THE MARK SACKS LECTURE
Identity, Individuation and Substance
Oxford OX1 3BN
The paper takes off from the problem of finding a proper content for the relation of identity as it holds or fails to hold among ordinary things or substances. The necessary conditions of identity are familiar, the sufficient conditions less so. The search is for conditions at once better usable than the Leibnizian Identity of Indiscernibles (independently suspect) and strong enough to underwrite all the formal properties of the relation.
It is contended that the key to this problem rests at the level of metaphysics and epistemology alike with a sortalist position. Sortalism is the position which insists that, if the question is whether a and b are the same, it has to be asked what are they? Any sufficiently specific answer to that question will bring with it a principle of activity or functioning and a mode of behaviour characteristic of some particular kind of thing by reference to which questions of persistence or non-persistence through change can be adjudicated.
These contentions are illustrated by reference to familiar examples such as the human zygote, the Ship of Theseus and Shoemaker's Brown-Brownson. The first example is hostage for a mass of unproblematical cases. The problems presented by the second and third sort of examples arise chiefly (it is claimed) from an incompleteness in our conceptions of the relevant sort—the what the thing in question is. That incompleteness need not prevent us from knowing perfectly well which thing we are referring to. In the concluding section, sortalism is defended against various accusations of anthropocentrism.
The paper touches on the interpretation of Heraclitus, Leibniz's theory of clear indistinct ideas, the difficulties of David Lewis's ‘perdurantist’ or stroboscopic view of persistence, four-dimensionalism, and the relation of personal identity both to experiential memory and to the particular bodily physiognomy of a subject. At some points—as in connection with the so-called Only a and b rule—the paper corrects, supplements or extends certain theses or formulations proposed in the author's Sameness and Substance Renewed (2001).
My subject is identity and individuation. By identity I mean being the same as. By individuation I mean something done by a thinker. Among acts of individuation I include (1) singling out something which is a g (a donkey, say) as a g; (2) distinguishing that g from other gs; (3) singling something out when coming upon it again and recognizing it as that g, the same g again.1 It will appear in due course how I take identity and individuation to be connected. By a substance I intend, with tradition, something singular or individual. Unlike a universal/type/sort/ kind/clone/character, a substance does not have specimens or instances. Nothing falls under it, exemplifies it or instantiates it.2
Forty four years ago I published a short monograph called Identity and Spatio-Temporal Continuity, henceforth ISTC (Wiggins 1967). Once I saw it in print, I started putting one or two things right. From this process arose Sameness and Substance, henceforth S&S, (Wiggins 1980) and later Sameness and Substance Renewed, henceforth S&SR (Wiggins 2001). Ten years further on, noting the virtual disappearance of the sortalist view of identity from present day discussions, I wonder sometimes whether the third of these efforts was found to be unreadable. What I know for certain is that, over the passage of time, the philosophical scene has changed. It is no longer wise to assume, as I was apt to do, that everyone with a serious interest in the metaphysics of identity will know Aristotle's distinction between what a thing is (i.e. what fundamental kind of thing it is) and what the thing is like, or be eager to read such texts as Categories, Chapters 1–5. Nor can the other Aristotelian resonances by which I once set such store be relied upon any longer to enlighten or remind. If they have any effect, it is rather to discredit the claim to have arrived at a perfectly general account—an account not at odds with anything that modern science reveals to us—of the identity and individuation of objects which are extended in space and persist through time.
So putting to one side the insights of Aristotle—who will enter now only at the point where the argument simply forces our attention onto him—we shall proceed here more simply and single-mindedly, starting from the bare logic of the identity relation and setting the still underestimated requirements of that logic in authority over the judgements of same and other into which we are constrained by the effort to make sense of the world of perpetual alteration in which we have to find our way.
In partial illustration of the extent and nature of the perpetual alteration aforesaid, let me set the scene for our enquiry by drawing from a work of science which was as important in its day as it was lucid of expression:
[In the living animal] the large and complex molecules and their component units are constantly involved in rapid chemical reactions … Part of the pool of newly formed small molecules constantly re-enters vacant places in the large molecules to restore the fats, the proteins, and the nucleoproteins … Components of an animal are rapidly degraded into specific molecular groupings which may wander from one place to another. The chemical reactions must be balanced so delicately that, through regeneration, the body components remain constant in total amount and in structure. … All regeneration reactions must be enzymatic in nature. The large molecules, such as the fats and the proteins, are, under the influence of lytic enzymes, constantly being degraded to their constituent fragments. These changes are balanced by synthetic processes which must be coupled to other chemical reactions, such as oxidation or dephosphorylation. After death, when the oxidative systems disappear, the synthetic processes also cease, and the unbalanced degradative reactions lead to the collapse of the thermodynamically unstable structural elements. In general, every regeneration reaction involving an increase in free energy must be coupled with another process. In order to maintain structure against its tendency to collapse, work has to be done. The replacement of a brick fallen from a wall requires energy, and in the living organism energy debts are paid by chemical reactions … (Schoenheimer 1942: 62–4)
In other words:
All constituents of living matter, whether functional or structural, of simple of complex constitution, are in steady state of rapid flux. (Ibid.: 3)
Heraclitus, the first Western thinker to recognize the cosmic significance of change, is commonly reputed to have denied, precisely on the basis of the processes of change, all possibility of identity through change. But he did not deny it:
Upon those who step into the same rivers different and again different waters flow. The waters scatter and gather, come together and flow away, approach and depart. (Fragments 12 and 91, as reunited by Geoffrey Kirk in Kirk 1954)
On the view I take of Heraclitus, it was the maintenance or perpetuation of the world order—and within that order the persistence through time of things such as rivers (‘the same rivers’)—that Heraclitus set out to describe, redescribe and explain.3 However obscurely or allusively his account of these matters anticipates Schoenheimer's. But one will understand these accounts best if one does not misconstrue the common sense of identity.
We begin upon that common sense with the bare logic of the relation. First we have the obvious truth where everybody begins, the reflexivity of identity:
For all x, x is the same thing as x.
In second place, we have Leibniz's principle, the Indiscernibility of Identicals. This requires that, if x is the same thing as y, then x and y have all the same properties:
If x is identical with y, then x is F if and only if y is F4
From these two principles, taken together, there follow the symmetry and transitivity of identity. Suppose x = y and y = z. Then x has any property y has. But y is z. So x is z. That gives transitivity. Now symmetry. Suppose x = y. Then y has any property x has. One of x's properties is being the same as x. So y too has that property. So y is x.
There are three further consequences. The first is the necessity of identity:
If x is the same thing as y, then x is
necessarily the same thing as y.
