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Vagueness and Identity

Loretta Torrago
University of Utah

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ABSTRACT: The view that identity can be vague holds that there are statements of identity which are neither true nor false. The view that composition can be vague holds that unities can have borderline constituents — that is, elements that are neither parts nor non-parts of some larger unity. The case for vague identity is typically made by way of an argument for the vagueness of composition. In this paper, however, I argue that the thesis that composition can be vague is actually incompatible with the thesis of vague identity. The argument for the incompatibility of these two views arises out of a demonstration of the way in which constituency facts (even vague constituency facts) are grounded in the other facts about how a larger unity is configured. Thus, I show that composites that are allegedly vaguely identical are actually different configurations. Hence, the alliance of vague composition with vague identity is taken to be all that is needed in order to show that compositional vagueness is indefensible.

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It is sometimes held that, like other things, identity can be vague.But care should be taken about what this means. The claim that identity can be vague is best understood as the claim that there can be statements of identity which are indeterminate in truth value. This view gains in attractiveness when the precision of the concept of identity is contrasted with the lack of precision endemic to various criteria of identity. As Sainsbury notes, diachronic artifact identity must surely be governed by principles such as this: "Replacing some, but not too many, parts of an artifact does not destroy it, but leaves the very same artifact". Such principles are vague. How could the identity relation, which they determine, be precise? Considerations like these extend to members of natural kinds like mountains and cows as well. What's consistent throughout these views is that identity requires enough of the appropriate sort of continuity. This reliance on continuity goes for not only the way we re-identify things over time, but for the way we individuate objects at a time as well. So for example, spatio-temporal continuity at least partially explains how it is that at Broadway and 42nd I am standing on the same road I stood on when I was at Broadway and 41st. Since identity deciding conditions like continuity and contiguousness can be weak or strong or more or less, it appears the vagueness of those concepts has a limiting effect on how precise identity claims can be.

There is disagreement about the possible sources of vagueness in identity statements. On some ways of accounting for indeterminate identity statements it is considered possible that there are two instances of determinate reference such that it is vague whether what is referred to in the first instance is identical to what is referred to in the second instance. These types of indeterminate identity statements, hereinafter referred to as "vague identity statements", need to be contrasted with identity statements which are indeterminate in truth value owing to referential indeterminacy (hereinafter referred to as "referentially indeterminate identity statements"). For example, the statement "The greatest ruler is the wisest ruler" may very well be indeterminate in truth value but unlike those statements of vague identity, the

indeterminacy of the statement, "The greatest ruler is the wisest ruler" most obviously has to do with the indeterminacy surrounding just which leader was wisest and likewise, just which leader was greatest.

It is the former notion of vague identity statements and not the latter notion of referentially indeterminate statements of identity which has been attacked by Gareth Evans in his "Can There be Vague Objects?" Relying on little else but the principle that discernables (objects which differ on a property) are distinct, Evans attempts to show in a five step proof that the assumption that there can be vague identities leads to contradiction. To summarize informally, assume for reductio that the terms "a" and "b" determinately refer and that a and b are vaguely identical. In that case, b has the property, "is indefinitely identical with a". Now a is surely not indefinitely identical with itself so a lacks the property, "is indefinitely identical with a". But then b has a property a lacks in which case, by Leibniz's Law, a is not identical with b contra the initial assumption.


Defenders of vague identity respond to Evans in either of two ways. First, there are those who claim that Leibniz's Law governs only definite discernability. What goes with this is the claim that the subjects a and b are not determinately discernable but only indefinitely discernable and that, it is argued, is consistent with vague identity (or, at least, LL can't show that it isn't). This line of argument misses the point of Evans. Successful or not, the proof should be seen as an attempt to derive a definite difference between alleged vague identicals. Since no one denies that definite discernables are distinct, the heart of the proof is the demonstration that indefinite identicals must determinately differ in their properties. More to the point is the second strategy which attempts to show that Evans is not entitled to make the property attributions required for discernability. Most recently Peter Van Inwagen has offered a three-valued semantics according to which the inference from a's definite identity with a to the claim that a lacks the property " is indefinitely identical with a" is not, in general, truth preserving., If Evans isn't entitled to his property attributions no discernability has been established. Against this, one might wonder: How can a claim be true in the absence of the relevant truth-maker? Isn't it because a is self-identical that a lacks the property of being indefinitely identical with a? Doesn't the very same state of affairs in virtue of which "a=a" is true give us all we need to make "a does not have the property of being indefinitely identical with a" also true? In what follows I argue that these questions tell against Van Inwagen's "property attribution" response to Evans. Of the two possible responses to Evans then, one is implausible while the other is largely beside the point. But in fact, the case for vague identity is worse than even this. In what follows I argue that the vagueness of composition, on which the case for vague identity is thought to depend, is actually incompatible with it. This incompatibility will help shed light on just why the "property-attribution" response to Evans is inadequate.


