© 1985 Ralph E. Kenyon, Jr.*

November 14, 1985

Quine poses and discusses the problem of identity in Identity, Ostension, and Hypostasis₁.

Identity is a popular source of philosophical perplexity. Undergoing change as I do, how can I be said to continue to be myself? Considering that a complete replacement of my material substance takes place every few years, how can I be said to continue to be I for more than such a period at best?

It would be agreeable to be driven, by these and other considerations, to belief in a changeless and therefore immortal soul as the vehicle of my persisting self-identity. But we should be less eager to embrace a parallel solution of Heraclitus's parallel problem regarding a river: "You cannot bathe in the same river twice, for new waters are ever flowing in upon you."₂

When is an object itself if the substance of which it is composed may be undergoing continuous replenishment?

Traditional solutions to the problem are that objects have essences, or that there are no objects. Quine doesn't like either of these. He proposes to solve the problem by differentiating between 'river stages' and 'river kinship'. His premises and conclusions include:

1. Objects are composed of a sequence of stages (of an object).
2. Two stages of an object stand in the kinship relation.
3. Two stages are never identical.
4. We can point at an object stage, but we cannot point at an object.
5. People do not make non-sensical affirmations.
6. People affirm that two distinct object stages are identical.
7. Since two stages are not identical, then such affirmations appear to be [false].
8. Since people do not make non-sensical affirmations, something else must be going on.
9. If one appears to be affirming that two different stages are identical, then what is really going on is that one is pointing at the object of which the stages are composed.
10. When one affirms identity of non-identical stages, then one is not pointing at the stages.
11. A limited sequence of pointed-to stages can be part of many objects, so this pointing is ambiguous. Therefore, what is pointed to is learned by induction.
12. A limited span of pointed-to object stages can be part of many objects, so this pointing to is just as ambiguous. Therefore, what is pointed to is learned by induction.₅
13. Objects have both temporal spread and spatial spread, and the pointing is equally uncertain.₅

The concept of identity, then, is seen to perform a central function in the specifying of spatio-temporally broad objects by ostension. . . . Pure extension plus identification conveys, with the help of some induction, spatio-temporal spread.₃

I don't think Quine has accounted for the problem of identity. He has deferred the problem of the identity of an object to the problem of the identity a stage of an object. He has accounted for how larger, extended or composite objects may be indicated using identity of object stages. His approach can be generalized; I think he was on the right track, but didn't go far enough.

I will use the terms "object" and "thing" in a specialized way here. When I say what physically exists I shall use the term "thing"; when I say what is perceived, or what I perceive, I shall use the term "object". We perceive objects. That which causes, results in, gives rise to, or etc., the objects we perceive are things. In keeping with functionalism, it will be appropriate to say that an object is a response of our perception system. I do not wish to deal with the complication which would arise from admitting such 'objects' as hallucinations, sensations from 'phantom limbs', etc., so I will assume that we have some way to disallow those.

If the relation between things and objects is one-to-one, then we could 'identify' the thing with the object and dispense with the distinction (the position of naive realism). The relation from things to objects is many-to-one; our sensory apparatus equivocates among many things in its response as a single object.

I am not committed to the existence of things. If I were an atomist, I might be committed to atoms as the only existing things (taking atoms in the Epicurean sense as indivisibles). Like the Skeptics, I believe that whatever gives rise to our experiences cannot be directly known. Presuming that there are things which give rise to our objects of perception imports far too much structure. Instead of referring to a 'universe of things', I speak of 'the implicate order'; the objects I perceive are explications by my perception system from the implicate order. However, in most contexts I will speak of objects as if they were things. Just as relativistic mechanics gives way to Newtonian mechanics for most engineering work, Skepticism gives way to naive realism for most everyday activities.

Since different instances of perception of an object may have been caused by different putative things, does it make sense to speak of whether two things are the same? Could we ever know?

