that the person moves into Athens partwise because say the Acropolis is part of Athens Or would he allow that someone can move into Athens per se Again why is it that the subject changes per se into the color white and accidentally into what is being thought of rather than the other way around

It is not possible to settle these questions now but I will mention two plausible approaches which might be taken to answering them We will see that the two approaches yield different results and this will I hope give the questions some clarity and point

The first approach begins from the following observation Aristotle says that someone moves into Europe partwise because Athens is part of Europe If we consider how things stand after the motion is over it seems very plausible that the person is in Europe ndash perhaps partwise at any rate per aliud ndash because Athens is part of Europe16 Similarly just as the subject changed into color because white is part of color so after changing the subject is colored because white is part of color and the subject is white Again turning to the accidental case just as the subject changes into what is being thought of because white is being thought of so after changing the subject is what is being thought of because white is being thought of and

(Code) nor compounds of a substance with an accident (Lewis) nor accidental unities whose existence depends on the compresence of a feature in a substance (so-called lsquokooky objectsrsquo Matthews)16) See Phys 4 2 209a31-b1 and the discussion of this passage in Benjamin Morison On Location Aristotlersquos Concept of Place Oxford (2002) pp 55-66


the subject is white17 We might suppose that the reason why these end-points are changed into per aliud is precisely the fact that they are going to be occupied per aliud

This suggests the following principle a subject changes per se into a given place or condition under a given description only if if and when the change has been completed the subject occupies per se that place or condition under that description (This is at best a necessary condition on the per se endpoint To get a sufficient condition we would need clauses (a) ensuring that the subjectrsquos occupation of the place or condition results appropriately from the change and (b) accommodating incomplete inter-rupted changes)

A second approach is to invoke the teleological structure of change Things typically change for the sake of occupying the endpoint of change I walk to the Acropolis for the sake of being in the Acropolis for example We might suggest then that if a subject changes proximately for the sake of occupying a given place or condition under a given description then the subject changes into that place or condition under that description per se The blossom turns white per se because being white (as opposed to being colored or bearing the color I am thinking of ) is the proximate end for which it changes The proximate end of a change if any is the changersquos per se endpoint (This is at best a sufficient condition on the per se end-point To get a necessary condition we would need a clause accommodat-ing aimless changes)

The two approaches yield different results Consider for example a walk to the Acropolis No person is as large as the Acropolis and therefore nobody ever has it as his primary place one is in the Acropolis because he occupies a smaller place ndash ultimately a proper place containing nothing beyond him ndash and that smaller place is contained in the Acropolis (see n 16 above) It follows on the first approach that nobody ever goes to the Acropolis per se Whenever someone goes to the Acropolis he is going per se to some person-sized place within it By contrast if we consider the goals with which people travel it is implausible that we always aim to arrive at a definite person-sized place Someone might walk with the aim of arriving at the Acropolis while being indifferent to where exactly on the

17) The first lsquoisrsquo in lsquothe subject is what is being thought of rsquo does not express identity but predication Compare lsquothat sofa is my favorite colorrsquo


Acropolis her walk will take her18 If people sometimes move with a proxi-mate end no more specific than that of arriving in the Acropolis then according to the second approach people sometimes go to the Acropolis per se

The two approaches could of course be reconciled if we were to insist that every change has a perfectly determinate proximate end If we are not willing to make such a strong assumption however then we must admit that they conflict Both approaches have intuitive appeal but they cannot both be correct I am not sure which if either ought to be adopted

As we have seen Aristotlersquos distinctions between changing per se part-wise and accidentally give rise to several questions whose answers are uncertain Since I will be appealing to the distinctions in what follows it seemed important to acknowledge the uncertainties that are involved But I hope that these unanswered questions do not make Aristotlersquos distinc-tions seem confused or without content On the contrary my intention was to make them more clear and plausible Even though I have not settled on a completely determinate interpretation I hope that by framing the questions I have framed and by pointing out some of the different options for answering them I have made it plausible that coherent interpretations can be found

Once he has introduced these distinctions Aristotle narrows his atten-tion for the remaining discussion to cases of changing per se

Let accidental change be set aside for it is in everything and always and of all things Whereas non-accidental change is not in everything but is in contraries in intermedi-ates and in contradictories (Physics 5 1 224b26-9)

Although he speaks only of accidental change we should understand him as setting aside partwise change as well19 In the remainder he will often

18) At PA 1 1 641b23-5 Aristotle identifies the τέλος of a change as that at which the change ends if nothing interferes While the person was walking to the Acropolis her motion was going to end in the Acropolis provided that nothing interfered but (it seems to me) there is no person-sized place such that her motion was going to end there provided that nothing interfered This is an argument for the claim that the proximate end of the motion was the Acropolis and not some smaller person-sized place in the Acropolis19) It is fairly common for Aristotle to use lsquoaccidentalrsquo in a broad sense equivalent to lsquoper aliud rsquo (see for example the shift in DA 1 3 from lsquoper aliud rsquo at 406a4-5 to lsquoaccidentallyrsquo at 406a14 ff Aristotle subsumes lsquopartwisersquo under lsquoaccidentallyrsquo at Phys 8 4 254b8-12 and


talk about the endpoints of changes while omitting the qualifier lsquoper sersquo but we should read him as if it were there Likewise I ask the reader to sup-ply it when in the following pages of this essay I occasionally omit the phrase for the sake of brevity

3 Κίνησις versus μεταβολή

Let us now turn to the second major distinction presented in Physics 5 1 that between changes that are motions (κινήσεις) and changes that are not motions This distinction will raise metaphysical issues concerning the existence and individuation of changes and will also yield a small lesson for the interpretation of Aristotlersquos theory of perception

31 Change between contradictories distinguished from motion

Every change involves a subject that changes a starting point from which the subject changes and an endpoint to which the subject changes Aristo-tle makes a broad distinction between two sorts of character which a start-ing point or endpoint might have Approximately each may have on the one hand a positive or determinate character involving the presence of a characteristic to the thing (or the thingrsquos presence in a place) or else on the other hand a negative or indeterminate character involving the absence of a characteristic from the thing (or the thingrsquos absence from a place) The two possible characters for each of the two endpoints of a change may be combined in four possible ways and Aristotle begins his classification of change by listing all four combinations

Since every change is from something to something that which changes might do so in four ways either (i) from a subject into a subject (ii) from a subject into not a subject (iii) not from a subject into a subject or (iv) not from a subject into not a subject By lsquosubjectrsquo I mean what is disclosed by affirmation (Physics 5 1 224b35-225a7)

he seems to use lsquoaccidentallyrsquo in a correspondingly broad sense at Phys 1 8 191b18 and 24 4 5 212b11-13 6 10 240b9-12) It is likely that he is doing so here After all if partwise change were being counted as lsquonon-accidentalrsquo then Aristotle could not truly say that non-accidental change is always between contraries intermediates or contradictories for example a thing can change partwise from black to colored (224b20 cf also the change from animal to dog at Phys 1 8 191b20-3)


