Donald L. M. Baxter

Two things become one thing, something having parts, and something becoming something else, are cases of many things being identical with one thing. This apparent contradiction introduces others concerning transitivity of identity, discernibility of identicals, existence, and vague existence. I resolve the contradictions with a theory that identity, number, and existence are relative to standards for counting. What are many on some standard are one and the same on another. The theory gives an account of the discernibility of identicals using phrases like “insofar as”. And it holds that standards for counting remain or shift depending on our purposes.

Ordinary usage gives a way to think of identity through time: the Pittsburgh of 1946 was the same city as the Pittsburgh of today is--namely Pittsburgh. Problem: The Pittsburgh of 1946 does not exist; Pittsburgh still does. How can they have been identical? I reject the temporal parts view on which they were not but we may speak as though they were. Rather I argue that claiming their identity is not contradictory. I interpret ‘the Pittsburgh of 1946’ as ‘Pittsburgh as it was in 1946’ and suggest that the apparent contradiction results from an ambiguity in the scope of ‘as’.

Hume argues that there are steadfast objects - objects not themselves successions at all, yet which co-exist with successions. Given Hume's account of moments as abstractions from temporal simples, there being steadfast objects entails there being single moments that co-exist with successions of moments. Thus time is more like a wall of variously sized bricks than like a line. I formalize the assumptions behind this surprising view, in order to make sense of it and in order to show that it is consistent. I note also that this view justifies the common-sense assumptions that time flows and is unlike space.

How is it possible for David Hume to be both withering skeptic and constructive theorist? I recommend an answer like the Pyrrhonian answer to the question how it is possible to suspend all judgment yet engage in active daily life. Sextus Empiricus distinguishes two kinds of assent: one suspended across the board and one involved with daily living. The first is an act of will based on appreciation of reasons; the second is a causal effect of appearances. Hume makes the same distinction, only he extends the sort of assent involved in daily life to theoretical matters as well. He is a skeptic both in finding no reason to grant the first sort of assent and in being subject to the second.

Pace Perry, wondering whether perceived things are identical is thinking about them, for Hume, with no thought of perceptions of them. Hume is not a proto-Fregean; Hume's Difficulty is not a version of Frege's Puzzle. Pace Falkenstein, wondering about an identity is not wondering whether clearly distinct things--stages, surfaces, names--are connected in some way. Pace Garrett, wondering about the identity of an observed object is wondering whether it is really one or two things, not whether there is one F or two Fs. Second, Humean consciousness is apperception, not immediate awareness. Third, Hume finds nothing with epistemic merit.

Construing the instantiation of a universal by a particular in terms of my theory of aspects resolves the basic mystery of this "non-relational tie", and gives theoretical unity to the four characteristics of instantiation discerned by Armstrong. Taking aspects as distinct in a way akin to Scotus's formal distinction, I suggest that instantiation is the sharing of an aspect by a universal and a particular--a kind of partial identity. This approach allows me to address Plato's multiple location and One over Many problems, Bradley's problem concerning the instantiation of relations, and the problem of change.

Hume discusses the distinction of reason to explain how we distinguish things inseparable, and so identical, e.g., the color and figure of a white globe. He says we note the respect in which the globe is similar to a white cube and dissimilar to a black sphere, and the respect in which it is dissimilar to the first and similar to the second. Unfortunately, Hume takes these differing respects of resemblance to be identical with the white globe itself. Contradiction results, undermining his theory of abstraction. The way out is apparently to admit an intrinsic complexity in even simple things.

Hume argues that the idea of duration is just the idea of the manner in which several things in succession are arrayed. In other words, the idea of duration is the idea of successiveness. He concludes that all and only successions have duration. Hume also argues that there is such a thing as a steadfast object—something which co-exists with many things in succession, but which is not itself a succession. Thus, it seems that Hume has committed himself to a contradiction: A steadfast object lacks duration because it is not a succession, but has duration because it co-exists with something which has duration. I am not going to discuss why Hume thinks these things. My goal is simply to show that what he thinks is consistent. To do so, I will offer a Humean temporal logic.

Armstrong has loose identity be an equivalence relation, yet in cases of something becoming something else, loose identity is not transitive. My alternate account has an attribution of loose identity be really two: a true attribution of an underlying relation (perhaps not transitive) and a false attribution--a Humean feigning-of strict identity. The feigning may become less appropriate as the underlying relation grows more distant. What makes it appropriate initially is that the underlying relation supports a predictable change in some collective. The importance of the predictably changing collective is signaled by regarding it as a single thing.

Hume’s account of virtue (and beauty) entails that distinct things--a quality in the contemplated and a perception in the contemplator--are the same thing--a given virtue. I show this inconsistency is consistent with his intent. A virtue is a composite of quality and perception, and for Hume a composite is distinct things--the parts--falsely supposed to be a single thing. False or unsubstantiated supposition is for Hume the basis of most of our beliefs. I end with an argument that for Hume secondary qualities are composites, not powers.

