# Identity Amid Difference

Identity Amid Difference

What is the most fundamental fact about reality? Is it that the world is the totality of facts (not things)? Is it that reality divides into particulars and universals? Is it the spatiotemporal manifold? The substance-accident distinction? Events and processes? The plurality of possible worlds? These are reasonable answers to a good question—a question of basic metaphysics. I am going to argue for a different answer, namely that the one-many distinction is fundamental. More exactly, I will defend the view that reality consists fundamentally in identity in the midst of difference—what I call the “identity-difference nexus”. Not just identity *and* difference but identity *within* difference. No doubt this sounds obscure, or even contradictory, but bear with me; I promise this will be sober analytical stuff. Intuitively, identity is always accompanied by difference, embedded in difference, dependent on it even. Identity and difference each presuppose the other. For example, the identity of material objects as they move through space presupposes differences within space, i.e., distinct places. Identity through time presupposes differences of times (moments, durations): to be identical over time is to exist at different times. The same object can present different appearances, have different modes of presentation,[1]be denoted by different names, belong to different groups of things. Identity of object is accompanied by differences in other respects. So, identity exists against a background of diversity; judgments of identity (identity facts) depend upon the existence of a multiplicity of other things. The material world consists of identities within differences—one thing in the context of many things. An object remains constant as it interacts with varying entities (for want of a better term): places, times, appearances, modes of presentation, names, groups. Each of these entities has its own identity, of course: each is self-identical. But the identity of a material object allows it to occupy or display different such entities—to exist alongside those entities. We experience the world as consisting of self-identical objects existing cheek by jowl with a realm of distinct and distinguishable things; and this is because that is the very structure of the world. Equally, a single word essentially occurs in different sentences, a number exists in a series of distinct numbers, a thought in a sequence of distinct thoughts, an event in a series of causally connected events. We could say: For every object *x*, there in an object *y*, such that *xRy* and x is not identical to y, where *R* is a relation of some sort (e.g., the relation of occupying in the case of material objects and places). Difference presupposes identity and identity presupposes difference. Everything is both self-identical and other-distinct (an object is not identical to its appearances, for example). There is no world consisting of *only* identity or *only* difference; they come as a package. For example, no world could consist of a single material object and nothing else, because an object needs space in which to exist and space is a multiplicity of different places (ditto events and time). In any case, the world as we have it consists of identity amid difference and difference amid identity (trivially, because distinct things are all self-identical). We have an interlocking duality. Identity and difference are polar opposites—they couldn’t be more different—but they each presuppose the other. And the distinction is as metaphysically basic as anything could be—the distinction between one and many, individual and multiple, singular and plural. Our conception of reality is a conception of objects retaining their identity against a backdrop of diversity: *that* stays the same while *they* vary. And this is because that is the basic structure of reality. It is more basic than the particular-universal distinction, because that distinction requires the idea that the same particular exemplifies different universals and the same universal is exemplified by different particulars. Space and time are built of distinct places and times (each being self-identical). And the same for events, matter, mind, and possible worlds: these are all predicated on notions of sameness and difference. If you want to build a world, you have to factor in this basic distinction. Even logic requires deployment of these concepts: subjects are different from predicates, a single subject can satisfy many predicates, a single predicate can apply to many subjects, there are many different propositions, recurrence of variables signifies identity of value, conjunction is different from disjunction, etc. There is really no thinking about anything without the identity-difference distinction (it’s not a *dogma* of anything). The actual world is self-identical and possible worlds are different from it. Mind is different from matter (or it is not). God is different from the observed universe (or not). Knowledge is the same as true justified belief, unless it isn’t. Etc. Thought itself is identity within difference. The identity-difference nexus thus has a strong claim to metaphysical fundamentality—as the basic structure of any world and any way of thinking. What is surprising is how closely the two concepts interlock; it’s hard to say which of them is basic. Quine used to say “No entity without identity”; we could also say “No entity without diversity”.[2]

[1] In Frege’s system every reference necessarily has many modes of presentation, i.e. senses, so that identity of reference is always accompanied by differences of sense. This is what makes informative identity statements possible. Our thought of identical objects is always permeated by differences of sense. This is a clear instance of the identity-difference nexus. It reflects the fact that objects always have many different aspects or properties. Thought and reality thus march in tandem. The One and the Many.

[2] A Pythagorean might add that this conception of the fundamental structure of reality makes number salient, because where there is identity and difference there must be counting—any world worthy of the name is a countable world. We can count the sheep in a meadow and count the number of places they occupy, and these will generally not be the same. That is basic to being able to describe the world. Mathematics lies at the root of reality; it’s not an optional extra. Hence, count nouns.

There would, in a sense, be no mathematics if identity did not contain difference. By this I mean that every non-trivial identity is not strictly an identity. A trivial identity such as 1=1 is not worth stating. Non-trivial identities such as 99+1=51+49, or 2x(3+4)=2×3+2×4, or 3^2+4^2=5^2, are worth stating. They are worth stating because what are being equated are not identical. To be explicit, the arithmetic (more generally, algebraic) expressions are different, but their valuations (more generally, composition of algebraic expressions) are equal. Behind this is the notion of function (or more generally transformation). In this case we have a function ev: E -> V from a set E of arithmetic expressions to a set of V of values (numbers here). We can have different elements e1, e2 in E for which ev(e1)=ev(e2): what were different in the domain of the function become the same in the codomain. The primacy of transformations in mathematics is the basis for the subject called category theory, which is in a sense an algebraic language in which many mathematical constructs seem to be able to be, quite remarkably, expressed naturally. The word algebra, I believe, comes from the Arabic al-jabr ‘the reunion of broken parts’.

Or we could simply adopt Frege’s sense-reference theory to explain informative identity statements.