Confusingly Aristotle describes the two possible characters of a starting point or endpoint in terms of its being lsquoa subjectrsquo or lsquonot a subjectrsquo Up to now I have been using the term lsquosubjectrsquo in conformity with Aristotlersquos usual practice to denote the thing that undergoes a given change and not to describe any special character which this thingrsquos initial and final condi-tion may or may not exemplify20 Every change has a preexisting subject in this sense so Aristotlersquos admission of case (iii) makes it clear that a different and special sense is at work in the present passage21 The last sentence quoted is naturally read as a stipulation of that special sense here (and not elsewhere) lsquosubjectrsquo shall mean anything lsquodisclosed by affirmationrsquo

On the face of it Aristotle is offering a purely linguistic criterion for subjecthood a subject is something you can express without using the word lsquonotrsquo (or a similar negating particle) Presumably however he intends to invoke a metaphysical distinction perhaps between positive and priva-tive or perhaps between determinate and indeterminate22 One reason to think this is his assumption to the effect that (necessarily) no two subjects are contradictory to each other (see n 23) though they may be contrary to each other It is only doubtfully true and surely not necessary that

20) The term lsquosubjectrsquo reverts to its normal use at Phys 5 2 225b17 This normal use in descriptions of change was introduced in connection with the verb lsquoto underliersquo from which it derives at Phys 1 7 190a31 ff (see esp a34-6 b12-17) Additionally the term lsquosubjectrsquo is often used to refer to the bearer of a property or to the matter of a composite substance21) Here I agree with Ross ad loc (pp 616-17) and disagree with Hans Wagner Physikvor-lesung Aristoteles Bd 11 Berlin (1995) p 593 If more argument is needed a subject in the normal sense is a substance or some matter perhaps described as qualified in a certain way (a man a white man a white entity) The starting points and endpoints of change in Phys 5 1 by contrast are properties or places see especially 224b13-15 22 where the words lsquoἐπιστήμηrsquo lsquoθερμότηςrsquo lsquoλευκότηςrsquo and lsquoτὸ λευκὸν χρῶμαrsquo make it clear that Aristotle means qualities and not qualified entities Hence starting- and endpoints cannot be sub-jects in the normal sense22) I suspect that subjecthood is rather a matter of determinacy than of positivity Aristotle allows for a subject to be a privation (στέρησις) such as black or naked (225b3-5) Further-more every motion will turn out to involve a pair of contrary subjects so Aristotle must admit privative subjects if as he sometimes suggests every pair of contraries has one posi-tive member and one privative member (see for example Metaph Γ 6 1011b15-20 Θ 2 1046b4-15 DC 2 3 286a25-6) (On the other hand Aristotle draws a sharp distinction between the relation of contrary to contrary and the relation of having (ἕξις) to privation (στέρησις) in Cat 10-11 see also Metaph Ι 4 1055a35-8)


there is no pair of contradictory properties each of which can be expressed without using the word lsquonotrsquo For example there could have been a word lsquoreluctantrsquo having exactly the same meaning as lsquonot willingrsquo in that case there would be a pair of contradictories reluctant and willing each of which was expressible without using the word lsquonotrsquo Similarly there may have been and surely could have been a pair of thus related words in ancient Greek

I will not attempt any more precise characterization of subjecthood than the one Aristotle gives For the present we must simply hope that we can tell a subject when we see it I will assume that there are such subjects as white sad happy mad sleepy and bored and that the contradictories of these subjects ndash not white not sad and so forth ndash are not themselves sub-jects With this provisional understanding of a subject Aristotlersquos four combinations for a changersquos starting- and endpoint can be illustrated as follows

The lamb changes (i) from sad to happy (subject to subject) (ii) from mad to not mad (subject to non-subject) (iii) from not sleepy to sleepy (non-subject to subject) (iv) from not amused to not (non-subject to non-subject) bored

In case (i) the lamb changes from being some particular way to being some other particular way In case (ii) it changes from being some way to not being that way Case (iii) is the reverse the lamb changes from not being some way to being that way In case (iv) the lamb is said to change from not being some way to not being some (other) way

Aristotle quickly rules out changes of type (iv) on the grounds that there is no opposition between not being some way and not being some (other) way He has asserted shortly beforehand that the endpoints of a change are always either contradictories or contraries or at least lie along a range bounded by contraries (224b28-9) In case (iv) each of the end-points is described as the contradictory of a subject and it is assumed ndash rightly or wrongly ndash that two terms of such negative character will never be contrary or contradictory to each other (225a10-12) This leaves three forms that a change might take Two of them namely (ii) and (iii) are forms of change between contradictory endpoints A change of type (iii) is


a generation and a change of type (ii) is a perishing ndash either generation and perishing without qualification as when a lamb comes to be and ceases to be or generation and perishing lsquoof a sortrsquo (γένεσίς τις φθορά τις) as when a lamb comes to be sleepy and ceases to be sleepy (225a12-20) Aris-totle says that the remaining form of change namely (i) always proceeds between contraries or between endpoints lying intermediate along a range bounded by contraries (225b3)23

Aristotle next gives a series of arguments designed to show that only the kind of change which proceeds between subjects that is between contrar-ies or intermediates qualifies as what he calls lsquomotionrsquo (κίνησις) I use the traditional translation of Aristotlersquos Greek term note that whereas in Eng-lish lsquomotionrsquo is normally restricted to locomotion the term it translates in Aristotle extends also to changes of size and quality At least this much is common just as all locomotion is change but not vice versa so all Aristo-telian motion (κίνησις) is change (μεταβολή) but not vice versa

The argument for restricting the title of motion to changes of type (i) while withholding it from any change between contradictories is difficult to follow in its details A brief outline must suffice The main premise is that it is impossible for what is not ndash in any of various senses of not being ndash to undergo motion or at least to undergo motion per se By contrast it is possible for what is not to undergo generation per se Perhaps the thought is that sentences such as lsquowhat is not white moves per sersquo are never true whereas sentences such as lsquowhat is not white becomes (white) per sersquo are sometimes true24 Aristotle first supports this premise simply by reviewing a few different cases of non-being (225a21-5) He later gives

23) Aristotlersquos rejection of type (iv) and his claim about type (i) seem both to be grounded in the assumption that there are no pairs of contradictory subjects To see this suppose that there were a pair of contradictory subjects plus and minus In that case a change from plus to minus although a change between two subjects and hence a change of type (i) would be a change between contradictories not between contraries or intermediates Second since plus and minus are contradictory to each other not plus and not minus would be con-tradictory to each other as well thereby falsifying the reason Aristotle gave for rejecting changes of type (iv)24) Aristotle may back off slightly from this idea at 225a27-9 perhaps what is not under-goes generation only accidentally But he says lsquostill it is true to say that not being applies without qualification to what comes to bersquo The remark is difficult it echoes a similarly dif-ficult remark at Phys 1 8 191b15-16 where Aristotle explains how his account of change accommodates the familiar doctrine that lsquonothing will come of nothingrsquo There he says that


a brief argument which is that whatever undergoes motion is in a place whereas what is not is not in a place (225a30-2) hence what is not does not undergo motion25 Since what is not does undergo generation and does not undergo motion it follows that generation is not motion The conclusion is then extended to perishing on the grounds that the contrary of a motion is a motion and generation and perishing are contraries Hence if perishing were motion generation would be motion as well but it has been shown that generation is not motion so perishing is not motion either

