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Identity And Universals: A Conceptualist Approach to Logical, Metaphysical, and Epistemological Problems of Contemporary Identity Theory
Chapter 7, Spatiotemporal Continuity And the Discernibility of Non-Identicals: Criteria for Non-Persons
by Carolyn Ray

Date: 11 Nov 98
Copyright: Carolyn Ray

The Encyclopedia of Philosophy says that the problem of identity is "the problem of trying to give a true explanation of those features of the world which account for its sameness, on the one hand, and its diversity and change, on the other" (Stroll, "Identity," p. 121). But this question is distinct from the question, What makes us want to say something like 'this is the same tree?' The former question seems to weight the case in favor of universals as mind-independent entities--at the very least, the universal sameness.

I do not want to account for the sameness of the tree. I take the "sameness" of the tree as a given in most cases. What is interesting is why I am even inclined to say that this is the same tree.

Spatiotemporal Continuity

I want to say this is the same tree because of the simple fact of spatiotemporal continuity. I assume that this is the same tree, because it is in the same place that I planted it. Since the soil is not disturbed, I assume that, even when I was not watching it, it did not move to another spot and then move back. Since I have never had any reason to judge that things sometimes cease to exist, and then later come back into existence, I assume that the existence of the tree was temporally continuous as well.

This may at first seem like a monstrous proposal--simply assume that it is the same tree because it is in the same place? That's it? Even though things move around all the time, because of people, earthquakes, fire, flood, and any number of other causes that we cannot think of off hand?

Imagine what it would be like to not assume this--to be surprised every time you went into your yard and the same, that any tree was there, since you cannot assume that it is the same tree simply because it is the same, is it the same yard? You were there yesterday, or at least you think you were there yesterday. Or maybe that was not you, maybe it was someone else, or maybe you're just imaging this. What is this place? Where are we? We have already seen that some damaged human beings live this way.

Given our dependence on knowledge of the external world for survival, we might suppose that we develop the concept PERSISTENCE on the basis of our observations of persistent objects outside ourselves, and then infer the persistence of ourselves on this basis. Yet this cannot be the case. Objects go out of my sight all the time. The thing that I know most certainly by direct experience to persist is me.

Whatever I may be, I know that I am something. No one needs to demonstrate this fact to a properly functioning human being. And in fact, no one can: to demonstrate it would be to assume it; and to deny it would be to assume it as well.

Everything else has to measure up to my self. Since I know that I persist, I assume that other things work this way too. I even have some contrast objects: some things do not persist the way I do. My favorite possession is smashed into bits; no matter how much I want it back, it has ceased to persist and will not be back. People die, while I continue to live. And I do not have any evidence that things go out of existence and come back later.

Similarly, I get a lot of evidence that the things in my external world, like me, follow smoothly continuous paths through space and time. I move through a spatiotemporally continuous path; so I infer that other things that move, move the way I do. As much as I and my fellow fantasizers wished it as children, we were never able to "skip space" and end up in a place discontinuous with the starting point. After a little bit of induction, any time I found an inanimate object where I did not expect to find it, I assumed that someone else had picked it up and moved it there through a continuous spatial path. Things that do not move, like trees--well, their "path" through space is pretty simple to trace. And I have never been given any evidence to the contrary.

I know that I am spatiotemporally continuous, and I have good evidence to think that other things are too. I implicitly conclude from these facts that spatiotemporal continuity is good enough as a rule for judging identity. If this is the evidence that I have, then I will use it and I will not be wrong. I use it all the time in my everyday life. The hummingbirds who frequent my feeder all look alike to me. At first, I thought there was only one; then I saw them fighting over territory and realized there were at least two. There are times when I can say, "This bird has been here 3 times this morning; I watched it fly over to that branch and sit, and then come back." The fact that there were other birds in the neighborhood at the time from which I could not distinguish this one by comparing their respective attributes, did not tempt me to think that they were identical; those others were not spatiotemporally continuous with the first.

Spatiotemporal continuity, then, is a criterion of identity on which I rely for most of my judgments of identity. Is it a metaphysically sufficient condition for the persistence of an object? Obviously not; a tree can burn until it is just a pile of ash, though there were no leaps through space or time. Is it a necessary condition? Apparently so, in my experience, and in the experience of a vast number of people who have expressed their opinions on the subject either implicitly or explicitly.

Radical Changes

In addition, I have some sense that the nature of an object persists. As I trace objects through their spatiotemporal careers, I see them displaying the same sorts of characteristics and causally affecting other objects in similar ways. Consider the concept BUTTERFLY. Most people use this concept easily, yet the spatiotemporal careers of butterflies are characterized by massive transformation--by discernibility in the extreme. How do we come to be puzzled by this transformation? To understand this, we must examine some mental history.