Proof: x is necessarily x. So, by the Indiscernibility principle, the object y has the same property as x has, namely the property of being necessarily the same thing as x.5 Moreover the very same scheme of argument guarantees the absolute determinacy of identity6:
If x is the same thing as y, then x is
absolutely and determinately the same thing as y
For x is absolutely and determinately the same thing as x. Similarly we have the permanence of identity:
If x is the same thing as y then x is always the same thing as y.
Proof. x is always the same thing as x. So y, which is the same as x, has x's property of always having x identical with it.
What flows from these findings?
Downwind from the necessity of identity we have the thought that, if x is the same thing as y, then their identity will hold regardless of how matters stand with other things. The identity of x with y will not then involve or depend upon anything that is different from or independent of x or y. The identity of x and y may of course be discovered in all sorts of ways that involve reference to other things, but constitutively the identity of x and y involves only x and y.7
Downwind from the Indiscernibility Principle itself we have an Adequacy Requirement: whatever grounds the identity of x with y must ipso facto, and by that same token, ground the indiscernibility of x and y.8 It follows that, in the presence of an adequate reason to think that x is the same as y, one of the things we must be able to say is that, for all z, however x is to z, so too will y be to z. The importance of this requirement will appear—along with the sortalist way of meeting it—when one confronts questions of splitting or fusion. Our claim will be that nothing can count as a ground of identity unless it arises from a conception of a kind or sort of thing which x and y each exemplify and the conception confirms the unqualified or ceteris paribus presumable transitivity of the relation. See Section 10.
Consider next the permanence of identity. The identity of an object or a person is altogether unlike a hat or garment that one can take off or put on. In the literal sense there is no such thing as something's or someone's getting a new identity. The one way in which a thing that persists cannot change, so long as it maintains the steady state of rapid flux that is essential to it, is in respect of being the changeable thing, the cow, horse, human being … that it is. There are not two relations among substances, namely simple identity and identity over time or through change—no more than there are varieties of sameness (unless mere similarity is what is at issue). Identity over time or through change is the simple or ordinary identity of things that last over time or through change. It is the identity relation as restricted to things that change.
Consider next the absoluteness and determinacy of identity.9 This discourages us from trying to make sense of objects or of identities that are vague or indeterminate, but not from maintaining that we can have a to some degree indeterminate or vague conception either of this or that object itself or of the sortal concept it falls under—or of both.10 Section 16 ad fin returns to this matter.
From the determinacy of identity we may advance further perhaps. Where identity is concerned, it seems impossible to make sense of ‘almost’ or ‘nearly’. Why? Well, x is neither almost x nor almost not x. So, if y is x, then y is not almost x or almost not x. That flows from indiscernibility. Given also the principle of permanence, one then arrives at the thought that y never was almost x or almost not x. Nor then can it have been a close run thing for y to have been the same thing as x. By contrast, consider growing tall enough to be a guardsman or strong enough to lift 50 kilograms. One can describe what more it would take or would have taken to do that. Where identity is concerned, there is no describing anything like that.
If identity is all or nothing and leaves no room for nearly or almost, doesn't that rule out saying of someone that he just missed being the King of Sweden or was almost the first to discover oxygen? No. Once one thinks for a moment what is being said here, it is clear that in neither of these cases is there anybody whom he is being said to be almost identical with. All that is being said is that he came close to being crowned King of Sweden or almost discovered oxygen before anyone else discovered oxygen.
So far we have been following through the necessary conditions of identity. But what are the sufficient conditions?
Here philosophers often deploy a principle of Leibniz's, the Identity of Indiscernibles:
If x and y have all their properties in common then x is y.
If we admit properties such as being the same person as Caesar or being the same building as the Pantheon, this principle is undeniable. But we need a sufficient condition which does not presuppose identity.
One could follow Leibniz a little more closely. Conceiving every individual as unique and claiming on the basis of his Principle of Sufficient Reason that there could never be two individuals indiscernible from one another, Leibniz believed that relations, including relations that appear to us as temporal and spatial, supervened or depended on the totality of the successive states of the true substances of the world. In this spirit, one could interpret the Identity of Indiscernibles in a way that excluded from among the properties that it speaks of all properties that presuppose the prior determinations of identity or difference. Maybe, as Leibniz supposed, every true substance really is in fact unique.11 (Never mind the doubt whether his principle of Sufficient Reason required that.) But, even where every substance is unique, the identity of indiscernibles is still a questionable basis for a properly general definition or explication of identity.12 It is worth noting, moreover, that in the world as we know it one cannot exclude the possibility of an extended object that is perfectly symmetrical about all planes which bisect it. In the terms prescribed how is one to distinguish one half of the thing from its other half?
Let us put the monadic interpretation to one side and try another approach. Let us admit relational properties but purify them of all reference to particular objects already identified. Now however—as is well known—the Identity of Indiscernibles encounters another problem concerning symmetry. Consider square 22 and square 43 on the chess board (Figure 1) that Strawson gives on page 123 of his book Individuals (Strawson 1959).
Strawson writes ‘Think of a chess board. The universe we are to consider is bounded by its edges. The universe consists therefore of a limited arrangement of black and white squares … Even if the view from each square is allowed to comprehend the whole board, [it] is still impossible to differentiate square 43 from square 22. The view from each over the whole board is the same: each has two white squares going away from it in one direction and five in the other …’ In other words, one who inhabits the universe Strawson describes and relies upon the principle of the Identity of Indiscernibles will be bound to identify the distinct squares 43 and 22.
At this point friends of the Identity of Indiscernibles13 will object that, even if squares 22 and 43 cannot be separated by reference to properties provided for in Strawson's set-up, these squares are ‘relatively discernible’; 43 is to the left of 22, for instance. Nor is it true, they will say, that whatever square directly adjoins 22 directly adjoins 43. But where does such a defence leave us? It raises questions about what principles ought to govern such enquiries as this. In constructions or thought-experiments such as Strawson's, what can or cannot be taken for granted concerning the chessboard-dwellers' grasp of left/right, and their capacity to keep track of objects whose discovery they mark by a demonstrative? More importantly, it reminds us of the difference between (A) a workable sufficient condition which can be applied or appealed to by an enquirer who is on the ground (so to speak) and in the presence of objects which at once persist and change; and (B) a Leibnizian condition of identity whose satisfaction can appear or be verified only at the conclusion of explorations and labours conducted on the basis of a workable sufficient condition based in some thought other than the Identity of Indiscernibles—a sufficient condition presupposed perhaps to the self-orientation of the observer in Strawson's chessboard example.