Metaphysicians do consider the question of whether two things are the same to be valid. There is a puzzle about this; if two things are the same, then there wasn't two things to begin with, merely the one thing which was not known (to be itself), and then was known (to be itself). This would suggest that two things can never be the same, otherwise they would not be two things. The puzzle about this comes from confusing metaphysical issues with epistemological issues. Metaphysically, two things are never the same; there is either one thing, or there are two things. The epistemological issue is that it is the change in the condition of knowledge from not knowing to knowing, which is to say 'recognizing' that what appeared to be two things appears to be (the same) one thing.

But we can never recognize things, we can only recognize objects. Let us say that recognizing an object results in knowing that a previously perceived instance (of an object) 'is' the presently perceived object. Prior to recognition, the previously perceived instance was not known to be the same object as the presently perceived object. The simplest way of knowing this, is to have the object continuously in our perception; that is, we only perceive an object once (with an extended duration). If there is an intervening period in which the object is not perceived, how can the object be recognized? In such a condition there are two instances of an object (or two instances, each of different objects, since 'identity' has not been shown).

To recognize an object, a first instance must first be perceived, marked for identification, and remembered (stored in memory) as marked; a second instance must be perceived, and compared to the remembered instance. The process of comparing must report no differences (except for the mark). Since the object is an equivocation among many putative things, a little equivocation in determining the differences between two objects would hardly matter. It is clear that the two instances will differ at least by the state of being marked for identification. There must be some way of distinguishing the two instances for it to be know that there are in fact two instances. Determining that these two instances 'are the same' requires equivocating between them by at least the means of distinguishing them.

Nothing said here so far is at all at odds with any of our theories of measuring. We know that it is fundamentally impossible to perform 'exact' measurements. (Note: performing an 'exact' measurement would be nothing more that determining whether two 'things' share one particular attribute, by determining if distinct instances of that attribute are 'the same'.) Formal measurements require the specification of a margin of uncertainty. Two 'things' have 'the same measure' only within that margin of uncertainty. Stating that they have the 'same' measure requires equivocating among measures within this margin of uncertainty. Use of the term "same" in the context of measurement is only approximate; it entails equivocation.

We are accustomed to thinking of measuring as inexact and counting as exact. Stuff is measured; 'things' are counted. It is clear that we cannot determine when two instances of a 'thing' are one by measuring its attributes or properties, since measurement is inexact.

Of course, the question of whether two things are the same or not is moot if we cannot first decide the prior question of when a thing is itself, that is, what constitutes 'thingness'. The question may not matter about things, but I think it does matter about objects. Like Plato, we believe knowledge is based upon perception, in particular, our perception of objects. We have knowledge of objects; but, we have only models of putative things, things whose existence we postulate and infer gave rise to our objects. We might even say that our objects 'refer' to the putative things.

While the relation of 'reference' between words and 'things' (or objects) has been subject to much philosophical controversy, such a relation between putative things and objects seems open to empirical investigation. These problems will have to be solved in order to apply what is known about objects to things.

Just as is the case with putative thing, whether two objects are the same depends upon the prior question of when an object is itself. Let us look, for a moment, at the response aspect of an object. Each instance of an object is a distinct response of the nervous system. However, since the nervous system is continuously responding, it is unclear, in principle, where one 'response' leaves off and another begins. The answer is certainly not to be found by measuring the responses. To distinguish objects, we must view the nervous system as carrying information, and that it is the information content of the responding which must be isolated and compared. If we were to say that this information was grouped in units which we could call "messages", we see that where a particular message ends and another begins is more or less arbitrary. That would not solve the problem of what is an object, it would merely defer the problem of what is an object to the problem of what is a message. In both cases what constitutes a whole is fundamental to the solution to the problem.

As enumerated above, objects arise as a result of equivocating among things, and two objects are seen to be the same as a result of equivocating among instances. The question of when an object is itself has the same answer. Equivocation among continuous perceptual responses (sensation) is required to yield an instance of an object. Equivocation among instances is required to recognize an object. Without imputing things to the implicate order, we would say that it gives rise to sensation, which is shaped into objects by our perception system, and the fundamental mechanism is equivocation. There is evidence to suggest that this equivocation is a learned ability.