What gives rise to the concept BUTTERFLY? This concept, for most of us, is developed in childhood. We pick out similarities in shapes and color patterns, the simultaneous up-and-down and horizontal motion, protrusions, fuzz. We learn the word 'butterfly' after seeing perhaps only one of these, and then develop the concept by seeing several variations or several instances of them and differentiating these objects from others like beetles and birds.

Many of us develop the concept CATERPILLAR independently of the concept BUTTERFLY, and both are certainly valid concepts, each of which picks out one temporally and developmentally distinct aspect of this insect's entire life cycle. What makes us want to say that a butterfly is at some point in its life a caterpillar? Spatiotemporal continuity. We eventually come to integrate the two concepts when we learn that the caterpillar's spatiotemporal career is continuous with the butterfly's. Why do we not say that caterpillars become bears? Because caterpillars are never spatiotemporally continuous with bears--that is, not without losing their "caterpillar" nature by being killed and eaten by the bears. Thus, we say that it is part of the nature of a caterpillar to become a butterfly, and more generally refer to butterflies as things which go through several transformations, including a stage during which they are caterpillars.

This example shows that the process of concept formation is at least in some cases intimately connected with spatiotemporal continuity. It is the existence of a thing considered in the context of space and time. The spatiotemporal location of a thing is part of its identity. Being able to determine the nature of a thing is dependent upon being able to trace it as spatiotemporally continuous. Wanting to say that this is the same tree, or the same butterfly, results from our noticing that continuity.

One final thought on radical changes: Although I chose the butterfly as paradigmatic of a real-life yet surprising transformations, it is important to realize that massive changes are the rule, rather than the exception. The human fetus at 3 weeks bears very little visually-apparent similarity to a human adult, and there is no indication that even older fetuses have any of the psychological characteristics we take to be essential features of persons; seeds bear no apparent resemblance to tomato plants; and a pile of wood does not look like a tree. True, many changes are unnoticeable by us; but that this is so does not alter the fact that massive transformation is an aspect of the things that follow spatiotemporally continuous paths. So not only does our ability to form many concepts depend on the metaphysical condition of spatiotemporal continuity, but spatiotemporal continuity is an adequate criterion for reidentification as well.

Objections To The Spatiotemporal Continuity Criterion

Not all identity theorists would agree with this aspect of the Naive View. Eli Hirsch contends that the criterion of spatiotemporal continuity looks more coherent than it is. I will consider two of his objections.

Part-Loss And Part-Addition. If a space time path is the "volume" in space that a thing takes up, then part addition and loss are changes that can result in spatiotemporally discontinuous changes. For example, a tree can suddenly lose a large branch, resulting in a large difference in the amount of space the tree takes up. A car having its tire changed suddenly loses a large part and then gets a new one in its place. There has to be a point at which we can say that each of these things definitely included the part, and a point at which they no longer included it (Hirsch, pp. 12-14). How does one say, given these large, sudden, qualitative changes?

Reply: This objection requires the implicit premise that spatiotemporal continuity is dependent on the size of the object at any given moment. There is no good reason for such an assumption. Spatiotemporal continuity consists of the car itself following a path such that it does not jump through space and such that it remains in existence at all times. The tire, too, follows such a path. The tree's and the branch's movement through space and time is also continuous.

I suggest that Hirsch thinks that something discontinuous has happened because he focuses on irrelevant measurements, and he does so because of his commitment to temporalism, which makes him look at objects as object stages. Then he has to figure out how this larger tree-with-branch stage could be continuous with this smaller tree-without-branch stage. But such arbitrary posits cannot explain anything but other arbitrary posits.

Which Path Is The Right Path? For any object, there are an infinite number of ways that we could trace its path, some including the whole thing, some including the whole thing and then a part and then back to the whole thing. For example, I might trace the tree's path by noting that at t1 it included the whole tree, at t2 it just included the bottom of the trunk, at t3 it included just the whole trunk, and at t4 it included the branch and the trunk again (Hirsch, pp. 30). How do you know which one to pick?

Reply: To answer this question, we have to ask, What is the purpose of tracing a spatiotemporally continuous path? We sometimes do it automatically; for example, when I am tracking a bird that is heading for my feeder. Other times we do it deliberately, to find the thing at the end of the path; for example, if I lose my watch on a walk, I will retrace my steps because unless someone picked it up, it will still be there. Still other times, we do it to prove that we are in the same place by pointing to stable objects in the vicinity, the presumption being that the spatiotemporal "paths" of those stable objects is extended quite a bit temporally, but not at all spatially: "Remember? We were sitting on this bench watching the sunset, and that building was behind us."