The claim that compositional vagueness entails vagueness in identity is best seen when examining those cases used to support the vagueness of identity. Parfit offers the following: a neurosurgeon is performing an experiment in the early stages of which just a few of the subject's actual memories are replaced with Napoleon's memories. As the experiment progresses, the subject looses more of his own memories to more of the memories of Napoleon. Along with changes in memory are changes in character. At the end of the experiment the subject's character is very much like Napoleon's and the subject has a full set of Napoleonic delusions. Few believe the original subject survives. Yet there appears to be no last removal the subject survives and no first removal the subject does not survive. Rather, there seem to be a range of cases for which it is indeterminate whether the resulting person is identical to the original.

In terms of synchronic identity, Cowles' and White's example is typical. Consider an object Mt. Rainier*, which is 'exactly like' Mt. Rainier except that, for one point p, it is indeterminate whether Mt. Rainier contains p and p is determinately contained by Mt. Rainier*. Our intuitions tell us that it is indeterminate whether Mt. Rainier is identical to Mr. Rainier*. After all, there is no point such that it is determinately the case that one mountain contains it and determinately the case that the 'other' mountain fails to contain it.


For purposes here, I'll rely on a conception of composition that takes parthood to be grounded in the holding of certain continuities and dependencies. Since these can be more or less, unity of composition must be a matter of degree. With this comes the possibility of borderline cases - that is, the possibility of elements which are mere borderline constituents of some object's temporal or spatial extent. Let us characterize the vagueness of composition in terms of the possibility of borderline constituents. Recall the case of personal identity Parfit introduces and call the person at the beginning of the experiment "Original" and the person at the middle of the experiment "Josephine". Using the expression, "time-slice" as theoretically neutral between "temporal-part" and "career-stage" (or, in other words, as acceptable to endurentists and perdurantists alike) in terms of time-slices, that Original and Josephine are vaguely identical must mean that it is indeterminate whether that collection of time slices that compose the temporal extent of Original is the same collection of time slices as those which compose the temporal extent of Josephine. More simply, x and y are diachronic vague identicals if it is indeterminate whether x and y have the same temporal extent.

Let us focus on some problematic time-slice midway into the experiment for which it is indeterminate whether that time-slice is included in the temporal extent of Josephine or included in the temporal extent of Original and call this time-slice, " tp". To simplify, suppose that tp is the only time-slice problematic in this way. Clearly if tp were (determinately) a constituent of both or (determinately) not a constituent of both then either the temporal extents would be identical or distinct respectively and so Original and Josephine would be either identical or distinct. Since the identity between Original and Josephine is indeterminate, it must be that the temporal extent of either (but not both) Original or Josephine includes (or excludes) tp and for the temporal extent of the other, tp is a borderline constituent. Put generally, the claim of the diachronic vague identity defender seems to be that where temporal extents "disagree" only in their borderline time-slices the "disagreement" between those temporal extents is not sufficient for difference and hence is not sufficient for distinctness. Returning to the case of Mt. Everest and Mt. Everest*, we can formulate the claim of the defender of synchronic vague identity as the claim that where spatial extents "disagree" only in borderline constituents, the "disagreement" between those spatial extents is not identity-destroying.


It is part of the thesis of vague identity that so long as disagreement is not determinate disagreement, the possibility of vague identity has not been excluded. Well, what sort of determinate disagreement does the vague identity defender have in mind such that vague identicals do not disagree in that way? Presumably, what is meant here by determinate disagreement (DD) is, (DD) x and y determinately disagree and thus determinately differ just in case, with respect to some element p, x contains p determinately and y determinately does not contain p. Fair enough; x and y determinately differ if x is determinately one way (p-containing) and y is determinately some other way (not p-containing). True enough, if things are determinately different ways, then they determinately differ. Trouble is, things can be determinately different ways without any condition as strong as DD being met. In fact, things have to be different ways if different constituency facts are going to be true of it. So much becomes apparent on the observation that, intuitively, for a given element, its constituency status, determinate or indeterminate, is grounded in some determinate fact about it. When comparing elements of a collection in terms of constituency status, that some cell is "a determinate constituent" while some other cell is "a determinate non-constituent" is presumably not arbitrary, but grounded in the micro-physical facts about where those elements are in terms of the others and whether the continuities between them are weak or strong.

