Vagueness

Delia Graff, Timothy Williamson

• Publisher: Taylor & Francis
• Year: 2017
• eBook ISBN: 9781351876193
• Edition: 1
• Topic: Philosophy
• Subtopic: Philosophy History & Theory

Vagueness, volume XX, contains twenty-seven essays, with issues covered including: nihilism, phenomenal sorites, degrees of truth, epistemicism, higher-order vagueness, contextualism, and intuitionism. Written by leading contemporary philosophers, these essays will be of interest to researchers in philosophy of language, philosophical logic, metaphysics and epistemology; as well as those in natural language semantics, artificial intelligence and cognitive science more generally. A substantial introduction written by the editors provides a guide to the topic and to the essays in the volume.

Part I
Nihilism

[1]
PETER UNGER


THERE ARE NO ORDINARY THINGS

Human experience, it may be said, naturally leads us to have a certain view of reality, which I call the view of common sense. This view is tempered by cultural advance, but in basic form it is similar for all cultures on this planet, even the most primitive and isolated. According to this prevalent view, there are various sorts of ordinary things in the world. Some of these are made by man, such as tables and chairs and spears, and in some ‘advanced’ cultures also swizzle sticks and sousaphones. Some are found in nature such as stones and rocks and twigs, and also tumbleweeds and fingernails. I believe that none of these things exist, and so that the view of common sense is badly in error. In this paper, I shall argue for this negative belief of mine.

It shall not be my business here to offer arguments concerning the question of whether there are any people, or conscious beings. I contrast these putative entities with mere things, and trust that my usage of the latter term follows one common way of allowing for such a distinction. Further, among such things, I shall discuss only those which are not living or alive; perhaps I may call them ordinary inanimate objects. Nothing of basic importance depends upon any such a division; it serves only to restrict my topic conveniently.

A second restriction I impose on myself is not to discuss certain more general concepts which are intended to delineate in a ‘thing-like way’ suitable portions or aspects of ‘the external world’, or of ‘physical reality’. Accordingly, while I shall argue that our concept of a stone, for example, is devoid of application, I shall not make any such claim for our concept of a physical object, or for any similarly general idea. So far as these present arguments go, then, there may well be various physical objects, indeed, even of a great variety of shapes and sizes. But whatever the shapes and sizes of any such objects, none will ever be a table, a stone, or any ordinary thing. At the same time, my arguments do not require the existence of any physical objects, but leave that question entirely open.

The arguments I will offer for my negative beliefs are variations upon the sorites argument of Eubulides, that incomparable Greek genius who also disclosed the paradox of the liar, the problems of presupposition and those of intentionality.¹ In its original form, the sorites argument appears to have concerned how many items, say beans, or grains of sand, or even some of each, will be sufficient to constitute a heap. None or one is insufficient. But, if there isn’t any heap before us adding a single grain or bean, it seems, will not produce a heap. Hence, even with a million beans quite nicely arranged, there will be no heap of them. By generalization, this is a compelling argument that there are no heaps, and that our concept of a heap is relevantly incoherent. It is, we might say, a direct argument for this idea and, I believe, it is a sound one. Conversely, we may begin by supposing that there are heaps, and that a million beans typically arranged gives us an instance of that concept. But, then, removing a single peripheral bean gently from such a typical heap, it seems, will not leave us with no heap before us. Hence, we must conclude that even when we have but one bean left, or none at all, we still have a heap of beans. But this is absurd. Hence, we have reduced the original supposition of existence to an absurdity, and we may generalize accordingly. This, we may say, is an indirect argument that there are no heaps, and that our concept of them is not a coherent one. It is also, I believe, an adequate argument. Now, Eubulides’ seminal contribution has long labored under the misnomer of ‘the sorites paradox’. But, in any philosophically important sense, there is no paradox here. Rather, we are given two demonstrations of the non-existence of heaps, while no important logical problems come from accepting the conclusion. It is hoped that as this paper develops, we shall better appreciate our true inheritance from Eubulides.

As a clarificatory note, let me point out that the sorites arguments just presented did not involve the notion of identity in any interesting way; we never said, or cared, which heap was present. Indeed, if that idea is involved at all, which I doubt, it is only in the manner in which any terribly general idea may be presupposed by, and so involved in, any argument at all, or virtually any. The arguments that I shall presently deploy similarly avoid any interesting involvement with identity. By introducing the notion, I suggest, we may obtain further arguments to the same effect; so our avoidance of it will only make things harder for our Eubulidean efforts. But even with sparse materials, it will be seen, the existence of all ordinary things may be disproved. Indeed, this may be done several times over, in each of a variety of complementary ways. In each case I shall try to keep the reasoning quite simple and straightforward: for the fundamental issues, I believe, are themselves of such a nature.

In the final section of this essay, I will discuss what I take to be the implications of these present rather restricted reasonings.

1. ORDINARY THINGS AND THE SORITES OF DECOMPOSITION

By ordinary things, as I have indicated, I mean such things as pieces of furniture, rocks and stones, planets and ordinary stars, and even lakes and mountains. This is not the only way that this expression may be used, but it surely represents no philosophic eccentricity on my part. For example, my use of the expression appears fairly close to that of W. V. Quine in his influential book, Word and Object.² Despite certain engaging departures from accepted common sense, such as his views on “the indeterminacy of translation”, Quine’s book does, nevertheless, operate on a foundation of common sense assumptions. The first section of the work is called, aptly enough, ‘Beginning With Ordinary Things’, and the book’s body begins with this sentence: “This familiar desk manifests its presence by resisting my pressures and by deflecting light to my eyes.” For Quine, then, a desk is a paradigm of an ordinary thing; his usage is much like mine. The difference between us, of course, is that while he thinks, along with almost everyone else, that there are such objects, I hold that there are no desks, nor any other ordinary things. It will not serve much of a point, I suppose, for me to list those philosophers whose usage is similar to my own. Nor shall I try to catalogue the various philosophies which rely on the supposition that there are ordinary things, however inexplicit they may be on the matter. For the nature of the issue is clear enough, and that it is of moment to various philosophers is also rather obvious.

