Greek σωρίτης (sōritēs), from σωρός (sōros), "heap"; also called the heap argument or the sorites paradox.
1. The Argument
One grain of wheat is not a heap. Adding a single grain to something that is not a heap never seems to turn it into a heap. So, step by step, it seems to follow that no number of grains is ever a heap, though everyone can see a heap when one is in front of them. The same chain of small questions can be run on almost any ordinary word: how many hairs must a man lose before he is bald, how much money makes a man rich, how many trees make a forest.
In the ancient schools the argument was not a puzzle for its own sake. It was a weapon. Its users pressed a chain of questions, one small step at a time, to show that our words have no fixed boundaries, and from there to argue that true and false cannot be told apart, and so that nothing can be known.
2. The Ancient Debate
The fullest ancient account is in Cicero's Academic Questions. Speaking for Antiochus, Lucullus condemns the sorites as a "vicious and captious" way of arguing, and shows how it is used to slide from a merely probable false vision to one that cannot be distinguished from the truth: the same trick, he says, would prove that wolves and dogs are the same animal.
And in the first place, they are blameable in this, that they use a most captious kind of interrogation. And the system of adding or taking away, step by step, minute items from a proposition, is a kind of argument very little to be approved of in philosophy. They call it sorites, when they make up a heap by adding grain after grain; a very vicious and captious style of arguing. For you mount up in this way: -- If a vision is brought by God before a man asleep of such a nature as to be probable (probabile), why may not one also be brought of such a nature as to be very like truth (verisimile)? If so, then why may not one be brought which can hardly be distinguished from truth? If so, then why may there not be one which cannot be distinguished at all? If so, then why may there not be such that there is actually no difference between them? -- If you come to this point because I have granted you all the previous propositions, it will be my fault; but if you advance thither of your own accord, it will be yours.
Cicero, answering for the Academic skeptics, turns the argument against the Stoic logicians. Dialectic rests on the rule that every statement is either true or false, yet it cannot say at which grain the heap begins. Chrysippus' advice was to fall silent before reaching the doubtful step; Carneades answered that he might as well snore, since the questioner would simply resume where he stopped.
What then, you will say; are we to be blamed for that viciousness? The nature of things has not given us any knowledge of ends, so as to enable us, in any subject whatever, to say how far we can go. Nor is this the case only in respect of the heap of wheat, from which the name is derived, but in no matter whatever where the argument is conducted by minute questions: for instance, if the question be whether a man is rich or poor, illustrious or obscure, -- whether things be many or few, great or small, long or short, broad or narrow, -- we have no certain answer to give, how much must be added or taken away to make the thing in question either one or the other.
But the sorites is a vicious sort of argument: -- crush it, then, if you can, to prevent its being troublesome; for it will be so, if you do not guard against it. We have guarded against it, says he. For Chrysippus's plan is, when he is interrogated step by step (by way of giving an instance), whether there are three, or few, or many, to rest a little before he comes to the “many;” that is to say, to use their own language, ἡσυχάζειν. Rest and welcome, says Carneades; you may even snore, for all I care. But what good does he do? For one follows who will waken you from sleep, and question you in the same manner: -- Take the number, after the mention of which you were silent, and if to that number I add one, will there be many? You will again go on, as long as you think fit. Why need I say more? for you admit this, that you cannot in your answers fix the last number which can be classed as “few,” nor the first, which amounts to “many.” And this kind of uncertainty extends so widely, that I do not see any bounds to its progress.
3. The Epicurean Response
No statement by Epicurus himself on the heap argument survives, but his position follows from his canon of truth. Epicurus rejected dialectic as superfluous: our words get their meaning from the sensations, the anticipations, and the feelings, not from definitions with sharp boundaries (see Dialectical Logic And Radical Skepticism Cannot Determine Truth and The Criteria of Truth).
They [the Epicureans] reject dialectic as superfluous, saying that it is sufficient that natural philosophers should proceed in accordance with the words belonging to things. (tr. Long & Sedley)
Seen this way, the heap argument is a trap made of words rather than a discovery about the world. That no one can name the exact grain at which a heap begins does not mean we cannot recognize a heap: a borderline case does not abolish the clear cases on either side of it, any more than dusk abolishes the difference between night and day. To conclude from the argument that nothing can be known is the position Epicurus answered directly (see He Who Says Nothing Can Be Known Knows Nothing).
The question also reaches into Epicurean physics. A heap, a forest, or a living body is real, and it has qualities that no single grain, tree, or atom has, even though it is made of nothing but those parts. Epicurus held that the qualities of bodies arise from the coming together of atoms and are real while the combination lasts (see The Universe Operates Naturally Through Atoms and Space).