To see how this makes trouble for the vague identity defender who takes DD as a requirement on distinctness and discernability, consider the collection of particles that constitutes Mt. Everest and two problematic particles c and n on the mountain's periphery. Now suppose c, though peripheral, is near enough a region of sufficient density that c manages to be a determinate constituent of Everest. Presumably that c is determinately a constituent is a fact about c that is settled by where c is and how c stands in relation to the rest of the mountain. For c to be a determinate constituent requires that c have the right spatial and continuity relations to the other mountain peripherals and to the surrounding atmosphere. On the other hand, suppose peripheral n is determinately not a constituent of Everest. As for c, n's constituency status depends on where n is and how strong or weak the continuities are in that area. So, for example, n's status as a determinate non-constituent might be largely dependent on n's great distance from the periphery. Even for q, a borderline constituent of Everest, it is still the case that q's constituency status is decided, to the extent that it is, by where q is. For q to be borderline, it takes being not quite as outlying as n, but not quite as inlying as c. So, for q to change its constituency status from borderline to determinate, something about q's relation to Everest must also change. In this sense, constituency facts supervene on the physical facts which characterize the collection - facts about where the center of the collection is, where the continuities are strongest and so on. As in all cases of supervenience, the supervening facts don't change until the subviening do. Just so, differences in the supervening facts, in this case the constituency facts, represent differences in the subviening facts, in this case facts about the collection.

Taking the synchronic and diachronic cases together, if the foregoing is correct, then what seems incredible is that given two collections x and y, one for which cp is a determinate member and another for which cp is a borderline member, x and y are not in consequence, two configurations. For what could it mean to say that a difference in cp's constituency status, determinate or indeterminate with respect to some candidate, represents no difference in the facts, either relational or intrinsic, about cp? If with respect to x, cp is a determinate member that must be because cp is strongly continuous with the rest of the constituents of x. And if, with respect to y, cp is a mere borderline constituent, that must be because cp is only weakly continuous with the rest of y. What is important in either case, is that constituency status is grounded in various relations and continuities with the result that differences in constituency status represent differences in those relations and continuities. There is then, no disagreement in constituency status without a difference in how things stand relative to that constituent.


Doubts about whether identity is a real property, whether or not these can be sustained, nonetheless reflect a deep insight about identity propertiesnamely, that identity properties are grounded in other somehow more real properties. Only somewhat less obscurely, identity properties are not the sorts of properties a thing possesses simpliciter, but dependently on other properties. A thing x does not get to be identical to Scottie Pippen by acquiring the property "being identical to Scottie Pippen", rather a thing x is identical to Scottie Pippen by, well, being Scottie Pippen and that consists in having certain other properties. As it is for identity properties, so it should be for vague identity properties (if there are any). The apparent fact that x is vaguely identical to y reflects the fact that x has almost everything it takes to be ythat given just a little something extra, x would be y. The idea that vague identity rests on vagueness of composition attempts to characterize that little extra x lacks in terms of what x lacks, in a way, only indeterminately. Trouble is, indeterminacy is like any other property, a grounded propertythings don't have the property of having borderline constituents as a brute matter about them just as things don't have the property of being red as a brute matter about them. Rather, to have the property "being red" takes having a certain microphysical arrangement and having certain reflectance properties. So too, x's having the property, "has c as a borderline constituent" takes having a certain dispersion pattern, one that places c near enough to the rest of x's constituents but not so near as to make c a determinate constituent.

All this to say that Evans' heart was in the right place. The thing about so-called vague identicals is that they do determinately differ after all. But it's a trivialization of what characterizes so-called vague identicals to concentrate on their identity properties. This makes it seem as if denying that the objects referred to really had those properties, or had them determinately, could make vague identity consistent. But really, x has the property "is vaguely identical with y" by having other properties which, when taken together, make x almost but not quite exactly like y. What stops x from being y is not x's lacking the property "is identical with y" but x's lacking other thingsthings which, if they were to be given to x would automatically bring with them the property "is identical with y". Just so, what (seemingly) makes x vaguely identical to y is not that we notice x has the mysterious property "is indefinitely identical to y" by x's having other rather more ordinary propertiesproperties like having c determinately where y has c only in a borderline way. But once the ground which makes the attribution to x of the property "is indefinitely identical to y" seem attractive, all the determinate differences needed to render implausible what is nonetheless attractive, are already in place.

Taken the other way around, once we have a case for vague identity, we have whatever case there is for the relevant property attributions. Whatever facts about composition that made it tempting to claim of x that it is vaguely identical to y, are just the facts that make us want to say of x that it has the property of being vaguely identical to y. What is important is that if identity claims are grounded at all, so too are vague identity claims. But once we admit that there is something in virtue of which a vague identity claim is true, it seems impossible to block inferences to the relevant property attributions. Once we have the relevant property attributions, however, we have all Evans required to derive determinate differences.

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