What makes me so sure that there must be some other thought? Well, we do arrive at judgements of identity. We do so almost effortlessly in many (but by no means all) ordinary cases. Yet imagine the process of trying to do so by enumerating all the properties of x and comparing them with all the properties of y. Without yet knowing any identities concerning x—without knowing properties of x other than those which are manifest at the moment of attempting the comparison—how could one assemble all the properties of x itself in order to check them against all the properties of y? There must be some other way—a way accessible in principle to someone who looks out at an object for the first time, keeps track of it and learns in due course to recognize it when coming upon it again. At this point the metaphysics of identity has no alternative but to reconstruct the thoughts that organize the epistemology of the relation and to reconstruct what thinkers actually do when they single out an object in experience, at once observing the thing's behaviour, speculating what it does when out of view and searching for the distinguishing marks (if any) by which this one may be distinguished from other members of its kind and (however fallibly) reidentified as one and the same.
According to the so-called sortalist conception of identity which I have tried over the years to defend and propound, the question that organizes the efforts of one who seeks to track an object continuously through the changes that it undergoes is this: ‘What kind of a thing is this object before me? What is it? How does such a thing behave?’ Moreover, at this point, having been driven hither by the search for a workable sufficient condition of identity—driven by nothing less than the logic of the matter—we have no option but to attend to Aristotle. For the what is it? question is Aristotle's question. According to him, substantives such as man, apple tree, horse … not only determine the appearances of the things we single out under these denominations but imply also a phusis or nature. The phusis of a thing is its mode of being. It is the principle of activity of a kind whose members share and possess in themselves a distinctive source of development and change. Compare Metaphysics 1015a11, Physics 192b21.
The problem we had with a sufficient condition of identity was that we could not find any general condition. But the reason why we couldn't—or so it now appears—is that there is no such unitary condition to discover. When we ask whether a is the same as b, we must be ready to ask what a is and what b is. Despite their divers analogies and structural resemblances, the phuseis of things are many and various.
Here I offer a small supplement to Aristotle. What guides our efforts to make sense of the world, to track things, and to reconstruct that which befalls them outside our view, is a rough and ready but developing conception of what a man, an apple tree, a horse … is. Leibniz would say it is a clear indistinct idea, an applicable and practically effective conception of such a thing, but a conception ready and waiting to be supplanted by what Leibniz would call a more distinct idea of it—an idea or conception that is better informed and more analytical or articulated.14 As we enquire into the nature of what confronts us, we subsume it provisionally and tentatively under more and more specific conceptions of the phusis which it instantiates, simultaneously inquiring into that phusis and correcting or refining our ideas about the phuseis of a host of other kinds that we encounter. (Compare Aristotle, Posterior Analytics, II, 19.) It is a natural suggestion that our aptitude for this kind of work is all of a piece with our practical capacity to apprehend the meanings of the substantives for thing-kinds which we learn not from verbal definitions but from examples that we encounter or that are shown to us.
Here let us expect an objection. There is simply no difficulty, it may be said, in keeping a thing under continuous observation without making reference to any sort or kind. Indeed it simply has to be possible to do this. Otherwise we could never fix upon a thing in order to ask what is it?
To the second and more threatening of these two points I reply by emphasizing Leibniz's distinction between clear (workable/operationally applicable) ideas or conceptions of a thing-kind and more distinct (more analytical and scientifically or otherwise spelled out) ideas or conceptions. In this connection Leibniz might also point out that, if we did not bring to experience something not itself of experience, we should be unable to make anything of experience. Innate within us there has to be not only an eagerness to look for continuities and a willingness to associate one presentation with some earlier presentation, but also a predisposition to search out certain particular kinds of thing. No doubt different animals have evolved to search out different kinds. But everywhere the instinctual and pre-experiential idea which is implicit in our strivings and presides over them, has, I claim, to be an instinctual or innate conception or idea of an object or substance of some sort f—more precisely the conception: object or substance endowed with its principle of activity/functioning.15 It is not the bare idea of an object or the idea of a bare object to which might then be superadded just any nature or way of being and behaving. That is not the idea we work from. But suppose we did work from it—rather than from some, however provisional, determination of the idea of an object or substance of a sort endowed with its own discoverable principle of activity or functioning. Then what judgements of identity or difference could be available to us, working either from that bare idea or from the idea of such a bare thing, when we witnessed the metamorphosis of the pupa into a chrysalis and the chrysalis into the moth or butterfly? Or suppose we watch a warehouse fire in which a bronze statue is reduced to a molten lump of metal. Everyone will agree that the statue is now a molten lump of metal. But what does it mean to say that? The continuity criterion requires that this verdict be taken to be a verdict of identity. But that reading is at fault.16 The notion of identity it invokes does not subject itself to the requirements we have derived from the logic of the relation. Apply Leibniz's Law (the Indiscernibility of Identicals, not the Identity of Indiscernibles). The lump of metal has survived the fire. The statue has not survived it. The statue was made by Rodin (say); this mass of metal was not. And now consider transitivity. In the subsequent adventures of the lump, what else will the bare continuity theorist be forced to say the statue is identical with? What else will he end up identifying the statue with? Bare continuity supplies no principle, no rhyme or reason.17
Until we reached the question of a sufficient condition, the logic of identity seemed simple and austere. The ragged and discursive character of everything that I have been claiming since we abandoned the Identity of Indiscernibles has none of that simplicity or austerity. So it needs to be shown how the sortal conception of identity can satisfy the formal requirements we began with.
Let us begin here with the best case, namely where we have a natural kind whose members, the gs, share in a phusis which brings with it an empirically discoverable real principle of activity or nature which underlies, in ways that Putnam and Kripke (and in his own way Leibniz) have each described, the use of certain ordinary substantives or sortal predicates. (Not the use of all substantives, of course, but the use of the kinds of substantive that I am beginning with.) Where the workings of such a nature serve to demarcate a kind of organism with a settled single-track pattern of coming to be, maturation and passing away, and where that nature enters into the sortal concept under which we single out members of the kind,18 we are assured that the judgements of same and other which we arrive at on the basis of our conception of that nature will determine a relation that shadows or recapitulates the way in which properties come to qualify particular organisms of this type. We have here everything we need to meet the Adequacy requirement which was explained in Section 4, Paragraph 3. We are assured, moreover, that the transitivity of the relation we are invoking in making these judgements flows from something inherent to the kind of thing we are concerned with.19 These judgements order a sequence of states or phases that are made for one another as states or phases of a kind of thing that is possessed of a whole complex of dispositions and other properties which underlie its mode of behaviour or activity.20
Consider now a case in which the formal properties of identity may seem to be in jeopardy. Where twins will be born, the zygote divides. The logical questions—and, in the human case, the moral questions—that flow from such splitting are addressed by thinking of the organism as starting upon its proper existence or life from a point after which division is embryologically impossible. In so far as this shaping of our idea of the life span of the creature is applied to all the organisms in question (not only to cases where the zygote does in fact divide), it fills out the idea of that kind of continuant or substance and enlarges our understanding of its moral and metaphysical import. Above all, it is the idea thus refined and delimited of such a substance that makes it possible to arrive at a ground of identity that meets the standard set by the Adequacy Requirement.21 (See Section 4, Paragraph 3.)