To jolt our minds away from common sense thinking, and toward the denial of desks and stones, a bit of ‘general science’ may be of more help than any celebrated philosophy. Even from the early grades, we are given some simple scientific learning which in broad outline, and with fatal incoherence, is this: our ordinary things, like stones, which most certainly exist, comprise or consist of many atoms, and even many more sub-atomic particles. The point here has little to do with any niceties of such a term as ‘consist’, but may be put this way: in any situation where there are no atoms, or no particles, there are in fact none of our ordinary things. This should move us to deny, with proper reasoning, the existence of all alleged ordinary things.

The reasoning for this denial does not require atoms or particles. But for jolting the mind, I have found it helpful to cast it in such terms. I will do so here, choosing stones as my ordinary things and atoms as removable constituents. Accordingly, we may express these three propositions, which reasoning informs us form an inconsistent set:

(1) There is at least one stone.

(2) For anything there may be, if it is a stone, then it consists of many atoms but a finite number.

(3) For anything there may be, if it is a stone (which consists of many atoms but a finite number), then the net removal of one atom, or only a few, in a way which is most innocuous and favorable, will not mean the difference as to whether there is a stone in the situation.

The reasoning here is simple. Consider a stone, consisting of a certain finite number of atoms. If we or some physical process should remove one atom, without replacement, then there is left that number minus one, presumably constituting a stone still. Whether what is left is the same stone, as it presumably is, or whether it is another one makes no difference to our cautious reasoning here: thus do we make good our resolve to foreswear reliance on considerations of identity. (Indeed, we may be more cautious still, writing our third premise so that we require only that at least one stone is left.) Now, after another atom is removed, there is that original number minus two; so far, so good. But after that certain number has been removed, in similar stepwise fashion, there are no atoms at all in the situation, while we must still be supposing that there is a stone there. But as we have already agreed, in (2), if there is a stone present, then there must be some atoms.

There is, then, a rather blatant inconsistency in our thought. However discomforting it may be, I suggest that any adequate response to this contradiction must include a denial of the first proposition, that is, the denial of the existence of even a single stone. Whatever one then thinks of the other two propositions is a further, much more minor matter. Whether one eventually deems them straightforwardly true, vacuously true, without truth-value, or whatever, will not be of any surpassing importance.

I call this argument, the sorites of decomposition or, more fully, the sorites of decomposition by minute removals. It is an indirect argument for the conclusion that there are no stones and, by generalization, no other ordinary things.³ I believe this indirect argument to be not only compelling but sound. Let us consider a number of points of commentary which may help us to assess this belief of mine.

The first point we may consider is that, while this sorites of decomposition works well against the supposed existence of our ordinary things, it does not, in contrast, work as compellingly to deny the existence of physical objects. For no matter how small a thing is removed, if anything is left, which that first has been removed from, that remaining item, for all we can compellingly argue, may be a physical object. It takes some doing to argue to the contrary, and any such extra effort will only begin to approach, at best, our argument against any ordinary things. Now, none of this is to say that physical objects cannot be made to cease to exist, by cutting into them, so to say, or in any other way; nor is it to deny that. I wish only to notice the difference between how compellingly our sorites works to deny an ordinary thing, a stone, for example, and how much less powerfully it works against physical objects (if, indeed, it has any power at all with regard to the latter).

Now, if one appreciates this contrast, it follows that he will be finding our sorites of decomposition quite compelling as deployed against our ordinary things: against stones and rocks, desks and tables, and planets and certain stars. While he may wish to alter the argument thus deployed, the alterations are, then, only a matter of details and niceties. While he may wish an explanation, in some depth, of why supposed ordinary things fall prey, that too presupposes agreement that our argument surely appears quite sound. The correct explanation of this appearance is, I suggest, the simplest one: the argument is as it appears to be, that is, it is a sound one. A contrast may also be drawn between ordinary things and certain particulars which are prominent in the physical sciences. A compelling argument of this sort may be given to deny stones, planets and at least certain stars, but not electrons, hydrogen atoms, and water molecules, or so it now appears.

A second point worth noting is that the central idea of this argument does not depend on atoms, or on anything else so very minute. For example, we may remove ‘a speck of dust’s worth’ at a time to the detriment of any putative stone. For certain artifactual items, like a table, possible future cases might require decremental units which fall below the level of of unaided perception. For example, someone might conceivably construct a table ‘smaller than a speck of dust’. With the proper equipment on his part, I am not sure that facts of material structure would prevent him from getting things into the intended shape, etc. And, perhaps the resulting item would be termed a table by common sense judgement. But the removal of tiny units woul...

Table of contents

• Cover
• Half Title
• Title Page
• Copyright Page
• Table of Contents
• Acknowledgements
• Series Preface
• Introduction
• Part I Nihilism
• Part II Observational Predicates
• Part III Degrees of Truth
• Part IV Epistemicism
• Part V Higher-Order Vagueness
• Part VI Contextualism
• Part VII Intuitionism
• Name Index