With this conclusion established Aristotle goes on to announce at the end of chapter 1 and to argue during most of chapter 2 that motion can occur with respect to exactly three categories of predicate quality quan-tity and place (Physics 5 1 225b5-5 2 226a26) Motions in these respects are given the names alteration growth or diminution and locomotion (226a26-33) Thus we arrive at the following picture

things come to be only accidentally from what is not and explains lsquofor a thing comes to be from a privation which is per se something that is notrsquo25) Again the qualification lsquoper sersquo must be understood whatever moves per se is in a place per se but what is not is not in a place per se Compare DA 1 3 406a12-16 where Aristo-tle argues from the claim that the soul is not in place per se to the conclusion that the soul does not undergo motion per se


Aristotlersquos division of motion according to categories of predicate supple-ments the division of change into motion on the one hand and change between contradictories on the other It is a subdivision of motion as determined by that initial division26 This is shown by the fact that Aristotlersquos stated reason for excluding substantial changes such as the com-ing into existence of a cat from the class of motions is that predicates in the category of substance ndash for example cat ndash do not have contraries but only contradictories (Physics 5 2 225b10-11) (He ought to have made a stronger claim namely that these predicates do not lie along any ranges bounded by contraries The stronger claim is also plausible) By contrast predicates in the categories of quality quantity and place do lie along ranges bounded by contraries and Aristotle gives this as a reason why there is motion in respect of such predicates (Physics 5 2 226a24-6)

An alteration then is a change between contraries or intermediates in the category of quality A growth or diminution is a change between con-traries or intermediates in the category of quantity A locomotion is a change between contraries or intermediates in the category of place

So much for change between contraries or intermediates What about change between contradictories What varieties does this kind of change include We know that it includes substantial changes the coming into existence of a cat for example and the going out of existence of a cat Aristotle indicates that there are other varieties as well Substantial changes he says are generations and perishings lsquowithout qualificationrsquo but there are also generations and perishings lsquoof a sortrsquo He gives the example of a change from not white to white ndash a generation into white ndash and he hints at the example of a change from white to not white ndash a perishing from white27 White is a quality so apparently Aristotle admits changes between contradictories in the category of quality We may call them qual-itative generations and perishings For all he says there might also be gen-eration and perishing in quantity and place but I will focus on the category of quality

26) Pace Ross who says that lsquoa fresh principle of classification is introduced by the mention of the categories in 225b5-9rsquo (Ross p 616) See pp 85ndash6 below27) For generation into white see Phys 5 1 225a14-15 5 5 229b10-11 For perishing from white see 5 1 225a19-20


Aristotlersquos classification of change in Physics 5 as I have now interpreted it incorporates a rather fine distinction On one side are alterations for example from white to black which are motions on the other side are qualitative generations and perishings for example from white to not white which are not motions28 On the face of it nothing can both be a motion and not be a motion so the distinction may not be straddled Aristotle requires then that something can be say a change from white to black without also being a change from white to not white and that some-thing can be a change from white to not white without also being a change from white to X for any quality X

For many purposes to insist upon this distinction would be hairsplit-ting and Aristotle typically does not insist on it Outside of Physics 5-6 he appears to count any change in respect of quality as an alteration without pausing to scrutinize whether it is a change between contraries or whether it is after all a change between contradictories and therefore according to Physics 5 not an alteration but a sort of generation or perishing29

Even so I believe the distinction is of intrinsic interest and also that it carries implications for the interpretation of other important Aristotelian texts An example is the discussion of perception in De Anima 2 5 When an animal comes to perceive a sensible quality says Aristotle its perceptive

28) For statements to the effect that changes between contradictories in addition to being generations and perishings are not motions see Phys 5 1 225a26 32 35-b129) At Cat 14 15b11-12 Aristotle says lsquoalteration is change (μεταβολή) in respect of qual-ityrsquo Metaph Λ 2 1069b9-14 also suggests that every change of quality is an alteration


soul undergoes a rather special sort of transition which may be compared with but must be distinguished from alteration30 Recently Hendrik Lorenz has offered to elucidate the special nature of this psychic transition as follows it is a lsquoquasi-alterationrsquo differing from ordinary alteration inso-far as the latter is lsquodestructiversquo consisting in the loss and replacement of some initial quality whereas quasi-alteration is lsquonon-destructiversquo not con-sisting in the loss of any initial quality31 Now it seems that Lorenzrsquos descrip-tion of lsquonon-destructive alterationrsquo is satisfied by qualitative generation It is unlikely however that the psychic transition undergone in perception is a qualitative generation because the latter is classed as a change (μεταβολή) and is subject to the general theory of change elaborated in Physics 5-6 For example a qualitative generation must be temporally extended and its subject must be divisible By contrast the transition by which Callias starts to see green would seem to be instantaneous not temporally extended and it is doubtful whether its subject Calliasrsquo perceptive soul is divisible in the relevant way Thus given Aristotlersquos admission of qualitative genera-tion we see that Lorenzrsquos account of quasi-alteration fails to yield a distinc-tive feature of the transitions involved in perception

Or at least we see this if we find that Aristotlersquos distinction between alteration and qualitative generation is a genuine and sustainable one Some commentators have thought that it is not Ross for example com-ments as follows

But it will be noticed that under the heading of γένεσίς τις and φθορά τις Aristotle introduces the very same changes which are also κινήσεις The fact is that the same process may be described in either of two ways Describe it as a thingrsquos acquisition (or loss) of whiteness then it is γένεσίς (or φθορά) τις Describe it as a thingrsquos passage from contrary to contrary eg from blackness to whiteness (or from whiteness to blackness) and it is κίνησις32

30) Here I follow the interpretations of Myles Burnyeat lsquoDe Anima II5rsquo Phronesis 47 (2002) 28-98 (cf pp 58 67 72) and Hendrik Lorenz lsquoThe Assimilation of Sense to Sense-object in Aristotlersquo OSAP 33 (2007) 179-220 For recent argument on behalf of a competing interpretation see Robert Heinaman lsquoActuality Potentiality and De Anima II5rsquo Phronesis 52 (2007) 139-187 According to Heinaman Aristotle is talking about perceiving not transitions into perceiving and he does not contrast perceiving with altera-tion but classifies it as a particular kind of genuine alteration31) Lorenz p 18732) W D Ross Aristotlersquos Physics A Revised Text With Introduction and Commentary Oxford (1936) p 616 (ad Phys 5 1 225a35-b9)


If Ross is correct then Aristotlersquos distinction flirts with contradiction Each qualitative change both is and is not a motion being both a change between contrary or intermediate endpoints such as white and black and a change between contradictory endpoints such as white and not white We could avoid contradiction by holding that the title lsquomotionrsquo must be relativized to descriptions but this would not be terribly satisfying Aristotle gave the impression that his distinction was a physical one grounded in physical principles about motion place and being and not a mere matter of onersquos choice of description

Rossrsquos own response to the difficulty is to claim that at the end of Phys-ics 5 1 Aristotle abandons the distinction between changes with contrary endpoints and changes with contradictory endpoints The introduction of categories of predicate at 225b5-9 yields a lsquofresh principle of classificationrsquo33 according to which every change of quality quantity or place is a motion and all and only substantial changes are not motions However this claim goes against the plain meaning of Aristotlersquos text As we saw Aristotle does not merely stipulate but actually argues that there is motion precisely in respect of quality quantity and place and some of his arguments rest on the claim that motion proceeds between contrary or intermediate but not contradictory endpoints The categories do not provide a fresh principle of classification but an elaboration of the classification Aristotle has already made