Where the nature of a thing is not nomologically grounded in the way just described—as also in cases which involve interference in the normal workings of an object's principle of activity—it is only to be expected that our theories of identity and individuation will encounter numerous difficulties. That will trouble us soon enough. (See Sections 16 and 17 following.) First though I want to review the defences of the conception which we have been taking for granted of the world of changeable, enduring objects that are extended in space and persist through time.
Parmenides, asking how something that is could possibly come to be from what is not, gave logical arguments to show that that which truly is—the real reality—must be changeless, imperishable, one, unique, boundless on all sides, ‘motionless in the limits of mighty bonds’, continuous and without spatial or temporal differentiation. His argument was effectively disarmed when Aristotle showed that the challenge Parmenides had set out could be divided and then answered piecemeal. But the question of change never goes away, it seems. The most recent challenge comes from a new picture and a new argument. If we are to understand change, it is urged, we must replace our everyday or endurantist conception of substances by a less familiar so-called perdurantist—or, as I might prefer to say, stroboscopic—conception. The things we take to be enduring (it is argued) are really successions of changeless, distinct and instantaneous temporal parts.
David Lewis writes:
Sometimes you sit and then you are bent; sometimes you stand or lie, and then you are straight. How can one and the same thing have two contrary intrinsic properties? How does it help to say [as the endurantists say] that it has them at different times? (Lewis 2002: 441)
Lewis's explanation of ‘intrinsic’ may be given as follows:
We distinguish intrinsic properties, which things have in virtue the way they themselves are, from extrinsic properties, which they have in virtue of their relations or lack of relations to other things. (Lewis 1986: 61)
Lewis is right to insist that being straight and being bent are not extrinsic properties. For these are not relational properties. But does the fact that I was (at t1) sitting and was later (at t2) standing really render such properties relational?22
If I am seated now, today, in front of a wooden table, does the involvement of the wooden table, the time and the place make my being seated into a relational state? How can they do that? In so far as there is a relation here, I protest, it surely holds between (1) the non-relational and faultlessly intrinsic state of my having sat down or being seated, the state itself resulting from the action/event that initiated the state; and (2) the scene (at that table/that time/that place) where that action or event of sitting down took place.
For formal purposes there may be a reason to represent ‘David was seated at table t during the period p …’ by R(d,t,p …). But this notation was never designed to reveal the full nature of the verb/predicate R or the plurality and diversity of everything that might be supplied to further argument places within the brackets.23 We learn nothing from the notation about the serious idea of relation that David Lewis needs to call in evidence if he seeks to insist upon the intrinsic character of being bent, straight … sitting, standing… .
A word now about the conclusion itself that Lewis draws from his account of intrinsic properties. Is it not a strange business to transfer onto a noun the temporal indication that seems to qualify a verb? It is one thing for a physicist to seek to displace the world-view of substances and their alterations—and to displace it entirely—by an altogether different one, as in the spirit of Ernst Machs's assertion:
bodies are bundles of reactions connected by law … that which is constant is always the connection of reactions according to law and this alone. This is the critically purified concept of substance which scientifically ought to replace the vulgar one.24
It is another thing to seek to correct the more inclusive world-view at which philosophy seeks to arrive and to replace ordinary objects by successions of thing-moments—this-horse-at-t, that-river-at-t, or David-Lewis-at-t. At one and the same time, how can we deny ordinary substances their status as proper continuants, insist that ordinary substances are really constructs, yet lean shamelessly upon our ordinary understanding of substances when we come to specify that from which these constructs are to be seen as constructed or assembled? (Within a straightforward advocacy of Mach's proposal one would not even attempt such a thing. One has left all that behind.) Are thing-moments such as this-horse-at-t to be introduced or explained not in a way that presupposes horses and times but directly and simply by definition—creative definition—or by simple postulation?25 Even as one considers that sort of question, moreover, one must ask one more: could one bestow upon an object so defined—durationless as it has to be (given the argument on which the whole construction depends)26—all the properties of shape, disposition and attitude upon which the perdurantist aspired to found the intrinsic properties of sitting, standing … bent, straight … and the like on which the original argument depended?
It is not an option for philosophy to reject the four dimensional conception of the world urged upon us by some philosophers and metaphysicians of science. But in accepting it one is not committed to see things, people and organisms in perdurantist fashion as made up of instantaneous temporal parts. Instead, let us think of a three dimensional substance in the ordinary endurantist way, then think of the space-time region the substance occupies, then take a thing-moment as an instantaneous cross-section of that region.27 On these terms, one arrives at the four-dimensional view by beginning from an endurantist conception of a substance, without having to cut off a branch that one is sitting on or resorting to creative definition. Proceeding thus, one can advance philosophically unimpeded to the metaphysical relation of substances to their four-dimensional counterpart.
We distinguish effortlessly between Socrates and the succession of events that makes up Socrates' life history. Can we not make a philosophical distinction then between Socrates himself and a succession of thing-moments in four-dimensional space-time? At any moment in Socrates' life we can answer the question which person Socrates is. But, we cannot say which space-time region Socrates is identical with until Socrates has departed this life and the series of events in space-time that make up his life is complete. We can say of Socrates that he could have adopted a different defence at his trial at Athens in 399 bc. But of a completed series of events or thing-moments in space-time we can hardly say that that very series might have comprised different occurrences. (A set-theoretical object such as a succession has its members necessarily.) We can of course say that, in the place of this or that succession or series of events in space-time, a different one might have existed, comprising perhaps a similar initial section. But it won't be enough to say that sort of thing if we want to take it fully seriously that the real Socrates might have mounted a different defence. To speak simply of a different succession of events from the actual events of Socrates' life including an alternative defence does not make room for Socrates himself to mount an alternative defence—unless of course we are ready to distinguish between the person Socrates and a succession of events. More generally, consider predication. Can one predicate of a succession of events, as one can of a person, the properties weak, cowardly, capable, resolute, opportunistic, erratic, honest, a fair-weather friend, or (the Emperor Galba's special attribute) capax imperii nisi imperasset?28
Should such thoughts and attributions as these be dispensed with altogether then? Or should we seek for some compromise that hunts down four-dimensional surrogates for these properties? Better still, I think we should hold on to the proper recipients of such attributions, and rest content with the fact that the enduring substances we normally think and speak of register perfectly satisfactorily within the four-dimensional continuum (see again Carnap, as quoted in note 27). It is true that the three-dimensional things that have these histories are not singled out under concepts that have application in space-time physics or cosmology. But that will not exempt the things themselves from the laws of nature that govern the material world.