What motive could someone have for "tracing" a tree's spatiotemporal path by at first including it as a whole, then taking it to have become its branch, then going to the bottom third of the trunk? Were someone to do this seriously, I would be convinced that he or she simply did not understand idea of an object, and was unable to pick out a unity. Given the kinds of brain damage I have already talked about, it is not hard to imagine a damaged human being making mistakes like this. But those mistakes have no bearing on my normal criteria of identity, or on how I come to formulate them.

The Discernibility of Non-Identicals

My claim, then, is that, while our own persistence is given and undeniable, the persistence of other things is usually ascertainable by means of tracing their space-time paths. There are other views.

Baruch Brody argues that the Identity of Indiscernibles says it all. It is the definition of identity, the necessary condition of identity, the sufficient condition of identity, and the criterion of persistence through time. The necessary conditions for the truth of identity claims regarding all entities can be stated thus: Where F is a property (i.e., "anything that is had by an object"),

(x) (x = x)


(x) (y) (F) [(x = y) -> (Fx <-> Fy)] (The Indiscernibility of Identicals)

Add to these the Principle of the Identity of Indiscernibles,

(x) (y) [(F) (Fx <-> Fy) -> x = y]

put the conditionals together in a biconditional to form a definition of 'identity,'

x = y =def [(F) (Fx <-> Fy)]

and the theory of identity is complete (Brody, Identity, pp. 7-8). Thus, if "two" things have all their properties in common, then they are identical; and to know that a and b are identical is to know that they have all their properties in common. Brody denies that we need to talk about any other conditions (and criteria, evidently), and that all attempts to discuss conditions of identity based on the type of object are misguided (Brody, ibid, pp. 4-6). Everything admits of analysis in terms of this theory.

How do we apply the theory, since we are probably not acquainted with all the properties of most things? To know that a and b are identical, we check some of their properties and see whether they have them in common. If they do, we infer that they have all their properties in common (Brody, ibid, p. 13). If there is one property that two different objects cannot share, the inference is deductive; if it is a set of properties that it is unlikely that two things share, "then we infer that a is identical with b as a way of simplifying our explanatory account of things" (Brody, ibid, p. 14).

This spare, subtle theory is attractive; it is easily formalized, works well with modern logic, and is delivered in 8 pages. It seems at first glance to fit into the Naive View: we probably do assume a lot about the properties of everyday objects; I see Oreo's familiar-looking little rat-face peeking out of her den in the morning and assume that it is Oreo, and given that it is Oreo, I assume that everything else about her is the same as it was the night before. But Brody has bigger projects in mind. It turns out that the phrase "as a way of simplifying our explanatory account" is key.

Brody argues from the doctrine of logical possibility that there is no reason to think that we need any other conditions or criteria to talk about identity. It is logically possible that spatiotemporal continuity is not a necessary condition for identity. Since indiscernibility is sufficient for identity (Brody, ibid, p. 43), and spatiotemporal continuity is not necessary for indiscernibility, we do not need spatiotemporal continuity, or any other criteria or conditions that identity theorists discuss. Unlike sci-fi thought experiments, his examples are given in abstract form, including diagrams of a discontinuously moving rectangle, to which he refers in the following:

....How, after all, do we know that the description of these examples are coherent? Perhaps, independently of the definition of "identity," there are conceptual impossibilities with the idea of discontinuous motion presupposed in these examples, difficulties that rule out these examples and that at least entail the necessity of spatiotemporal continuity (and perhaps even entail the sufficiency of that continuity) for the identity of physical objects?

It is hard to meet these doubts, for it is hard to prove the nonexistence of independent conceptual difficulties with the idea of discontinuous motion. (Brody, ibid, p. 45).

To back his case, he offers subatomic particles: electrons are physical objects that exhibit spatiotemporally discontinuous motion. But this is only the contingent part of the evidence. The fact that he can offer a "clearly coherent description" of the diagrams of discontinuous motion means that the requirement to describe them some other way is purely ad hoc. It is clear, then, that Brody's main motivation for defending this set of necessary and sufficient conditions comes from logical possibilism. Giving a "coherent" description means no more than "The claims in my account did not contradict one another or themselves." Having covered this topic at length elsewhere, that will not be the main focus here, and there are other questions that need to be raised.