There are better ways to answer the difficulty First we should recall that Aristotle is classifying changes by reference to per se descriptions of change So the trouble only gets started if it is true that when something changes per se from white to black (for example) it also changes per se from white to not white or from not black to black In the following section I will sug-gest that this is not the case that when something alters it changes only partwise or accidentally between contradictory pairs such as these

Suppose however that an altering subject does in fact change per se between contradictories as well as between contraries or intermediates Then the next question is whether its change from white to black (for example) is identical with its change from white to not white or its change from not black to black This question of identity can be answered in the negative with the help of topological theses from Physics 6 It can be shown

33) Ross p 616


that at least in typical cases the three changes occupy different intervals of time and therefore are not identical with one another

So when something alters either it does not undergo qualitative gen-eration or perishing at all (because it changes merely per aliud between contradictory endpoints) or its qualitative generation and perishing are distinct changes from its alteration On either approach Aristotlersquos distinc-tion among these different sorts of change is sustainable As we will see however there is some reason to prefer the first approach For given cer-tain additional theses from Physics 6 when we suppose every alteration to be accompanied by qualitative generation and perishing then we can derive strong and I think unwelcome constraints on the temporal struc-ture of alteration

If alteration does not involve qualitative generation or perishing we may wonder where in the world the latter sort of change is to be found I will close by proposing an example in which it seems plausible to say that something changes (per se) from not white to white

The per aliud approachWhenever something alters from white to black then before changing the subject is white and after changing the subject is not white In some sense therefore the subject changes from white to not white As we saw in section 2 however it does not follow from this that the subject changes per se from white to not white For comparison whenever something moves from Cairo to Athens then beforehand the thing is in Africa and afterwards it is in Europe but as we saw the thing moves only partwise not per se from Africa to Europe Or again when I am thinking of the color white (and of nothing else) and something turns white then before-hand the thing bears a color I am not thinking about and afterwards it bears the color I am thinking about but the thing changes only acciden-tally not per se from what is not being thought about to what is being thought about

It may be maintained then that in a typical case of alteration from white to black (and mutatis mutandis for other motions) the subject does not change per se from white to not white but only does so partwise or accidentally nor does it change per se from not black to black but only partwise or accidentally As we saw at the end of section 2 Aristotle set aside per aliud change before introducing the distinction between motion generation and perishing Therefore we should understand his distinction


as follows If in undergoing a given change the subject changes per se between contrary or intermediate endpoints then the change is a motion if in undergoing a given change the subject changes per se between contra-dictory endpoints then the change is a generation or perishing When a subject changes merely per aliud between contrary or intermediate end-points the subject does not undergo motion and when a subject changes merely per aliud between contradictory endpoints the subject does not undergo generation or perishing

I would like to say that when a subject changes per se from white to black the subject changes merely per aliud ndash that is either partwise or accidentally ndash from white to not white Therefore the subject undergoes motion but does not undergo perishing

Which is it partwise or accidentally It must be admitted that the pres-ent case is not neatly assimilable to Aristotlersquos examples of either kind of per aliud change Aristotlersquos examples of partwise change recall were that when something turns white it changes partwise into color and that when something moves into Athens it moves partwise into Europe His example of accidental change was that when something turns white and the color white is being thought of the thing changes accidentally into what is being thought of

The relation of white to color is the relation of determinate to determin-able The relation of Athens to Europe might be understood in different ways as the relation of (more) determinate location to determinable loca-tion or as a relation of containment between boundaries or as a part-whole relation among regions of land If we want to say that when something turns from white to black it changes partwise into not white then we must say that the relation between black and not white is the same as or at least closely analogous to the relation between white and color or the relation between Athens and Europe

If on the other hand we want to say that when something turns from white to black it changes accidentally into not white then we must say that the relation between the descriptions lsquoblackrsquo and lsquonot whitersquo is the same as or at least closely analogous to the relation between the descriptions lsquowhitersquo and lsquowhat is being thought of rsquo

If we wish to go the partwise route we might propose that not white is a determinable property one whose determinations include every color other than white as well as the property of lacking color altogether Then we could say that black is part of not white in just the same way as white


is part of color This claim is open to objection however When one prop-erty is a determination of another as in the case of white and color it seems right to say that something bears the latter property in virtue of bearing the former34 Thus for example the snowball is colored in virtue of being white Moreover it seems plausible to say that being white is a way of being colored where being yellow (for example) is a different way of being colored If black is a determination of not white then the same should go for these two properties Yet it does not seem right to say that the coal is not white in virtue of its being black We may grant that the presence of black necessitates the absence of white but the absence does not seem to be metaphysically grounded in the presence Nor does it seem plausible to say that being black is a way of not being white where being yellow (for example) is a different way of not being white Black and yellow are two different alternatives to being white but there is no evident difference in the way in which white is absent to a black thing and to a yellow thing

I find these objections difficult to weigh both what we ourselves should think of them and what Aristotle would think of them Much will depend both on the details of our metaphysics of qualities and on our understanding of such phrases as lsquoin virtue of rsquo At any rate however it is not simple and unproblematic to assert that altering from white to black involves changing partwise from white to not white (Likewise for chang-ing partwise from not black to black)

It remains to explore the accidental route As a first idea we might try to use the fact that black is not (that is is not identical with) white It follows that when something changes per se into black it changes acci-dentally into what is not white We could attempt to abbreviate this as the claim that the thing changes accidentally into not white This is not a satisfying line to take however It would equally well justify saying that since hot is not identical with white when something changes per se into

34) I have in mind a grounding or lsquoin virtue of rsquo relation such as is discussed in Gideon Rosen lsquoMetaphysical Dependence Grounding and Reductionrsquo in Bob Hale and Aviv Hoffmann (eds) Modality ndash Metaphysics Logic and Epistemology Oxford (2010) 109-135 See especially pp 126-130 Certain of Aristotlersquos uses of the causal dative can plausibly be taken to express this relation for example lsquoI call something primary if it is thus-and-so not because something other than it is thus-and-sorsquo (λέγω δὲ πρῶτον ὃ μὴ τῷ ἕτερόν τι αὐτοῦ εἶναι τοιοῦτόν ἐστιν) Phys 6 5 235b33-4


hot it changes accidentally into not white Changing accidentally into not white in this sense does not entail that the subject of change is no longer white once it has changed Our analysis ought to capture the fact that necessarily once something has changed from white into black the thing is no longer white

As a second idea we might appeal to the fact that black excludes white necessarily if something is wholly black then no part of it is white It fol-lows that when something changes per se into black it changes accidentally into what excludes white Given that what excludes white necessitates not being white we could try to infer that the thing changes accidentally into not white (The idea would be that the thing loses its whiteness derivatively by or in virtue of acquiring a color that excludes white)