To the philosophical four-dimensionalist who likes to think of substances as possessing temporal parts as well as spatial parts, the category differences just dwelt upon may appear pedantic and inconsiderable. But they point towards something of profound interest to us, namely the constraints upon any conception of body or substance which can be open to an organism or person that acts, deliberates, or enquires. A conscious being cannot think of itself—or of the persons, organisms or physical objects that it encounters—as having the shape of a complete succession of events and present only in part at the moment of action or deliberation. Nor can it think of itself as an event or an event in the making. To act and think as it does, a conscious being must think of its whole self as present at the moment of reflection, perception or action and poised to persist in that way in the future. It must think of itself at t as extending in space wherever its parts are at t. It must conceive its past as consisting not of its parts (in the sense in which it is spatially extended by its parts at t) but of the earlier phases or stages of the life of the whole being which it itself is.29
To hold out for the category differentiation that underlies these contentions is (in the pejorative sense) anti-scientistic, if you will. But it is in no way at odds with the scientific world-view itself. Indeed it vindicates modes of description that are natural, habitual and seemingly indispensable to almost all branches of science itself.30
Back now to identity and change. Suppose that we try to apply the ideas set out in Section 9 not to the individuation of natural substances but to the individuation of artefacts. Taking artefacts as things organized in such a way as to subserve some designated purpose or purposes, one might say that, just as a natural thing has a principle of activity, so an artefact has its mode of operation or functioning. But how close or illuminating is that parallelism?
Following the narrative of Plutarch's Life of Theseus, consider Theseus' ship as preserved through the centuries by the Athenians for its annual voyage from Piraeus to the shrine of Apollo on the island of Delos. Suppose, in the spirit of Thomas Hobbes' use of the example (see S&SR: 92–3), that even as the ship was refitted year by year with new planks or spars, a long line of cunning fathers and sons or daughters salvaged everything that was replaced and cast aside. Suppose that, in the end, some descendant of theirs found that he had collected everything he needed—or almost everything (and enough, it might be said)—to reassemble Theseus' original ship. Suppose he claimed that he now owned Theseus' original ship. He might issue the announcement: Never mind the constantly renewed ship plying its annual course to Delos. If you want to see the real thing, come and see the ship itself. Admission 10 drachmae.
In the cases where we had the phusis of a natural thing following its own course, such problems were excluded. For an artefact, however, there is no norm or law of development to exclude such happenings. Nor can we delegate the whole matter to a scientist who can delve deeper into the principle of activity for a ship or for that sort of ship. There is no such principle. The question at issue relates rather to the purposes of those whose artefact it is—purposes they may perhaps modify, reconsider, revise or refine as time passes.
On one reading of those purposes, Theseus' ship must be the ship that is constantly renewed. But if one says that, one must stare down the reconstructed ship. One must seek to discredit it. There is something doctrinaire about that. On another reading of those purposes, it may be said that we should balance a technical interest that users have in the purpose that is served by an artefact with the concern they have with the histories of things. Looking for a compromise they might attempt between those interests, its sailors might trace the ship through its usage over the years, yet rule at the same time that there is a limit to how far the process of renewal and material replacement can be carried—a limit which in the case that Hobbes imagined is exceeded. But then (alas) all sorts of disquieting or annoying further questions will appear.31
Rather than search further for a resolution or explore more subtle conceptions of a ship, let us advance to something more general and more important. It is this. If genuine identity is to be the thing at issue here, then (1) the dialectic of same and other within which all these questions are to be resolved must cohere with the account of what a ship (or a trireme or whatever) is; and (2) the said account of what the thing in question is must furnish a basis for adjudications of same and other which will be answerable in their collectivity to the formal requirements we began with in Section 2—and to the requirements of coherence among the ratiocinations that support the said adjudications. (Compare the requirements in a legal context upon the accumulated findings of equity/epieikeia.) Only where verdicts and grounds are answerable to this standard will there be a secure framework for the determination of genuine identity.
When one undertakes to debate seriously a question such as that of Theseus' ship, the question under debate is not then the relatively uninteresting question which ship shall receive the title or sobriquet Ship of Theseus, but the question of how to conceive the ship itself. When we reach that question, however, I think it would be wise for philosophy not to hold itself aloof from the thoughts and uses of those who ship it is. Typically, they will decide such a matter not once and for all but incrementally and in a way that the theorist needs to understand before he ventures to criticize. What happens at the beginnings of the ship casts a long shadow forwards upon matters still to be decided. Yet subsequent events and uses may retrospectively modify conceptions of what such a ship is and complicate or enrich the dialectic within which questions of same and other have to be decided.
It will be pointed out that, if one says what I have just said, then it will not be completely or fully determinate what exactly it was that Theseus built, sailed in and sent on an annual pilgrimage to Delos. And to that extent, it will be complained, indefinitely many questions of identity may remain indeterminate. Doesn't this conflict with the principle of the absoluteness and determinateness of identity given in Section 6?
I reply that there is no conflict. A line by line inspection of the argument given in Section 6 reveals that what is proved there is that there is no such identity as indeterminate identity. The proof as given does not however exclude the possibility of its being epistemically indeterminate whether x was or wasn't the same as y. For the proof depended on the transparency (non-obliquity) of the context ‘… is determinately x’. The proof leaves unaffected and to one side all non-transparent uses of ‘determinately’ or ‘definitely’.
There is another mistake to avoid here. If it is incompletely determinate at a given point in the lifetime of the ship what exactly Theseus' ship was, that does not imply that Theseus' ship itself was something vague or indeterminate. To think that would be nothing less than a confusion of sense and reference. Moreover, one who refers to the ship may know perfectly well which ship he has in mind despite his having an incomplete or only partially determinate conception of the sortal concept ship. From epistemic indeterminacy with respect to what (kind of thing) one should not simply conclude that there is epistemic indeterminacy with respect to which (thing). (Related questions, concerning Tib, Tibbles and the rest, are pursued at S&SR: 173–6.)
So much for the case where the thing-kind—the what a given object or substance is—is not nomologically grounded. After artefacts and the problems they present, let us revert to the kinds where there is a nomologically well-grounded principle of activity of a natural thing, but consider now the case where there is radical interference in the normal workings or output of that principle. In philosophy as it now is, the most conspicuous case is that of the person.32
Let us begin with the usual example in its original presentation, prescinding from endless variations and further complications that have been proposed—the case that is where Brown and Robinson each undergo an operation which involves the removal of the brain from the skull. Through a surgical blunder Brown's brain is placed in Robinson's skull. The resulting person, whom Sydney Shoemaker, the inventor of this example, calls Brownson (see Shoemaker 1963), has Brown's brain and Robinson's body; and his psychological states including memories, are those that one would expect Brown to have. Is Brownson then Brown?