Understanding Hume’s theory of space and time requires suspending our own. When theorizing, we think of space as one huge array of locations, which external objects might or might not occupy. Time adds another dimension to this vast array. For Hume, in contrast, space is extension in general, where being extended is having parts arranged one right next to the other like the pearls on a necklace. Time is duration in general, where having duration is having parts occurring one aft er another like the notes of a song. Hume’s diff erent view stems from his empiricism, his reliance on experience and observation as the foundation of our concepts. Nothing in our experience suggests a single vast array of locations. Rather, we simply notice that bodies are similar insofar as they have lengths that can be compared. Likewise, nothing in our experience suggests a single dimension of time. Rather, we simply notice that diff erent successions are similar insofar as they have durations that can be compared. Th eorizing that these observations show there to be a single multidimensional array goes well beyond the evidence for Hume. As a skeptic, he fi nds himself unable to assent to theories that stray too far beyond the deliverances of the senses. For Hume, the ideas of space and time are each a general idea of simple—partless— objects arrayed in a certain manner. He argues that the structures of the ideas of space and time refl ect the structures of space and time. Th erefore, space and time are not infi - nitely divisible, and they are ways simple objects are arrayed. Consequently, there is no such thing as empty space nor time without change.

I argue that an individual has aspects numerically identical with it and each other that nonetheless qualitatively differ from it and each other. This discernibility of identicals does not violate Leibniz's Law, however, which concerns only individuals and is silent about their aspects. They are not in its domain of quantification. To argue that there are aspects I will appeal to the internal conflicts of conscious beings. I do not mean to imply that aspects are confined to such cases, but the best way to start is to recognize them experientially. We can feel the conflicts within ourselves. In doing so we can feel some of our aspects. I will try to enhance our understanding of the concept of aspect by listing and formalizing some principles for its use. After that I will argue that all sorts of individual things have aspects, not just people who are conflicted.

One of the advantages of my account in the essay “Instantiation as Partial Identity” was capturing the contingency of instantiation—something David Armstrong gave up in his experiment with a similar view. What made the contingency possible for me was my own non-standard account of identity, complete with the apparatus of counts and aspects. The need remains to lift some obscurity from the account in order to display its virtues to greater advantage. To that end, I propose to respond to those who have grappled with it in print. There are various criticisms by commentators: that it is rendered absurd by the transitivity of identity, that it makes instantiation necessary instead of contingent, that it is unclear what counts are, that aspects are simply tropes, that my view does not capture multiple location, that I make an unclear reference to a theory of composition as identity, that the account suffers from problems with polyadicity, and that it is not a realist account of universals after all. I give responses to these objections.

In the Treatise Hume argues that the self is really many related perceptions, which we represent to ourselves as being one and the same thing. In the Appendix he finds this account inconsistent. Why? The problem arises from Hume's theory that representation requires resemblance. Only a many can represent a many recognized as such, and only a one can represent something as one. So for the many distinct perceptions (recognized as such) to be represented as one and the same, the many distinct ideas that reflect them must be one and the same. But the distinct cannot be identical.

Berkeley and Hume object to Locke's account of abstraction. Abstraction is separating in the mind what cannot be separated in reality. Their objection is that if a is inseparable in reality from b, then the idea of a is inseparable from the idea of b. The former inseparability is the reason for the latter. In most interpretations, however, commentators leave the former unexplained in explaining the latter. This article assumes that Berkeley and Hume present a unified front against Locke. Hume supplements Berkeley's argument just where there are gaps. In particular, Hume makes explicit something Berkeley leaves implicit: The argument against Locke depends on the principle that things are inseparable if and only if they are identical. Abstraction is thinking of one of an inseparable pair while not thinking of the other. But doing so entails thinking of something while not thinking of it. This is the fundamental objection.

Zu Arnauld und im Discours de métaphysique sagt Leibniz, daß alle Wahrheiten begrifflich (prädikativ) und manche gleichwohl kontingent sind. Ich untersuche das Problem im Hinblick auf mögliche Wesen, die ich als möglich auch betrachte und versuche nachzuweisen, daß die Position keinen Widerspruch enthält, weil Leibniz zwei Arten begrifflichen Enthaltenseins unterscheidet -logisch und kausal: Die erste ist notwendig, die zweite jedoch kontingent und nur hypothetisch notwendig, notwendig also lediglich unter der Voraussetzung des vorgegebenen freien Willens Gottes. Es gibt insofern auch zwei Arten vollständiger Begriffe - logisch und kausal vollständig: Kausal vollständige Begriffe sind logisch unvollständig und enthalten gleichwohl logisch (hypothetisches Enthaltensein) Gründe für die fehlenden Prädikate. Diese Begriffe sind Begriffe von zeitlichen Zuständen, die in einem Individuum durch Gottes wohlbegründete freie Ratschlüsse verbunden sind - solche Zustände lassen sich zwar separieren, jedoch nicht neu zusammenfügen. Diese Interpretation ist vereinbar mit dem inesse-Prinzip, mit Gottes Wissen um zukünftige zufällige Ereignisse sowie Leibniz' Ablehnung des Konzepts weltübergreifender Identität und kann durch die Einbeziehung des Kontingenz-Kriteriums einer unendlichen Analyse sowie einer Theorie der Gegenstücke zur Erklärung des Kontrafaktischen problemlos erweitert werden.