On this second idea the analysis of the thingrsquos changing accidentally is not strictly parallel with the analysis of Aristotlersquos lsquowhat is being thought of rsquo example In Aristotlersquos example the accidental endpoint was specified in terms of something predicated of the property acquired in the change being thought of was predicated of the color white On the present idea the acci-dental endpoint is something predicated of the subject of change itself not being white is predicated of the subject not of the color black This con-stitutes a significant extension of the notion of accidental change and we may worry whether it is legitimate Let me say something in its defense however Aristotle remarks at one point that change in respect of relational properties occurs only accidentally (Physics 5 2 225b11-13) Thus for example Theaetetus cannot change per se from being shorter than Socrates to being taller than Socrates but he can do so accidentally Aristotle does not offer an analysis of such an accidental change but it seems that it would have to share some features with our suggested analysis of changing accidentally into not white For example we might attempt the following Theaetetus grows per se to six feet and six feet is greater than Socratesrsquo height so Theaetetus grows accidentally into what is greater than Socratesrsquo height therefore Theaetetus changes accidentally into being taller than Socrates The accidental endpoint here is a relational property which is predicated of Theaetetus himself not of the quantity acquired by Theaete-tus when he grows There are still some differences between the lsquotaller than Socratesrsquo case and the lsquonot whitersquo case but it seems that Aristotle is com-mitted to allowing at least something in the direction of what we need35

35) A major difference it seems to me is this it is plausible to say that Theaetetusrsquo being


In sum when a thing changes per se from white to black it is not obvi-ously and straightforwardly true that the thing changes partwise or acci-dentally from white to not white The relation between black and not white is not exactly the same as any of the relations at work in Aristotlersquos own explicit examples of partwise or accidental change On the other hand it seems likely that Aristotle was prepared to extend his notions of partwise and accidental change in at least some ways beyond what his examples exemplify Given this it is within bounds to claim on his behalf that change between contraries such as from white to black involves changing merely partwise or accidentally between contradictories such as from white to not white and from not black to black

The multiple changes approachSuppose instead that whenever something changes per se from white to black it also changes per se from white to not white and from not black to black What should we say about the question of identity is the subjectrsquos change from white to black identical with its change from white to not white And with its change from not black to black

It would be convenient if we could appeal in answering this question to Aristotlersquos own discussion of oneness of change in Physics 5 4 Unfor-tunately Aristotlersquos discussion there does not apply to the present kind of case He states criteria according to which change K is one in genus or in species with change L and he states criteria according to which change K is one both in being and in number with change L but he gives no criteria according to which change K would be one in number yet not one in being with change L36 In the present case it is obvious that a change from white to black is not one in being with a change from white to not white (What it is to change from white to black is not the same as what it is to change from white to not white as shown by the fact that it is possible to do the latter without doing the former) Given this Physics 5 4 provides

taller than Socrates consists in his having a height which is greater than Socratesrsquo height But it is less plausible to say that a thingrsquos not being white consists in its having a property which excludes white So the last step in the derivation of lsquoTheaetetus changes accidentally into being taller than Socratesrsquo can be justified by a strong relation of ontological ground whereas the last step in the derivation of lsquothe thing changes accidentally into not whitersquo was justified by a relation of mere necessitation36) Oneness in genus Phys 5 4 227b4-6 Oneness in species 227b6-11 Oneness both in being and in number (lsquooneness without qualificationrsquo) 227b21-228a3


no instructions for determining whether the change from white to black is numerically one with the change from white to not white

Nevertheless I think that non-identity can be established on the basis of a difference in temporal extent This requires a premise to the effect that the temporal extent of a change is not description-dependent The premise is open to challenge but I believe it is widely accepted

In addition we will need two theses from Physics 6 In both the phrase lsquoper sersquo should be supplied ad lib The first thesis is this

Completed[a] When a change has first been completed the subject is wholly in the changersquos endpoint (Physics 6 5 235b7-8)37

[b] When a change has not yet been completed the subject is not wholly in the changersquos endpoint (Physics 6 4 234b11-13)

For example when a doormat has first completed a change from white to black then and not before the doormat is wholly black (that is it and every color-receptive part of it is black) When a doormat has first com-pleted a change from white to not white then and not before the door-mat is wholly not white (that is neither it nor any part of it is white)

The second thesis is this

Underway[a] When a change has gotten underway the subject is not wholly in the changersquos starting point (Physics 6 4 234b11-13)

[b] When a change has not yet gotten underway the subject is wholly in the changersquos starting point38

37) In Aristotlersquos statement of this thesis there is a word which might be translated either as lsquofirstrsquo or as lsquoprimarilyrsquo Ben Morison lsquoLe temps primaire du commencement drsquoun change-mentrsquo in J-F Balaudeacute and F Wolff (eds) Aristote et la penseacutee du temps (Nanterre Universiteacute Paris X 2005) 99-111 has argued for the second translation However Morison agrees I think that lsquowhen the thing primarily has changedrsquo turns out to denote a temporal instant which could also be denoted by lsquowhen the thing first has changedrsquo For my own present purposes then I attribute to Aristotle a thesis using the easier word lsquofirstrsquo38) I have not found a direct statement of underway [b] in Aristotle but an argument for it can be given on Aristotelian premises We may assume that at some time before a change the subject is wholly in the changersquos starting point (cf Phys 6 4 234b12-13) So long as the change has not yet gotten underway the subject has been at rest in the relevant respect


For example when a doormatrsquos change from white to black has gotten underway the doormat is not wholly white whereas so long as the change has not yet gotten underway the doormat is wholly white

Now suppose that in January I lay down a white doormat and that over the months this doormat undergoes an alteration from white via various shades of brown and grey to black We suppose that the doormat also undergoes a change from white to not white and a change from not black to black I will argue that neither of these latter two changes occupies the same interval of time as the alteration from white to black

There will be a time say in February when the doormat is no longer wholly white but when no part of the doormat has yet become black perhaps there are some white patches some brown patches and various shades of grey patches At this time the doormatrsquos alteration from white to black has gotten underway since the doormat is not wholly white (under-way [b]) By contrast the doormatrsquos change from not black to black has not yet gotten underway since the doormat is still wholly not black (under-way [a]) The alteration from white to black is underway at a time when the change from not black to black is not yet underway There will also be a time say in April when the doormat is wholly non-white but is not yet wholly black perhaps it now consists of brown and black patches At this time the doormatrsquos change from white to not white has been completed since the doormat is wholly not white (completed [b]) By contrast the doormatrsquos alteration from white to black has not yet been completed since the doormat is not yet wholly black (completed [a]) The change from white to not white is complete at a time when the change from white to black is not yet complete

Thus the change from white to black is underway earlier than the change from not black to black and is completed later than the change from white to not white It does not occupy the same time interval as either one

Given the premise that identity of change implies identity of temporal extent the doormatrsquos alteration from white to black is not identical with its change from white to not white nor with its change from not black to black

The upshot is that if we do not adopt the lsquoper aliud rsquo approach we should affirm that when something changes in respect of quality quantity

(Phys 6 1 232a12 6 3 234a32-3) So long as something has been at rest it is wholly the same as it was (Phys 6 8 239a27-9) Hence so long as a change has not yet gotten under-way the subject is still wholly in the changersquos starting point


or place then the thing undergoes three different changes a motion from the starting point to the endpoint plus a perishing from the starting point plus a generation into the endpoint

Drawbacks of the multiple changes approachAffirming this carries certain disadvantages To begin with it seems unpar-simonious we have three changes where there appeared to be only one This lack of parsimony can be mitigated if we propose that the generation and perishing are parts of the motion since it is widely agreed already that changes have other changes as parts39 But it is unclear how well-motivated the proposal would be40