The question created some excitement inside philosophy and even outside. It prompted the thought that all that counts in matters having to do with the identity of persons is psychological continuity, a relation which some claimed however implausibly to disentangle from all involvement with identity. Others reached for their response along other routes. Here is the sortalist approach. Brown is a person. How are we to think of a person? As an ego or self? As a self among a multitude of other selves? In the absence of anything more, that is not so much false as a useless starting point. (Self is not, on its own, a sortal or individuative concept. At best it is simply a determinable whose more specific determinations may be properly individuative.) What else can be said? Well, in practice, in our everyday thoughts, our paradigm for a person is a human being, an embodied substance, a creature with a certain bodily conformation, a creature that interprets other human creatures and is wide open to be interpreted by them. A person is not just any sentient or conscious being. A person is one of us.33 As such a substance grows up, lives and matures, the principle of activity of the substance becomes progressively more complex and its modes of agency, cognition and feeling, its powers and capacities, its fund of information, experience and memory all become more copious and more and more specific.
On these terms, shall one say that Brownson and Brown are the same human being? Have the events that Shoemaker describes resulted in Brownson's participating in Brown's very own principle of activity and holding on to Brown's very own life? The question needs to be considered under at least two main aspects, aspects which we will consider in this order: the aspect of cognition and awareness and the neurological-cum-characterological-cum-physiognomic aspect.
Prominent within Brown's store of information, experience, expectation and intention, some of it highly particular, is his experiential memory. Let memory be hostage for all the rest. Suppose that Brown, when he was 13 years old and playing in a parent-pupil cricket match on a school speech day, bowled out his father. Brown said he would never forget doing this. But what about Brownson? Well, Brownson says that he bowled out Brown Senior. But does Brownson really remember doing so? The only reason why he says he remembers is that he has been given Brown's brain. Mustn't we still ask whether Brownson was there at the cricket match? Was it Brownson himself, when he was 13, who bowled out Brown Senior on that occasion?
In reply to that question, some will respond by saying: ‘Never mind identity. Concentrate rather upon psychological continuity, where that embraces identity but does not definitionally require it’. But this is an unfortunate or mistaken response. I say this for three reasons.
First, in so far as the proposed relation of psychological continuity is not answerable to the Adequacy requirement, in so far as psychological continuity does not create even a presumption against the splitting of a (so-called) ‘stream of consciousness’ among multiple Brownsons, and in so far as it is not specified whether Brownson has the whole of Brown's brain or only one half,34 Brownson may have no clear title to be anything more than a propagule or a layered offshoot of Brown. In so far as we use psychological continuity as a surrogate for identity and no more is claimed than psychological continuity, we must be prepared to think of Brown not so much as a substance as a kind of substance, as the clone (-type) to which a potential plurality of Browns belong, or as a universal instantiated in different consciousnesses. We began with the question of identity, but now there has been a radical change of subject—in both senses of the word ‘subject’. Brown must span metaphysical categories.
The second point is connected with the first and no less important. Once we reconceive direct memory to the point where we cease to require of such memory that the rememberer should have him/herself been present at the event supposedly directly remembered, we remove direct memory itself from a role that is integral of our understanding of it. Within the fabric of human knowledge, not everything can depend on testimony. At some points somewhere, there have to be eye-witnesses possessed of direct or experiential memory. Without experiential memory as normally conceived, the idea of witness must go to waste (and with it received ideas of empirical knowledge). Understood in the received way, experiential memory can vouch for the claim that an event occurred and was thus and so. It can undergo cross-examination. The subject who remembers is in a position to try to place a remembered event within the whole course of his or her life and take responsibility for his or her account of what happened, what s/he saw or heard and how that was. Once memory is torn from the whole web of ideas where it belongs, however, shall we know even what we mean by ‘remember'? Can one really scrub out a key part of the meaning and expect all the rest to stand?35 And how then shall we understand the creation and accumulation of knowledge?
Thirdly, so far as Shoemaker's version of Brown and Brownson is concerned, it is entirely unnecessary to modify the idea of experiential memory. If we stay with the question as originally posed and if our way with it is to seek to determine whether Brownson participates in Brown's principle of activity or inherits Brown's very own life, the thing we have to be sure of is whether Brownson can recall some sufficiency of the other details concerning the cricket match, place it as an event in the narrative of a single life which is Brown's, report the event in the manner of a participant and so on. Once we know all that (and are satisfied mutatis mutandis with regard to other aspects of awareness), it will be time to pass to the neurological-cum-characterological-cum-physiognomical aspect of things.
Brownson's body is Robinson's body. But the character, mien, and typical responses of Brown depended in part on his physiognomy—on his whole bodily physiognomy (if I may stretch the meaning of the word so). The functioning of a human being, the capacity to express oneself in act, gesture and attitude, all depend on a mutual accord or co-adaptation, at once personal and lifelong, between the brain and the rest of the nervous system. (This is not on any sane understanding a mere contingency.) Not only that. These things depend also upon a settled co-adaptation, achieved over the passing of time and constantly adjusted, between the nervous system and the limbs—something again personal and lifelong. How could Brown-in-Brownson enjoy all of that? Nor must one omit to mention specifically the face. Brownson has the wrong face (as well as the wrong voice). It is true that a person we know may be wounded or disabled or paralysed or disfigured, even given a new face (or voice). This may represent a terrible subtraction from a going concern, but human life can allow for it. The trouble for Brownson is that his condition does not represent a stage in any going concern from which we can allow for subtraction.
At this juncture, departing suddenly from our appointed mode of enquiry in dissatisfaction with it, one finds oneself thinking as follows: if I were Brown then, if I had survived all these adventures, I should surely know that I had survived and should be able to say ‘Despite whatever has been happening to me, I still exist. There is still such a person as Brown. I am Brown.’ Enlarging on that thought, there is a temptation to insist that it is not for a philosophical theorist to say whether Brown can or cannot make it through the procedures that Shoemaker described. It is for the subject, namely Brown himself.
This can't be wrong so far as it goes. But let us try taking the subject's word for it. One question will still trouble us. When we hear the words ‘… I am Brown’, who is doing the speaking? Is it Brown-in-Brownson, that is Brown himself, or is it some new creature Brownson? A correct use of the word ‘I’ may raise more questions than it settles. Suppose the words issue from an atom-for-atom, property-for-property copy of Brown which was produced some time before Brown entered hospital. Suppose the copy says ‘I am Brown’. But, whatever the copy is or isn't, this isn't Brown himself we are faced with. Again, how tempting even is it to think that a subject we suddenly confront cannot make a mistake about who or what he is? IF subjects really can be made, copied or reconstructed, can they not be programmed to believe falsehoods about who they are or where they come from?