As a metaphysical characterization, I have no great problems with the Identity of Indiscernibles, at least on the surface. However, I do not think that it accounts for persistence the way he thinks that it does--that is, interestingly. It says, whatever properties a thing has at t1, it will have them at t2, unless they can change, in which case it will have properties that include the sort of properties that they can change into; and, there are not two things, but one, if that condition holds. I certainly believe that this is true, and clearly not in the least a priori or self-evident, since it is just the sort of thing that identity theorists have trouble remembering. The trouble is that the account relies on our knowing what sort of properties a thing could have in the future, were it to change (or, what sort of properties it might have had in the past), in order for the account to be meaningful. The description of persistence is hollow, and that is because the description of the thing at a given time is hollow. It does not take into account what we really mean by our concepts.

Brody is aware of the problem, and he offers an Aristotelian essentialist theory of change to add to his theory of identity. Some properties an object has essentially; without them, it would go out of existence. Some properties it can lose or replace and remain in existence.

I will not go into the details of this part of the project, which is realist in the extreme, imputing real existence to such universals as having walked on the moon, and the number four (which can undergo accidental changes such as ceasing to have the property of being Brody's favorite number (Brody, p. 75). I wish to direct attention only to the fact that offering this theory of change is Brody's admission that we do need to develop criteria of identity after all, contrary to his assertion, and those criteria are specific to the concept under which the object falls. I submit that Brody thinks that this is not strictly part of the condition, criterion, or definition of identity, because he wants to offer these in the form of a biconditional and be done with it. And again, I submit that the relation denoted by 'if_then_' is used equivocally, since in one direction it supplies the necessary and sufficient conditions for identity, and in the other it supplies the criterion of identity. Finally, I submit that Brody's project is irreconcilable with commitments to logical possibilism, since there is no way to specify the accidental and substantial properties of a thing given that it might logically possibly have any properties.

The identity theorist's search for varying conditions and criteria is initiated by the recognition of the fact that there are certain key properties that we need to check, howsoever the others may change, to see if we have the same thing at different times. And since we divide the things of the world into kinds according to those key properties, those kinds may very well require different criteria of identity.

Let us consider the biconditional broken into its component conditionals. To do so will provide me with another opportunity to show what is wrong with logical possibilism, and it will instruct us concerning what it takes to have a good criterion of identity. We will ignore any absurdity in saying that "a and b" are one thing:

Indiscernibility of Identicals:

If a and b are one thing, then they have all their properties in common.

Identity of Indiscernibles:

If a and b have all their properties in common, then a and be are one thing.

As an epistemological criterion, the Indiscernibility of Identicals is useless; therefore, the Indiscernibility of Identicals principle must state the metaphysically necessary and sufficient conditions. Now, what could it mean to say that a and b have all their properties in common? It just means that a (also known as 'b') has all the properties that it has. But notice that having all the properties that it has is the metaphysically necessary condition for a thing to have identity. If we grant that, then it is also true that having all the properties that it has is a metaphysically necessary condition for a thing to exist, since anything that exists has identity. In other words, it means that things are necessarily the way they are. This is an enormously strong claim. It happens to be one I believe, it is what Aristotle believed, and it seems to be what Leibniz, whose principle it allegedly is, believed; but it is quite inconsistent with logical possibilism, which holds that pretty much anything might be, or might have been, different than it is.

What about the sufficient condition? Is it true that, being only one thing, rather than many, is a sufficient condition for having only the properties it has, rather than others?" Again, that holds on my account, although why a logical possibilist would hold it is not clear, since it again seems to preclude the notion that things might be other than they are. So as far as the Naive View is concerned, if one wants to say something about the way metaphysical reality really is, one might as well say this.

Before taking a harder look at the epistemological criterion, I want to consider the very phrase "identity of indiscernibles" and whether it makes sense at all to specify conditions and criteria in this way. To do so, I need to address the question, "To what in reality does the concept DISCERNIBLE refer?" Let us say that I bring my golden retriever to your house. You are not very fond of dogs and do not get to know her. A few months later, I bring another dog to your house. But you think it is the same one, because you cannot tell the difference. For you, they are indiscernible.

Consider another example. You know that I like the writings of James Joyce, but you are not very literate yourself. You fan through some books at the store and find one by Virginia Wolff. You give it to me as a present, because you think it is the sort of thing I enjoy. But I do not enjoy it. In both style and mood, I find them very different. They are discernible.

This is the sort of fact one refers to when one uses the words 'discernible' and 'indiscernible.' They mean 'I can tell them apart' or 'I can't tell them apart,' respectively. Thus, the concept DISCERNIBLE is an intentional relation involving a conscious subject, and objects of the conscious subject's attention. It refers directly to a fact about human cognition. Thus, I submit, it is at root an epistemological concept.