Moreover it turns out that if every motion involves a generation into its endpoint and a perishing from its starting point ndash regardless whether these are parts or mere accompaniments ndash then significant constraints result on the structure of any motion This is because Aristotle defends a number of theses in Physics 5-6 which apply to all changes and in particular would apply to the generations and perishings which supplement each motion Their application to these additional changes yields constraints beyond

39) The proposal is inspired by a remark by Hendrik Lorenz though I am not sure he intended his remark in the sense in which I take it up He writes that in a normal alteration from F to G lsquoto undergo the change is in part to suffer the loss of F-nessrsquo (Lorenz p 183)40) Aristotle gives the impression that every part of a motion is a motion (cf Phys 6 4 234b22-3 235a9-13) just as a part of a time is a time of a line a line of a surface a surface of a body a body (Thanks to the editors for this point) It is at any rate unclear what sort of part the generation and perishing would be they are not straightforward temporal subseg-ments are they something like conceptual parts


what follows from their application directly to the original motion Aristo-tle defends for example the following three claims

Extended [a] Every change is temporally extended There is an interval of time during which the change has gotten underway and has not been completed (Physics 6 3 234a24)41

With underway [a] and completed [b] this has the corollary

[b] For every change there is an interval of time when the subject is neither wholly in the starting point nor wholly in the endpoint

Endtime [a] For every change there is an earliest temporal instant at which the subject has completed the change (Physics 6 5 236a10-13)

With completed [a] and [b] this has the corollary

[b] For every change there is an earliest temporal instant at which the subject is wholly in the changersquos endpoint

Starttime [a] For every change there is no earliest temporal instant at which the change has gotten underway (Physics 6 5 236a13-14)

With underway [a] and [b] this has the corollary

[b] For every change there is no earliest temporal instant at which the subject is no longer wholly in the changersquos starting point

If we apply these theses directly to the alteration of a doormat from white to black we obtain the following results Extended [a] The alteration is temporally extended and so [b] there is an interval of time during which the doormat is neither wholly white nor wholly black Endtime [a] There is a first instant when the alteration has been completed and so [b] there is a first instant when the doormat is wholly black Starttime [a] There is no first instant when the alteration has gotten underway and so [b] there is no first instant when the doormat is no longer wholly white

So far these are all plausible claims To illustrate why they might be expected to be true suppose that the doormatrsquos alteration can be repre-sented by a graph with two axes one representing time and the other rep-resenting the doormatrsquos overall level of brightness (At brightness 1 the doormat is wholly white at brightness 0 the doormat is wholly black and

41) See also Phys 6 4 235a12-13 6 6 237b3-7


at brightnesses in between the doormat is in between) Such a graph might appear as follows

The dark line representing the doormatrsquos alteration has been drawn without any gaps or breaks embodying an assumption to the effect that the alteration is continuous As represented the doormatrsquos alteration satis-fies extended endtime and starttime It extends from time 0 to time 1 and during this interval ndash at every instant later than 0 and earlier than 1 ndash the doormat is neither wholly white nor wholly black (its overall brightness is less than 1 and greater than 0) At time 1 the doormat is wholly black whereas at every instant earlier than 1 the doormat is not yet wholly black thus time 1 is the first instant when the alteration has been completed and when the doormat is wholly black At time 0 the doormat is wholly white whereas at every instant later than 0 the doormat is no longer wholly white thus given that there is no first instant after 0 there is no first instant when the alteration has gotten underway or when the doormat is no longer wholly white So far so good

Now suppose however that the doormatrsquos alteration involves also a per-ishing from white and a generation into black Aristotlersquos general theory of change would then govern this perishing and generation as well as govern-ing the alteration We would obtain the following new results

Extended perishing There is an interval of time when the doormat is neither wholly white nor wholly not white (applying extended [b] to the perishing from white) It follows that there is an interval of time when the doormat is partly white and partly not white

Extended generation There is an interval of time when the door-mat is neither wholly not black nor wholly black (applying extended [b] to the generation into black) Therefore there is an interval of time when the doormat is partly black and partly not black


Endtime perishing There is a first instant when the doormat is wholly not white (Applying endtime [b] to the perishing from white)

Starttime generation There is no first instant when the doormat is partly black (Applying starttime [b] to the generation into black)

If it is supposed that every motion involves a perishing from its starting point and a generation into its endpoint then these results may be general-ized for every motion there is an interval of time when the subject only partly occupies the starting point there is an interval of time when the subject only partly occupies the endpoint there is a first instant when the subject is wholly out of the starting point there is no first instant when the subject is partly in the endpoint

Would or should Aristotle be willing to commit himself to these four new claims Granted they appear to be satisfied by at least some motions As I described the alteration of the doormat above for example the door-mat stopped being white patch by patch and started being black patch by patch with the result that extended perishing and extended genera-tion were both satisfied We may imagine further that in the initial seg-ment of the alteration the white area of the doormat contracted in continuous fashion and that likewise in the final segment of the altera-tion the black area of the doormat expanded in continuous fashion In this case endtime perishing and starttime generation would also be satisfied The question is whether all motions are like this it seems to me highly doubtful that they are

Alteration It is natural to think and certain remarks of Aristotlersquos sug-gest that it is possible for something to alter with all of its parts in unison42 For example it seems possible for something to change temperature all together ndash that is in such a way that at any given instant within the change every part of the subject is equally hot or cold as every other part If some-thing alters in such a way then its motion will not satisfy any of our four new claims Since it alters all together there will not be any time when it only partly occupies the starting point nor any time when it only partly occupies the endpoint Again since it alters all together it is wholly out of the starting point when and only when it is not wholly in the starting point since moreover (applying starttime [b] to the alteration) there is no first

42) See for example Phys 8 3 253b24-6


instant when it is not wholly in the starting point there will be no first instant when it is wholly out of the starting point Finally since it alters all together it is partly in the endpoint when and only when it is wholly in the endpoint since moreover (applying endtime [b] to the alteration) there is a first instant when it is wholly in the endpoint there will be a first instant when it is partly in the endpoint

Growth and diminution It does not seem to me conceivable that a body only partly has a given size and hence that something only partly occupies the starting point or endpoint of a growth or diminution Furthermore for reasons similar to those given for alteration in unison it seems that in growth or diminution there will be no first instant when the thing (wholly or partly) lacks its initial size and there will be a first instant when the thing (both partly and wholly) has its final size Thus all four claims appear to be false for growth and diminution

In sum the view that every motion involves a perishing from the start-ing point and a generation into the endpoint leads to unattractive conse-quences Of course it is possible that Aristotle did not notice these consequences or did not agree that they are unattractive Thus it is possi-ble that he believed every motion to involve a perishing and a generation perhaps as parts Still these consequences provide at least some reason to return with a sympathetic eye to our first approach the lsquoper aliud rsquo approach They make it more attractive to hold that when something undergoes motion it only partwise or accidentally perishes from the starting point and comes to be in the endpoint of the motion

32 An example of qualitative generation

I have tried to show that one may coherently draw a distinction between changes that proceed between contradictory endpoints on the one hand and changes that proceed between contrary or intermediate endpoints on the other The distinction does not collapse in the face of the fact that one thing can be described in different ways Aristotle draws the distinction in Physics 5 1 and he implies that there are changes of quality falling on both sides of the distinction There are alterations from (for example) black to white and there are changes from not white to white