4. Epicurus' Own Use Of The Method
Norman DeWitt argued that Epicurus himself turned a sorites-style chain of questions against the Platonists, who called some pleasures good and others bad: subtract the pleasures of taste, of love, of hearing, of sight, and ask what is left to call good. The passage he relies on, translated by Cicero from Epicurus' On the End:
[Epicurus On The End] 'For my part I cannot conceive of anything as the good if I remove the pleasures perceived by means of taste and sex and listening to music, and the pleasant motions felt by the eyes through beautiful sights, or any other pleasures which some sensation generates in a man as a whole. Certainly it is impossible to say that mental delight is the only good. For a delighted mind, as I understand it, consists in the expectation of all the things I just mentioned - to be of a nature able to acquire them without pain... ' A little later he adds: 'I have often asked men who were called wise what they could retain as the content of goods if they removed those things, unless they wanted to pour out empty words. I could learn nothing from them; and if they want to babble on about virtues and wisdoms, they will be speaking of nothing except the way in which those pleasures I mentioned are produced.' (tr. Long & Sedley)
If now we begin to piece our evidences together it will be clear that Epicurus began his campaign with a frontal attack and went from one group to another heckling the practicing teachers in his usual irritating way. It will be clear also that he chose to make hedonism the issue. The following passage is first-class evidence; it was translated by Cicero with the text of Epicurus On the End before him: "Time and again I demanded to know of those who were called wise what they had to leave in the list of goods if they subtracted those pleasures (of taste, vision and other senses) unless they chose to pour forth a stream of meaningless words. I could get no information from them." That the locale of this questioning was Mytilene can reasonably be inferred. While yet a student in Rhodes the thinking of Epicurus would hardly have progressed to such a point as to impel a public challenge. In smaller towns like Teos and Colophon it is unlikely that many philosophers were available for questioning. After the removal to Athens in 306 B.c. he confined himself to his own house and garden.
It is also clear that his attack was directed against Platonists, with whom Aristotelians would be one so far as he was concerned. It must be remembered that he looked upon Platonists as "high-steppers." Cicero's translation proceeds: "These men, if they will only get rid of their fancy notions of virtue and wisdom, will mean nothing else than the means by which those pleasures which I have listed above are obtained." 10 Here there is little cause for hesitancy. The teaching of Epicurus was realistic; pleasure was the good; justice was practiced for the sake of it. The fancy notions at which he scoffed were the belief in absolute justice, in the theory of eternal ideas in general, and the concept of true knowledge as the apprehension of them.
This is not the limit of our information, however. It is fairly plain that Epicurus chose for his assault upon the Mytilenean philosophers one of the more irritating of all forms of argument, the "sorites syllogism." In the same context in which we learn of Epicurus making his rounds to nettle the practicing philosophers we find this statement: "For my own part I am at a loss to know what meaning I shall attach to the good, subtracting the pleasures of taste, subtracting the pleasures of love, subtracting the pleasures of the ears, subtracting also the pleasure of the eyes in beauty of form and beauty of movement."
The true import of this passage has escaped detection. It is the sorites syllogism in narrative form. The key word is "subtract." For a correct understanding the argument must be restored to dialogue form, where it belongs. It consists of a chain of questions: "Do you deny the name of good to the pleasures of taste?" "Yes." "Do you deny the name of good to the pleasures of love?" "Yes." And so on with the rest. At the end of the chain the interlocutor has denied the name of good to everything that the man in the street calls pleasure and there is left only the pleasures of the mind. That the argument did arrive at this termination is made plain by Cicero, who quotes the passage with more fulness. In his account is added: "Neither can this be said, that the pleasure of the mind alone is to be ranked among goods." It was thus that the imprudent Epicurus chose to exasperate his competitors.
Still to be found: DeWitt refers elsewhere, perhaps in a footnote, to a chain question, probably reported by Cicero, about how many parts of the body can be cut off while life is still worth living. If you come across it, please note it in the comments so this entry can be updated.
5. Podcast And Forum Discussions
- Epicurus' Response To The Sorites Argument / Paradox (forum thread)
- Lucretius Today Episode 349: Navigating Questions of Knowledge With Ships and Heaps
- Lucretius Today Episode 350: Addressing A Listener Question On The Flux And Real Life
- Lucretius Today Episode 351: Heap Big Trouble For The Stoic-Platonic Approach To Knowledge
- Lucretius Today Episode 352: Dogs, Wolves, And What Is That In Sheeps' Clothing?
- Lucretius Today Episode 353: The Worthless Argument Of Those Men Who Wish To Throw Everything Into Confusion
- Lucretius Today Episode 251: How Niagara Falls Helps Us Understand the Flux, the Heap, and the Epicurean Gods
- Lucretius Today Episode 294: Distinguishing Dogs From Wolves And Pleasure From Absence of Pain
- Lucretius Today Episode 312: Word Games Are No Substitute For Reality and Episode 313: Diagnosing When Words Are Empty Of Meaning
- Lucretius Today Episode 150: DeWitt, Development of the School in Mytilene and Lampsacus