In lieu of an abstract, here is a brief excerpt of the content:323 A DEFENSE OF HUME ON IDENTITY THROUGH TIME A durable complaint against Hume is that he blatantly begs the question in his Treatise account of our acquisition of the idea of identity through time. Green and Grose made the accusation in 1878; one hundred years later Stroud echoed the same accusation, its force and liveliness seemingly undiminished. I suggest that this accusation is based on a tempting but unwarranted assumption about Humean perceptions. It is unwarranted despite Price's arguments for it. When the assumption is corrected Hume is exonerated. This defense prepares the way for a new understanding of Hume's subtle and important theory of identity. Clarifying his theory is the goal; defending him is the means. I will merely summarize the Green and Grose interpretation, saving detailed examination for Stroud's. Stroud's version seems more tightly argued for and spares one the problems of interpreting commentators from a different philosophical tradition. Green and Grose run together Hume's account of the acquisition of the idea of identity, with his account of the application of that idea to a succession of related perceptions. This fully intended confusion can be explained by their understanding of Hume's claim that "impressions are... perishing existences." (T 194) They assume that for Hume no perception (impression or idea) is a unity if it exists at an interval of time composed of a succession of times. Rather the perception is really a succession of perceptions. Their assumed interpretation makes Hume seem to them to beg the question as follows: To acquire the idea of identity through time is to acquire the idea of something 324 which is unitary and exists at a succession of times. But any impression which might give this idea is really a succession of related impressions. A succession of related impressions can convey the idea of identity only by being confused with a unitary impression which exists at a succession of times. Such confusion would be possible only for someone who already had the idea of something unitary which exists at a succession of times. So the idea of 2 identity can be acquired only if it is already had. In other words, Hume claims that an impression had for a relatively long time gives the idea of identity. Any long impression is really a succession. A succession can give the idea of identity only if it is confused with something that has identity. That confusion requires the idea of identity already. So Hume begs the question. There are gaps in this argument. But its influence has been important and its structure is clear: If we assume that perceptions are exceedingly brief, then Hume begs the question. (I will call the assumption 'the prosecution's assumption.') Stroud's argument that Hume begs the question has the same structure, or so I will argue. The role of the prosecution's assumption is not immediately apparent, but it is a crucial role. Stroud's accusation is as follows: By Hume's definition, identity is the invariableness and uninterruptedness of an object through a supposed change in time. (T 201) However, on Hume's account of acquiring the concept of identity, the acquisition involves imagining a change in time without any variation or interruption in an object. But that just ¿s, by definition, to imagine the object's identity through the change in time. So acquiring the concept of identity requires an act of imagination involving the 325 concept of identity. So, Stroud concludes, on Hume's account the concept of identity can be acquired only 3 if it is had. Hume's account begs the question. I think it is usually unwise to attribute blunders to subtle thinkers. I will not do it to Hume, nor to his commentators. I will argue that what Hume presupposes in explaining identity through time is a little different from identity through time. Thus the presupposition is not question-begging. More specifically, I will argue that Hume distinguishes three technical concepts, three ways to take up time: (i) merely occupying an interval of time, (ii) having duration for an interval of time, and (iii) being identical through an interval of time. Concept (iii...

I argue via examples that there are cases in which things that are not two distinct things qualitatively differ without contradiction. In other words, there are cases in which something differs from itself. Standard responses to such cases are to divide the thing into distinct parts, or to conceive of the thing under different descriptions, or to appeal to different times, or to deny that the property had is the property lacked. I show these responses to be unsatisfactory. I then gather and systematize available ways of talking about such cases with phrases like ‘insofar as’, ‘qua’, ‘to the extent that’, ‘in some respect’, etc., while paying special attention to the scope of ‘not’ when used with these phrases. This allows me to show how we can speak of self-differing without contradiction.

This essay interprets Butler’s distinction between identity in the loose and popular sense and in the strict and philosophical sense. Suppose there are different standards for counting the same things. Then what are two distinct things counting strictly may be one and the same thing counting loosely. Within a given standard identity is one-one. But across standards it is many-one. An alternative interpretation using the parts-whole relation fails, because that relation should be understood as many-one identity. Another alternative making identity relative to sort fails, because whole and parts can be of the same sort.