I have yet to describe any concrete example of the latter kind of change To my knowledge Aristotle himself does not specify any We considered the view that such changes occur alongside of or as parts of alterations That view however ndash at least in its strongest form namely as the view that


every motion involves these kinds of changes ndash had unattractive conse-quences In a normal case I think when something changes from black to white it does not also change per se from not white to white I would like to propose a different sort of case as an example

Crack an egg into a hot frying pan The yolk is yellow the albumen is transparent For Aristotle transparency is not a color if something is transparent then it has no color43 Thus the eggrsquos albumen initially has no color As the egg cooks however it changes until its albumen is white Thus the albumen undergoes a change such that it initially has no color and finally bears the color white From what and to what does it change per se Not from transparent to white because these are not contradictories contraries or intermediates (They are not contraries or intermediates because the contrary of white is black and everything intermediate between white and black is a color whereas transparency is not a color) I can supply Aristotle with no better description than by saying that the eggrsquos albumen comes to be white that it changes per se from not white to white I propose this then as an example of qualitative generation

43) For the relation between transparency and color see DA 2 7

ltlt ASCII85EncodePages false AllowTransparency false AutoPositionEPSFiles true AutoRotatePages None Binding Left CalGrayProfile (Dot Gain 20) CalRGBProfile (sRGB IEC61966-21) CalCMYKProfile (US Web Coated 050SWOP051 v2) sRGBProfile (sRGB IEC61966-21) CannotEmbedFontPolicy Error CompatibilityLevel 13 CompressObjects Off CompressPages true ConvertImagesToIndexed true PassThroughJPEGImages true CreateJDFFile false CreateJobTicket true DefaultRenderingIntent Default DetectBlends false DetectCurves 00000 ColorConversionStrategy LeaveColorUnchanged DoThumbnails false EmbedAllFonts true EmbedOpenType false ParseICCProfilesInComments true EmbedJobOptions true DSCReportingLevel 0 EmitDSCWarnings false EndPage -1 ImageMemory 1048576 LockDistillerParams true MaxSubsetPct 100 Optimize false OPM 1 ParseDSCComments true ParseDSCCommentsForDocInfo true PreserveCopyPage true PreserveDICMYKValues true PreserveEPSInfo true PreserveFlatness true PreserveHalftoneInfo false PreserveOPIComments false PreserveOverprintSettings true StartPage 1 SubsetFonts false TransferFunctionInfo Apply UCRandBGInfo Remove UsePrologue false ColorSettingsFile (None) AlwaysEmbed [ true ] NeverEmbed [ true ] AntiAliasColorImages false CropColorImages true ColorImageMinResolution 150 ColorImageMinResolutionPolicy Warning DownsampleColorImages true ColorImageDownsampleType Bicubic ColorImageResolution 300 ColorImageDepth -1 ColorImageMinDownsampleDepth 1 ColorImageDownsampleThreshold 150000 EncodeColorImages true ColorImageFilter DCTEncode AutoFilterColorImages true ColorImageAutoFilterStrategy JPEG ColorACSImageDict ltlt QFactor 015 HSamples [1 1 1 1] VSamples [1 1 1 1] gtgt ColorImageDict ltlt QFactor 015 HSamples [1 1 1 1] VSamples [1 1 1 1] gtgt JPEG2000ColorACSImageDict ltlt TileWidth 256 TileHeight 256 Quality 30 gtgt JPEG2000ColorImageDict ltlt TileWidth 256 TileHeight 256 Quality 30 gtgt AntiAliasGrayImages false CropGrayImages true GrayImageMinResolution 150 GrayImageMinResolutionPolicy Warning DownsampleGrayImages true GrayImageDownsampleType Bicubic GrayImageResolution 300 GrayImageDepth -1 GrayImageMinDownsampleDepth 2 GrayImageDownsampleThreshold 150000 EncodeGrayImages true GrayImageFilter DCTEncode AutoFilterGrayImages true GrayImageAutoFilterStrategy JPEG GrayACSImageDict ltlt QFactor 015 HSamples [1 1 1 1] VSamples [1 1 1 1] gtgt GrayImageDict ltlt QFactor 015 HSamples [1 1 1 1] VSamples [1 1 1 1] gtgt JPEG2000GrayACSImageDict ltlt TileWidth 256 TileHeight 256 Quality 30 gtgt JPEG2000GrayImageDict ltlt TileWidth 256 TileHeight 256 Quality 30 gtgt AntiAliasMonoImages false CropMonoImages true MonoImageMinResolution 550 MonoImageMinResolutionPolicy Warning DownsampleMonoImages true MonoImageDownsampleType Bicubic MonoImageResolution 2400 MonoImageDepth -1 MonoImageDownsampleThreshold 150000 EncodeMonoImages true MonoImageFilter CCITTFaxEncode MonoImageDict ltlt K -1 gtgt AllowPSXObjects false CheckCompliance [ PDFX1a2001 ] PDFX1aCheck false PDFX3Check false PDFXCompliantPDFOnly false PDFXNoTrimBoxError false PDFXTrimBoxToMediaBoxOffset [ 000000 000000 000000 000000 ] PDFXSetBleedBoxToMediaBox false PDFXBleedBoxToTrimBoxOffset [ 000000 000000 000000 000000 ] PDFXOutputIntentProfile (GWG_GenericCMYK) PDFXOutputConditionIdentifier () PDFXOutputCondition () PDFXRegistryName () PDFXTrapped False Description ltlt CHS ltFEFF4f7f75288fd94e9b8bbe5b9a521b5efa7684002000410064006f006200650020005000440046002065876863900275284e8e9ad88d2891cf76845370524d53705237300260a853ef4ee54f7f75280020004100630072006f0062006100740020548c002000410064006f00620065002000520065006100640065007200200035002e003000204ee553ca66f49ad87248672c676562535f00521b5efa768400200050004400460020658768633002gt CHT ltFEFF4f7f752890194e9b8a2d7f6e5efa7acb7684002000410064006f006200650020005000440046002065874ef69069752865bc9ad854c18cea76845370524d5370523786557406300260a853ef4ee54f7f75280020004100630072006f0062006100740020548c002000410064006f00620065002000520065006100640065007200200035002e003000204ee553ca66f49ad87248672c4f86958b555f5df25efa7acb76840020005000440046002065874ef63002gt DAN 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 DEU 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 ESP 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 FRA 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 ITA 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 JPN ltFEFF9ad854c18cea306a30d730ea30d730ec30b951fa529b7528002000410064006f0062006500200050004400460020658766f8306e4f5c6210306b4f7f75283057307e305930023053306e8a2d5b9a30674f5c62103055308c305f0020005000440046002030d530a130a430eb306f3001004100630072006f0062006100740020304a30883073002000410064006f00620065002000520065006100640065007200200035002e003000204ee5964d3067958b304f30533068304c3067304d307e305930023053306e8a2d5b9a306b306f30d530a930f330c8306e57cb30818fbc307f304c5fc59808306730593002gt KOR ltFEFFc7740020c124c815c7440020c0acc6a9d558c5ec0020ace0d488c9c80020c2dcd5d80020c778c1c4c5d00020ac00c7a50020c801d569d55c002000410064006f0062006500200050004400460020bb38c11cb97c0020c791c131d569b2c8b2e4002e0020c774b807ac8c0020c791c131b41c00200050004400460020bb38c11cb2940020004100630072006f0062006100740020bc0f002000410064006f00620065002000520065006100640065007200200035002e00300020c774c0c1c5d0c11c0020c5f40020c2180020c788c2b5b2c8b2e4002egt NLD (Gebruik deze instellingen om Adobe PDF-documenten te maken die zijn geoptimaliseerd voor prepress-afdrukken van hoge kwaliteit De gemaakte PDF-documenten kunnen worden geopend met Acrobat en Adobe Reader 50 en hoger) NOR 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 PTB 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 SUO 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 SVE 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 ENU (Ghent PDF Workgroup - 2005 Specifications version3 (x1a 2001 compliant)) gtgt Namespace [ (Adobe) (Common) (10) ] OtherNamespaces [ ltlt AsReaderSpreads false CropImagesToFrames true ErrorControl WarnAndContinue FlattenerIgnoreSpreadOverrides false IncludeGuidesGrids false IncludeNonPrinting false IncludeSlug false Namespace [ (Adobe) (InDesign) (40) ] OmitPlacedBitmaps false OmitPlacedEPS false OmitPlacedPDF false SimulateOverprint Legacy gtgt ltlt AddBleedMarks false AddColorBars false AddCropMarks false AddPageInfo false AddRegMarks false ConvertColors ConvertToCMYK DestinationProfileName () DestinationProfileSelector DocumentCMYK Downsample16BitImages true FlattenerPreset ltlt PresetSelector MediumResolution gtgt FormElements false GenerateStructure false IncludeBookmarks false IncludeHyperlinks false IncludeInteractive false IncludeLayers false IncludeProfiles false MultimediaHandling UseObjectSettings Namespace [ (Adobe) (CreativeSuite) (20) ] PDFXOutputIntentProfileSelector DocumentCMYK PreserveEditing true UntaggedCMYKHandling LeaveUntagged UntaggedRGBHandling UseDocumentProfile UseDocumentBleed false gtgt ]gtgt setdistillerparamsltlt HWResolution [2400 2400] PageSize [14173229 14173229]gtgt setpagedevice