From this foray into the subject's side of things, a sortalist must conclude, I believe, that we were right to think that most of our difficulties have arisen from our uncertainty about the full nature and limits of personhood; that the only way forward is to develop and refine our conception of what a person is. In the multitude of ordinary cases, we shall know a person perfectly well for a person when we see one. In a large number of cases we shall know perfectly well which person he or she is. At the level of reference persons are not indefinite objects of reference or individuation. It is at the level of sense and idea that we find indeterminacy, the indeterminacy of our conception of what more precisely a person is—an indeterminacy we can only diminish by reflection and the exploration of our ideas of embodiment, of human presence, of agency, responsibility, solidarity, cognition … , but are unlikely ever to diminish to nothing. (Mutatis mutandis, compare Sections 16–17.)
It would be a mistake to suppose that it takes examples as extreme as Shoemaker's to bring home to us the uncertainty and incompleteness of our conceptions of what a person is. Let us remind ourselves of scenes which are entirely unspectacular. Suppose that in real life a woman in a very advanced state of dementia, already completely at sea in the old people's home to which she has been sent, catches pneumonia and is taken to the district hospital. Suppose that, when she gets there, it is the now habitual scene (no less familiar to the world of US medicine, I am told, than it is to tracts of the world of public medicine in Europe) of neglect and abject confusion. Suppose that she scarcely knows any longer who she is or where she has come from. She loses, it might be said, all sense of self. (Does she still ‘have’ a self? Advocates of the self to determine.) There is one residue. Her body still identifies her. Contrast Brown and Brownson. If the old woman is lucky enough, then her daughter-in-law can still find her and try very hard for a short span (the length of a visit) to ‘restore her to herself’. Even if that doesn't happen, there is still that possibility. The old woman has the potentiality perhaps to be restored to something of herself, or so we suppose. But, when we think of that possibility, how exactly do we have to conceive of a person in relation to the body that marks their presence? I am not sure. Again, I say, our conception of the human person is incomplete.
In discussion of Brown and Brownson it is often assumed that, if there were later mental events that were downwind from Brown before brain surgery, then the person Brown—or some person Brown—must have persisted somehow. But how strongly can a well-founded conception of person support that assumption? Again I am unsure.
In response to considerations such as figure in Sections 17–20, when I urged them upon him, Shoemaker proposed recently that the argument for counting Brown's life as continuing in Brownson is best made for the special case where Brown and Robinson, despite their difference of name, are identical twins.36 What a diminution of all the larger claims which have been made! But never mind. For the thing that matters much more than the Brown-Brownson question is the larger problem it illustrates, not for the first time. We have described it already. Where there is a claim of identity, what does it involve for the answer to match the question? There has to be more to the finding of identity between x and y than the discovery that y has moved smoothly into the place of x as the closest continuer for x, the best successor to x, the proper inheritor of x, or the perpetuator of the same clone- or person-type as x. The object y must arrive where x was in a way that manifests the unfolding of a nature inhering in a thing with the history of an individual substance—or else in a way which somehow converges upon that. On the sortalist view, it is that thought or some adaptation of that thought which must shape the whole dialectic within which we must try to decide questions of same and other.
The sortalist theory of identity and individuation may appear wide open to the accusation of anthropocentrism. But there is nothing anthropocentric about insisting that the judgement of same or other should have a content and be answerable by virtue of that content to the logic of identity. There is nothing anthropocentric about insisting that, as we learn more and think more, we should always be ready, at the level of sense, to adjust our ideas or conceptions of the thing-kinds under which organisms, other natural things, artefacts … are singled out. Only through fallacy (I have claimed) can the partiality, incompleteness or indeterminacy of our conceptions be transmitted from the level of sense to the level of reference, either to substances themselves or to their kinds.
It is of course a sort of anthropocentrism for us to focus our attention so intently upon the kinds of kind (ships etc.) that impinge on human life and human awareness. But (except in so far as it may be claimed that there is something special about scientific instruments and the like) such a focus does not amount to a claim of cosmic importance.
Sortalism is not a theory about the ultimate constituents of the universe. But like any other would-be respectable piece of philosophy, it leaves room for the idea of a completed theory of ultimate constituents. Such a theory would surely dispense altogether with continuants, their kinds and their qualities. (Radical developments of that sort are prefigured in the citation from Mach in Section 13.) Why though should those who will propound the completed theory want to deny the existence of the levels or categories of being that the ultimate constituents of reality subvene/sustain/make possible?
The sortalism I have defended sees itself as one component of a more general theory of identity and individuation, a theory embracing all sorts of other categories of being beside substance—categories of event, process, state, disposition, field, and heaven knows what else. Such a general account will of course confront questions and difficulties which I have not attempted or foreseen, concerning what it will take to assign their proper logical content to claims of identity that lie outside the category of substance.37
Some of the acts included in this list, like others I might adjoin, go beyond the dictionary definition of ‘individuate’. No matter. The word does no distinctive philosophical work here beyond suggesting some of the questions to be pursued and answers to be proposed.
It can of course be copied, but that is different. See further Section 15; also Wiggins 1995.
Compare fragment 125 which adjoins another illustrative instance and puts one in mind of the last portion of our first extract from Schoenheimer: ‘The barley drink disintegrates and loses its nature unless it is constantly stirred.’ Texts for this and other citations are given as B12, B91, B125 in Diels and Kranz 1952.On the interpretation of Heraclitus, see Wiggins 1982.
Cf. Quine 1972: 490. Here Quine interprets ‘F’ by specifying the intended replacements for this letter. He also explains the reason why this formal version is preferable to the informal version in terms of properties to which I often resort in the text.In the displayed version given in the text, the ‘is’ is intended timelessly. It may help against misunderstandings that prompt doubts concerning identities among things that change through time to spell out the Indiscernibility Principle as follows:
If x is identical with y (simply identical, whether timelessly or not) then, if and only if x is, was or will be F, y is, was or will be F.
In answer to questions that may be raised about the possibility of a referential opacity created by ‘necessarily’, see S&SR: 115 ff.
See S&SR: 188–92.
In S&SR, Chapter 3, Section 4, I tried to extend this near-truism into a principle D(x), the much controverted Only a and b rule. In replacing that rule by the Adequacy principle given in the next paragraph, I hope to confirm in another way certain results I sought to achieve through that rule.
Note that the grounds need not consist of a proposition. Still less will finding an identity always be a matter of deduction.
Timothy Williamson, afforcing earlier work of Prior and Kripke, has shown how, by the addition of one further logical principle beyond those we have started with here, we can vindicate the necessity and complete determinacy of difference as well as that of identity. See Williamson 1996.
For the Lockean term ‘sortal’ and its continuing usefulness, see Strawson 1959, Part Two.Anticipating the claims of the next paragraph let me say that I adjourn for another day questions that will arise about compound quasi-sortal concepts such as heap of coal, bar of soap, lump of clay, and the tolerance of the ‘indeterminate particulars’ that fall under them of diminution, replacement, exchange of their constituents vel sim. See S&S: 205–6; S&SR: 94, 37–40.