The conservation characteristic of sensory-motor intelligence takes the form of the notion of the permanence of an object [thing]. This notion does not exist until near the end of the infant's first year. If a 7- or 8-month-old is reaching for an object that is interesting him and we suddenly put a screen between the object and him, he will act as if the object not only has disappeared but also is no longer accessible. He will withdraw his hand and make no attempt to push aside the screen, even if it is as delicate a screen as a handkerchief. Near the end of the first year, however, he will push the screen aside and continue to reach for the object. He will even be able to keep track of a number of successive changes of position. If the object is put in a box and the box is put behind a chair, for instance, the child will be able to follow these successive changes of position. This notion of the permanence of an object, then, is the sensory-motor equivalent of the notion of conservation that develop later at the operational level.₄

It is the fundamental equivocation in any perceiving system which creates objects. Objects are artifacts of perceiving systems.

How is it possible? I will demonstrate the underlying mechanism. The difference between measuring and counting is one of distinguishing between discrete and continuous. In electronics, this distinction is instantiated by the difference between digital and analog circuits. Let us look at how this distinction is actually achieved. Consider a computer circuit which changes state from 0 volts to +5 volts as part of a square wave. The following diagrams graph voltage as a function of time.

In a computer a binary voltage change may look like this:

Figure 1.

+5 volts                *************************
                        *
                        *
                        *
*************************                        0 volts
0                      .5                        1 (seconds)


Changing the scale makes it look like this.

Figure 2.

+5 volts                             ****************
                              *
                       *
                *
*********                                        0 volts
.4999999995                                      .5000000005 (seconds)

The Typical switching time is .000000001 second, or one nanosecond.

In a computer, the system 'clock' is a square wave, or a circuit which alternates between hi and low. Design engineers go to great lengths to insure that these bistable devices do not 'hang-up' in some intermediate state. Most devices are synchronized to the system clock, so that the values of other circuits are only sampled or 'read' when the clock is stable at either the high value or at the low value. This is done by knowing the timing value selected for the system clock and allowing the falling or rising edge of the clock pulse to trigger a delay mechanism (or to have a design delay built in) so that the values of circuits are read at a time intermediate to the clock transitions by a margin of safety. Asynchronous devices still require these design delays, but 'watch' for clock pulse transitions before interfacing to the system. What does all this have to do with identity? If we look at a clock signal by sampling it in such a manner that we stay away from times when transitions might be occurring, then we will see either a hi (1) or a low (0) voltage. In this manner a 'counting' signal is generated by a measured signal. The result of sampling or reading a signal at certain points in time, is equivocation among possible signal states. In this manner a digital signal which can be used for counting can be generated from analog signals by equivocation. All possible values of the analog signal are equivocated into two distinct states, 1 and 0. We count objects, but as experiments in perception have shown, we must learn the fundamental equivocation involved in recognizing an object. When we ask if two things are the same, we are limited to determining if we know if two objects are the same. We have learned to equivocate among our sensations so as to create objects, and to impute the whole-ness of an object to some 'thing'.

Before the identity of a thing can be characterized, the notion of thing must first be available. Before thing, object; before object, we must be able to distinguish between measuring and counting. Counting can be achieved with measuring and equivocation.

I have shown that equivocation in measuring yields counting, equivocation in sensation yields objects, and that identity derives from equivocation. We could view identity as an abstract version of the strong sense of same, abstract in the sense that it allows equivocation in varying degrees, while same does not.

Quine was on the right track when he divided object into stages, but he just didn't go far enough.

References

1. Willard Van Orman Quine, From a Logical Point of View, 2ond Ed., Harvard University Press, Cambridge, 1980
2. Op. Cit., p. 65
3. Ibid., p. 68
4. Jean Piaget, Genetic Epistemology, Columbia University Press, New York, 1970, pp. 43-44
5. Revised and added to July 3, 2013, to "point out" that pointing is ambiguous with respect to both space and time.