INDIVIDUALITY, DISTINGUISHABILITY, AND IDENTITY

INDIVIDUALITY, DISTINGUISHABILITY, AND IDENTITY

Let us begin by outlining some philosophical distinctions. In a work such as this, there is always the question of exactly how much philosophical detail to go into. Too little, and we run the danger of blithely skating over important issues; too much, and we may find ourselves hopelessly lost in a thicket of metaphysical minutiae. Hopefully, we have found the right balance here.

We shall begin with a notion that will figure prominently in our discussions, namely that of identity. It has been said that this is 'utterly simple and unproblematic' ¹ since everything is identical to itself and nothing is identical to anything else. However, this blunt assertion can be understood as a reaction to the convoluted philosophical wrangling over this notion following the work of Frege, in particular, and continuing to the present day. Consider a statement of the form 'a is identical to b', written symbolically, 'a = b', such as, to take a famous historical example, 'Hesperus is identical to Phosphorus'. Such statements apparently assert that a relation holds, but between what?

According to one view (associated with the Frege of the Begriffsschrift), the identity relation holds between names, so two names, 'Hesperus', 'Phosphorus', stand in that relation if and only if th 11311u2022l ey refer to the same object. The sentence 'Hesperus is identical to Phosphorus' then expresses a (meta-linguistic) thought about linguistic entities, that is, the names. As is well known, this view appears to be supported by reflection on the difference between the statements 'a = a' and 'a = b'. The former appears to hold a priori, whereas the latter may represent an advance in our knowledge (as when we conclude that 'Hesperus is identical to Phosphorus'). But then how can there be such an advance when the relation concerned holds between linguistic entities, rather than the objects themselves?

Such concerns motivate the alternative view (associated with the Frege of 'On Sense and Reference') that the identity relation holds between objects, so two (putatively) objects stand in that relation if and only if they are the same object. The above sentence then expresses the thought that Hesperus and Phosphorus are the same object. On this view, the names 'Hesperus', 'Phosphorus' express different senses but refer to the same object and hence we can understand how identity statements of the form 'Hesperus is identical to Phosphorus' can be informative.

There is, of course, much more that we could say here and some of it we will say in later chapters but for the moment we will follow the latter Frege and insist that to state that 'item a is identical to item b', written symbolically, 'a = b', means that there are not two distinct items in reality, but only one, which may be referred to as either a or b. In particular, looking ahead to our discussions of the situation in physics, we shall take the statement 'Particles a and b are identical' to mean that there are not two particles at all but only one, referred to by different names. As we shall see, many commentators-physicists and philosophers alike-understand such statements as meaning that the particles are what we shall call indistinguishable. It is important to establish the terminology we shall use at this early stage. As far as we are concerned, the difference in names of a and b reflects at most an epistemological difference, ³ rather than an ontological one.

Now what about the statement 'a = a'? This asserts that a is identical to itself and hence it can be understood as an expression of the self-identity of the item concerned. It is this which is typically taken to be simple and unproblematic. ⁴ Why it is unproblematic depends on which of the above views one adopts. If one takes identity to hold between names, then as we indicated above, 'a = a' is true a priori. If, on the other hand, identity is understood as holding between objects, then 'a = a' expresses a fundamental relation an object has with itself, one which surely cannot be denied. ⁵ In either case, 'a = a' appears to be a logical truth and with '=' formalized as a two-place predicate in the language of classical first-order logic, 'a = a' is typically taken to be a fundamental postulate of classical logic with identity (often referred to as the 'Principle of the Reflexivity of Identity'). However, this is in fact more problematic than it seems. In particular, as we shall argue, if self-identity is tied to the notion of individuality and quantum entities are understood as objects which are non-individuals, then such entities fail to be self-identical and an alternative formal framework is required to accommodate them.

Of course, a number of fundamental issues immediately arise, of which we shall be particularly concerned with two: first, the sense in which self-identity

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can be understood as a relation and second, the manner in which it is represented formally. As we shall see, the two are not unrelated. Before addressing these issues, we need a little more conceptual apparatus.

First of all, 'Item' is used above as a neutral word that encompasses both universals and particulars. We shall refer to particulars that exist in the physical world as physical individuals or just individuals for short. Some particulars that one would naturally regard as individuals persist through time; others do not. Examples of the former include the particles of physics that we will primarily be concerned with; examples of the latter include space-time points, which we shall briefly consider, and instantaneous temporal parts under certain philosophical interpretations, which we shall not discuss. Those individuals that persist through time are referred to as continuants and can be said to possess trans-temporal identity. In these terms, physical individuals can be distinguished from other sorts of particular such as events or states of affairs that may be said to occur or obtain, rather than to persist (in the case of particles) or exist (in the case of space-time points). Individuals which have more or less well-defined spatial locations are typically referred to as 'things'.

Secondly, we shall insist on a conceptual distinction between individuality and distinguishability. Some may question the basis for such a distinction but, as we shall demonstrate in this work, a number of issues can be clarified by making it. We can approach the distinction by focusing on the particularity, or non-instantiability, of individuals, as contrasted with the universality, or instantiability, of their attributes. ⁶ The former pertains to something, some 'principle of individuality', as it is often called, which is 'internal' or 'particular' to the individual in the sense of being associated with it alone. ⁷ The latter involves the individual's relationship with other particulars and is therefore 'external' in some sense. One way of articulating the distinction is to imagine a possible world in which there is only one entity; this entity cannot be regarded as distinguishable from others-or so it is claimed-since there are no other entities, yet it may surely be considered to be an individual. ⁸

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Thus we shall take-unhelpfully perhaps-'individuality' to be that in virtue of which an individual is an individual and 'distinguishability' to be that in virtue of which an individual is distinguishable from other individuals. We say 'distinguishable' rather than 'distinct', since the numerical distinctness or diversity of entities can be understood in terms of either their distinguishability or their individuality. ⁹

Three fundamental questions now arise:

It might be argued that (1) is actually an empty question since there is simply no need for any conferring 'Principle' if individuality is taken as primitive. On such a view, it is not conferred by or grounded in anything else, whether-to jump ahead a bit-some subset of properties or something metaphysically beyond such properties. And on such a view, distinctness or diversity would also be primitive; that still leaves the question as to what renders an individual distinguishable from others. However, taking a concept as primitive runs the danger of losing the unificatory coherence and understanding offered by conceptual reduction. At the very least it needs to be argued that such reduction is so problematic or unhelpful that we should turn our backs on it. More importantly, as far as we are concerned, taking individuality as primitive will fail to illuminate certain fundamental issues that we are interested in and, as we shall see in Chapter 2, will lead to confusion. At this stage, we ask for the reader's indulgence: let us kick off with this conceptual framework of individuality and distinguishability and see how far we can take it. Returning to our questions, it may be that the answer to (1) can also serve as an answer to (2) and (3), in the sense that that which confers individuality upon an entity turns out to be the same as that which renders it distinguishable from other entities but what we want to insist on, at this point, are the conceptual distinctions involved.

To say what an entity's individuality consists in, in terms of this framework, is first to say that it consists in something having to do-metaphysically speaking-with that entity and no other and secondly to say what precisely that something is. To tackle the latter, we need to address question (1). Possible

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answers can be broadly divided into two kinds: (a) those that appeal to some subset or 'bundle' of the properties of the entity, and (b) those that appeal to something else, 'over and above' these properties. Let us consider each in turn.