For Leibniz's doctrine here, see S&SR: 62.
I note that this point is fully available to Leibniz himself—as is the claim I should make that identity is a primitive and indefinable notion. See New Essays on Human Understanding, Book I, Chapter 3 (Leibniz 1704: 102): ‘The ideas of being, possible and same are so thoroughly innate that they enter into all our thoughts and reasoning, and I regard them as essential to our mind’.How well does the claim of indefinability cohere with the claim some people make (but I know of no statement of Lebiniz's where he says this) that identity ‘supervenes on other qualities and relations’? For the doubtful plausibility or sense of the claim, see Wiggins 2002. See also Section 22 below.
See, for instance Hawthorne 2006: 8–11; also Quine 1960: 230–1.
Cf. S&SR: 80–5 and Wiggins 2007–8: Section 8. Do not be surprised that Leibniz should appear on both sides of this argument. That is the prerogative of genius fused with a mind open to everything.
That is to say that implicit in these instinctual strivings is the inarticulate grasp of a formal concept. Such a formal concept is a determinable whose determinations are more and more specific kinds of thing.
The true meaning must be that the statue was made up from the material which is now a molten lump. See S&SR: 39–43, revising similar passages in ISTC.
Compare Leibniz (Gerhardt 1875–90: II, 170): ‘La continuité toute seule ne constitue pas la substance non plus que la multitude ou le nombre la constitue … Il faut quelque chose qui soit numeroté ou répété ou continué’.
This is to say that that nature enters into any conception or idea of the sortal concept that is good enough to enable one who has that conception to single out members of the extension of the concept. See Wiggins 1993 and 2007–8. In my neo-Fregean usage, the concept lies at the level of reference (Bedeutung) and the conception or idea lies at the level of sense. Among conceptions of a concept some are conceptions of a sortal concept and thus conceptions (inter alia) of how a thing has to be and what it has to be in order to belong to the extension of the concept.
This assurance is not to be confused with an assurance against all error in the identification of things with that nature, or against other misconceptions of that nature itself. There is never such an assurance.
Compare the passage from Leibniz's preface to New Essays, quoted at S&SR: 84.
It may be asked why, in the cases where no division takes place, we shouldn't identify the zygote with the embryo—even as we shall identify the embryo with the foetus and the foetus with the baby. Answer: it flows from the logic of identity to demand that any true ground of identity should meet the Adequacy requirement, a requirement which is only the corollary of the Indiscerniblity Principle. The only source we shall ever have for a ground that will be in that way adequate is one that arises from the kind of things in question. But if that is so, then we must take care to subsume the organism within a sort or kind whose proper specification underwrites the presumption of transitivity. Contrast with that the choice of a putative kind whose specification has the organism begin as a zygote—or as an egg, or gamete, why not?—while allowing that some zygotes do and some zygotes do not end up as single whole embryos. The objection to thinking of the organism as belonging to such a sort is that a specification of it and its members, in the shapes of gamete, zygote, embryo, foetus … , creates no satisfactory presumption of transitivity. It makes no room for any properly Adequate ground of identity for members of the sort. At worst, the presumption of transitivity needs to be tractably defeasible. This is to say that where the presumption fails, this needs to have been predictable and explicable by reference to considerations provided for in a correct account of the sort of thing. See further Sections 16 and 17.
See Rundle 2009: 84–8.
Concerning the complexity of that which lurks below the surface appearance of such modes of combination, see the writings of Donald Davidson and James Higginbotham. See, for instance, Higginbotham 1998. For collateral considerations and arguments, see Wiggins 1985–6.
See Torretti 1999: 237.
For the power of creative definition—as of postulation—to create paradox or perplexity, see S&SR: 173–6, a discussion inter alia of Geach's Tib/Tibbles example; see also Suppes 1957: chap 8.
Compare Rundle 2009.
In effect Carnap does just that, simply and faultlessly, in Carnap 1958: 157–8: ‘A thing occupies a definite region of space at a definite instant of time, and a temporal series of spatial regions during the whole history of its existence. I.e. a thing occupies a region in the four dimensional space-time continuum. A given thing at a given instant of time is so to speak a cross-section of the whole space-time region occupied by the thing. It is called a slice of the thing or a thing-moment. We conceive a thing as the temporal series of its slices. The entire space-time region occupied by the thing is a class of particular space-time points which we speak of as “the space-time points of the thing”’.
Compare S&S: 168–9.
It is neither necessary nor sensible to try to set out these points in terms of a generic notion subsuming both an object's existence at a time or its persisting through time and its occupation of space or space-time. See Fine 2006: esp. 700–1.
Think what damage would result from expunging the distinction between substance and process/narrative/event from most ordinary scientific exposition. Indeed consider in that connection all the descriptions that figure in the citation given in Section 2.
For instance, if they are prepared in due course to find Theseus' ship in the dock where it is being reconstructed, can they avoid assigning a discontinuous spatio-temporal path to the ship? (A further development of a problem posed by the disassemblage of artefacts. Cf. S&SR: 99–102.) For what happened at the point in time when some minor renewal or replacement, the last ruled permissible, disqualified the ship in the water from being Theseus' ship?
Unless the most conspicuous case is still that of an earthworm which can be cut in half and be succeeded by two perfectly viable earthworms. Or so one is told. Subject to there being no scientific facts favouring one half over the other, the case appears analogous—so far as the logic of identity is concerned—to that of the amoeba, on which see S&SR: 72–3, 83–4.
An indexicality not lightly to be dispensed with. Cf. S&SR: 198 and Wiggins 1996: 244–8.
See ISTC, Part Four.
Cp. S&SR: 218–19. There is one account of experiential memory—of quasi-memory so-called—which lacks this defect. That is to say that it does not attempt an impossible subtraction from the given meaning of ‘remember’ (a meaning held in place not by a definition but by a whole pattern of thinking and speaking), but seeks to define quasi-memory from scratch. See Parfit 1984: 221. For criticisms of that definition, see S&SR: 213–30. Perhaps the most important of these criticisms is that what Parfit offers is a definition of ‘accurately-quasi-remember’ which it is impossible to turn into a definition of ‘quasi-remember’.
See Shoemaker 2004: 573–2 and 610–13, especially 612–13.
For comments received on the occasion of the lecture in Amsterdam drawn from this text I am indebted to the Editor and the Editorial Committee of the European Journal of Philosophy. I am indebted to Timothy Williamson both for that which I have applied from Williamson 1995 and for the specific comments that he gave me on the penultimate draft of the whole paper. I am also indebted to a conversation I had with Michael Martin at the time of writing the lecture.