1
Everything and Nothing

Graham Priest

1.1 Introduction

Everything - the totality (in some sense of totality) of all things - and nothing(ness) - the absence of all things - are strange objects. They certainly court paradox in various ways. And many philosophers, whether for this reason or for some other, reject them as objects at all. Or, to put it in a way that is not question-begging: they take the words "everything" and "nothing" either not to be in the category of names or, if they are, not to refer to anything.

In this chapter I will argue that everything and nothing are indeed bona fide objects - though, at least in the case of nothing, this does deliver paradox.

The first part of this chapter is devoted to a discussion of appropriate background matters. We will need to look at the question of what objects are, at matters mereological, and at the words "everything" and "nothing" themselves. After that, we will look at everything, and at some of the reasons that have been advanced against it. I will then turn to the much more contentious issue of nothing. I will argue that it is indeed a paradoxical object - both an object and not, both ineffable and not - but one which, in a sense to be made clear, is the ground of reality.1

1.2 Background

1.2.1 Objects

First, then, what is an object? An object is the kind of thing that one can name, be the subject of predication, be quantified over, be the object of an intentional mental state. Thus, Australia is an object, since one can refer to it by the name "Australia." It is an object, since one can say "Australia has six states," so predicating "has six states" of it. It is an object, since one can quantify over it, as in saying that some continents (such as Australia) are entirely in the southern hemisphere. And Australia is an object, since one can think about it, wish one were there, and so on.

In what follows, it will be useful to have some appropriate symbolism. Let me use Gx for "x is an object" ("G" is for Gegenstand). Gx can be defined in a very simple way:

• Gx:= y y = x

To be an object is simply for there to be something which is identical to it or, more simply, to be something.

A word on notation. I follow the convention of Priest (2016) here and use and for the universal and particular quantifiers, respectively. is read all. is read some. It is not to be read as some existent or there exists. The reason for this will soon become clear.

Now, given that x = x is a logical truth, so are y y = x and xy y = x. That is xGx: everything is an object - or, given the standard relation between the universal and the particular quantifiers, ¬x ¬Gx: nothing is not an object. No surprises here.

Next, note that some objects do not exist: Sherlock Holmes, Zeus, Vulcan (the sub-Mercurial planet whose existence was postulated in the late nineteenth century to explain the precession of Mercury's perihelion). Clearly, these can all be named; I have just named them. One can predicate things of them: Sherlock Holmes is a fictional detective (or even: Sherlock Holmes does not exist). One can quantify over them "Some objects that occur in works of fiction actually existed" (e.g., Napoleon); some did not (e.g., Sherlock Holmes); some things do not exist (e.g., Vulcan). They can be the objects of intentional states: the Homeric Greeks worshipped Zeus; anyone who reads Conan Doyle's stories thinks about Sherlock Holmes. By all the criteria of objecthood, then, some objects are non-existent. This is a view which may be called, following the late Richard Sylvan, noneism.

Given noneism, if one wants to attribute existence to an object, one may employ a one-place predicate, "x exists"; Ex, which pace the way that Kant is usually (mis)interpreted, is a perfectly good one-place predicate. In particular, if one wants to say that there exists something that satisfies the condition A(x), one can say x(Ex ? A(x)).2

Note also that, given this notion of objecthood, if n is any meaningful noun phrase, it refers, since there are grammatical (and true) sentences of the form "I am thinking of n", "n is self-identical", etc.).

1.2.2 Mereology

The next preliminary topic is that of mereology. This is the study of the relationship between parts and wholes. In contemporary philosophy, the study of this was introduced by Edmund Husserl and, as a formal theory, by the Polish logician Stanislaw Lesnewski. It is now a well-studied part of formal logic.3

Many things have parts. Books have chapters; symphonies have movements; people have arms and legs (etc.); (some) countries have states. We would not normally think of the whole as a part of itself, but it does no harm to do so, as a sort of limit case - an improper part. Parts that are not the whole - or the empty part, which is usually ignored in standard mereology; I will come back to this - may be called proper parts. So let us write x < y for "x is proper part of y.". We may then define "x is a (non-null) part of y" as x = y, where:

• x = y:= x < y ? x = y

Next, we need the notion of an overlap. When does one object overlap another? When they have a part (maybe the whole itself) in common. Thus, the time of the Western Roman Empire and the first millennium have a part in common (the time from 0 CE until the collapse of the empire). Turkey and Europe overlap, since they have a part in common (the part of Turkey in the Balkans). And Great Britain and England overlap, since they have a part in common, viz., England. So if we write "x overlaps y" as x y, this may be defined as follows:

• x y:= z(z = x ? z = y)

I note en passant that there is a question as to whether the identity of two objects can be defined in terms of a relationship between their parts. A standard answer is that it can be: two objects are the same if they overlap exactly the same things. This cannot hold if < does not satisfy anti-symmetry. In that case we may just have to use a more generic criterion of identity, such as having all properties in common.

We must next look at the notion of a mereological sum, or fusion. The mereological sum of a bunch of objects is the whole which you get when you put those things together. Thus, the sum of my parts (my arms, my legs, etc.) is me. Australia has six states.4 The sum of their geographical masses is the geographical mass of Australia. Beethoven's 9th Symphony has four movements; and their sum is the symphony itself.

Now, when does a bunch of things have a sum? In the examples given, it seems clear that the objects in question (my members, the states of Australia, the movements of the 9th Symphony) have a sum: the objects in question. Some philosophers hold that every bunch of objects has a sum. This is at least a simple view; but it has some odd consequences. Consider the objects which are my appendix, left thumb, and right eye ball. Do these have a sum? Certainly not one with a standard name. Or consider the objects which are the Buddha's left earlobe, the rings of Jupiter, and the Ode to Joy. Do these have a sum? A number of philosophers would say "no." To have a sum, the objects in question have to have some sort of connection, a certain integrity. They must not be a gerrymandered bunch, as are the examples above. It is remarkably difficult to say exactly what this means, but fortunately we do not have to worry about this here.5 For, in what follows, the only sums we will meet will not be of this gerrymandered kind.

So suppose that we have a bunch of things, say the things which satisfy some condition, A(x). (Thus, A(x) might be: x is a state of Australia or x is a movement of the 9th Symphony.) Let us write the sum of the things satisfying A(x) as sxA(x). When does something overlap this? Well, if something overlaps one of the states of Australia, it overlaps Australia; and if it overlaps Australia, it must overlap one of its states. So, in general, something will overlap an object just if it overlaps some part:

• y sxA(x) iff x(A(x) ? x y)

Indeed, we can characterize the sum of the xs which satisfy A(x) as an object, z, which satisfies this condition:

[S] y(y z iff x(A(x) ? x y))

Before we leave mereology, there is a subtlety here that should be noted. Whatever the condition A(x) is, sxA(x) is, in fact, a perfectly good object....