There is a special use in identity theory, however; discernibility is usually used in conjunction with the qualifier, 'in principle.' To be indiscernible in principle is to be indistinguishable even if we were omniscient. In any given situation, there can be only one such thing: each thing is in principle indiscernible from itself, because each thing has only the properties that it has, and does not have any properties that it does not have. This is not really anything that anyone discerns, however. It is just the way that things are. I submit, then, that the definition of identity that Brody gives, in terms of the principle of the identity of indiscernibles combined with the principles of the indiscernibility of identicals, is an elaborate restatement of "everything is some way." It adds no content whatsoever. I have no problem with elaborate restatements of simpler statements in general. But in this case, the complexity of the statement seems to be partly responsible for the conclusion that it is proportionately more complex in content. And I think that an equivocation on the word 'indiscernible' tends to push for that conclusion, since the more common meaning includes a conscious subject who is engaging in the epistemological activity of discerning.

Now, with that understanding of the various uses of 'indiscernible,' let us turn to the epistemological criterion, the Indiscernibility of Identicals, which allows the conscious subject to judge that, if it is unable to distinguish one thing from another, then they are identical. That seems reasonable--but only if the conscious subject picks out the right features.

The identity theorist's search for varying conditions and criteria is initiated by the recognition of the fact that there are certain key properties that we need to check, however the others may change, to see if we have the same thing at different timees. And since we divide the things of the world into kinds according to those key properties, those kinds may very well have different criteria of identity associated with them. All it means to specify a criterion of identity is to pick out which properties indicate which kinds of things.

Because Brody does not take this fact into account when constructing his theory of identity, he considers the electron to be the best real example of why nothing else is needed beyond indiscernibility. Since we can simplify our explanatory account of our observations of electrons by appealing to this theory, we may as well use it for everything else too.

This strikes me as a particularly bad idea. If there is one thing that we have trouble discerning, it is the electron, even with instruments. Given that electrons "move" at close to the velocity of light, it is still an open question whether they are sufficiently like the things we call 'physical bodies' to be counted as physical objects. And on top of that fact, there is the fact that, as best as we can observe them, they tempt physicists to describe them as moving discontinuously through space and time; this fact alone might persuade us that perhaps this phenomenon ought not to be counted as a physical body. Yet this is Brody's only real counterexample to the condition and criterion of spatiotemporal continuity. It seems rather that the electron happens along as an unverifiable instance of what he has already concluded as a result of logical possibilism.

Electrons are just the sort of anomaly that philosophers should cautiously categorize as a borderline case or for which they should create a new category altogether, rather than try to force it into the class of physical bodies at the expense of criteria that have been exceedingly useful for conscious subjects since life began.

Finally, I want to address Brody's claim that spatiotemporal continuity is not required for identity. It is not clear why he would think so, at least not for physical objects--the beings which are some way. Any unity is spatiotemporally continuous with itself, and it is not spatiotemporally continuous with anything else. If being the first man on the moon counts as a property for Brody, then surely being spatiotemporally continuous with oneself counts. But spatiotemporal continuity is a peculiar property, in that, if it is had by an object at t1, then it will be had by it at t2--the property extends, if you will, through time, by definition. So if the object is spatiotemporally continuous with itself now then it must be spatiotemporally continuous with itself at any time in the future, on pain of going out of existence. This property also extends through space. If an object is spatiotemporally continuous with itself over here, then it will be continuous with itself when it gets over there. Thus, if there is an "object" or "unity" that is not spatiotemporally continuous with itself, then either it is not one but two objects, or it is not a physical object at all, at least in the sense that we normally mean. And these are some considerations that ought to go into the classification of the electron, the nature of which does not seem to be clear to anyone as yet.

Concluding Remarks

What we have seen in this section is that the definition of identity in terms of the Indiscernibility of Identicals and the Identity of Indiscernibles principles does not seem to add anything to the Naive View's informal characterization of identity, and that it has the defect of equivocating on the expression 'if_then_.' In addition, 'indiscernible' is a dangerous word to use in a metaphysical context, since it seems to refer to epistemological events. We have seen that spatiotemporal continuity is a criterion on which we depend on a regular basis for making our identity judgments, and that, contrary to Brody's assertions, it is necessary for his conception of indiscernibility. We have also seen that Brody's definition of identity cannot be the one and only criterion of identity, since it is not obvious in any given case what subset of a thing's characteristics are good enough for making identity judgments. Instead, in order to answer the question, "Is this the same one?" we must first answer, "To what in reality does the concept correspond?"

Go to the next section.

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