the ontological question what change is (whether it is activity or other-ness or non-being or so forth) His aim here is to articulate the structural or topological features which any change must have For example he establishes that every change occupies not an instant but an interval of time and that changes (as well as spatial magnitudes and times) are con-tinuous He argues further that whatever is continuous is atomless all of its parts have further proper parts and thus in particular it has no point-like parts These and related theses have large metaphysical and empirical consequences they figure for example in the cosmological arguments of Physics 8 and in Aristotlersquos general theory of the generation and perishing of composite entities2

A further reason for interest in the treatise is that Aristotlersquos claims about change there may shed light on his understanding of certain other types of occurrence occurrences whose status as changes is (surprisingly) denied or whose relation to change is controversial For example Aristotle sug-gests that coming into contact and losing contact are not changes3 and perhaps one reason is that these transitions do not have the temporal struc-ture required of change in Physics 5-6 A more important example is Aris-totlersquos treatment of perception where his views about the role of alteration and change is under vigorous debate I believe that Physics 5-6 offers clues that can help move the debate forward there is not space here to justify this hope in detail but along the way I will offer a small example to illus-trate the point

This paper will focus on two distinctions made at the opening of Aristotlersquos treatise in Physics 5 1 first a distinction between changing4 per se and changing per aliud and second a distinction among changes (μεταβολαί) between those that are motions (κινήσεις) and those that are not motions The first is a special case of a ubiquitous and ever-

2) In GC 1 2 Aristotle explains that the atomless structure of bodies makes a crucial differ-ence to the proper account of their generation perishing and alteration Contemporary philosophers also have argued from the actual or possible existence of so-called lsquoatomless gunkrsquo to major theses about the metaphysics of composite entities See for example Theo-dore Sider lsquoVan Inwagen and the Possibility of Gunkrsquo Analysis 53 (1993) 285-289 Dean Zimmerman lsquoTheories of Masses and Problems of Constitutionrsquo Phil Review 104 (1995) 53-110 Jonathan Schaffer lsquoIs There a Fundamental Levelrsquo Noucircs 37 (2003) 498-513) DC 1 11 280b6-9 26-84) In this paper the verbs lsquochangersquo and lsquomoversquo are always used in their intransitive sense to undergo change or undergo motion


































































































































33) Ross p 616


































































41) See also Phys 6 4 235a12-13 6 6 237b3-7



























































































































































33) Ross p 616


































































41) See also Phys 6 4 235a12-13 6 6 237b3-7





















































































































































33) Ross p 616


































































41) See also Phys 6 4 235a12-13 6 6 237b3-7













































































































































33) Ross p 616


































































41) See also Phys 6 4 235a12-13 6 6 237b3-7




































































































































33) Ross p 616


































































41) See also Phys 6 4 235a12-13 6 6 237b3-7































































































































33) Ross p 616


































































41) See also Phys 6 4 235a12-13 6 6 237b3-7


























































































































33) Ross p 616


































































41) See also Phys 6 4 235a12-13 6 6 237b3-7





















































































































33) Ross p 616


































































41) See also Phys 6 4 235a12-13 6 6 237b3-7















































































































33) Ross p 616


































































41) See also Phys 6 4 235a12-13 6 6 237b3-7









































































































33) Ross p 616


































































41) See also Phys 6 4 235a12-13 6 6 237b3-7




































































































33) Ross p 616


































































41) See also Phys 6 4 235a12-13 6 6 237b3-7





























































































33) Ross p 616


































































41) See also Phys 6 4 235a12-13 6 6 237b3-7























































































33) Ross p 616


































































41) See also Phys 6 4 235a12-13 6 6 237b3-7

















































































33) Ross p 616


































































41) See also Phys 6 4 235a12-13 6 6 237b3-7









































































33) Ross p 616


































































41) See also Phys 6 4 235a12-13 6 6 237b3-7

































































33) Ross p 616


































































41) See also Phys 6 4 235a12-13 6 6 237b3-7





























































33) Ross p 616


































































41) See also Phys 6 4 235a12-13 6 6 237b3-7























































33) Ross p 616


































































41) See also Phys 6 4 235a12-13 6 6 237b3-7


















































33) Ross p 616


































































41) See also Phys 6 4 235a12-13 6 6 237b3-7














































33) Ross p 616


































































41) See also Phys 6 4 235a12-13 6 6 237b3-7









































33) Ross p 616


































































41) See also Phys 6 4 235a12-13 6 6 237b3-7




































33) Ross p 616


































































41) See also Phys 6 4 235a12-13 6 6 237b3-7































33) Ross p 616


































































41) See also Phys 6 4 235a12-13 6 6 237b3-7



























































































41) See also Phys 6 4 235a12-13 6 6 237b3-7





















































































41) See also Phys 6 4 235a12-13 6 6 237b3-7














































































41) See also Phys 6 4 235a12-13 6 6 237b3-7









































































41) See also Phys 6 4 235a12-13 6 6 237b3-7




































































41) See also Phys 6 4 235a12-13 6 6 237b3-7































































41) See also Phys 6 4 235a12-13 6 6 237b3-7




















































41) See also Phys 6 4 235a12-13 6 6 237b3-7












































41) See also Phys 6 4 235a12-13 6 6 237b3-7







































41) See also Phys 6 4 235a12-13 6 6 237b3-7























































































Documents

Motion and Change in Aristotle's Physics 5.1