At about 515 B.C. Parmenides was born in Elea, a Greek colony on the southern coast of Italy. He discovered a paradox that was to make “Eleatic” denote a group of philosophers who believe reality is a changeless unity.
“All is one” sounds positive. But Parmenides reaches this positive conclusion by relentless negative thinking. He revolutionized philosophy by turning attention from what is to what is not.
Parmenides would object to this characterization. He argued that it is impossible to think about what is not the case. What is not the case is not there to be thought about. We can only think about what exists.
The business tycoon Heinrich Schliemann refuted the statement “Troy does not exist” by digging up the remains of a city that fits Homer’s description of Troy in the Iliad. Walls were dynamited, tombs were pried open, officials were bribed.
Consider this tidier refutation: If “Troy does not exist” is about anything, it is about Troy. Just as an epitaph can be engraved only if there is a surface to be scratched, a statement can be about something only if there is something for that statement to be about. “Troy does not exist” is a self-defeating remark. It denies one of its preconditions for being meaningful. It is like saying “No one can refer to Athens.”
Yes, this armchair archaeology seems ludicrous. Although scholars before Schliemann had been mistaken about Troy’s nonexistence, they seem to have correctly asserted many other statements about what does not exist: “Atlantis does not exist,” “Zeus does not exist,” “Pegasus does not exist,” etc. How can these denials be true given Parmenides’ reasoning about about?
Twentieth-century philosophers dubbed this “the problem of negative existentials.” A negative existential is a statement that denies the existence of something. How can such a statement be true given that there must be something for the statement to be about?
One tempting solution is to say that “Pegasus does not exist” is about the idea of Pegasus. But if Pegasus is the idea of Pegasus, then “Pegasus does not exist” is false. The idea of Pegasus does exist. Remember that the problem is to explain how a negative existential could be true. In any case, Pegasus is clearly not an idea. He is supposed to be the winged horse of Bellerophon. Ideas do not fly.
Alexius Meinong (1853-1920) suggested that there might be some things that have a kind of being other than existence. According to him, Pegasus subsists. Meinong’s strategy is to challenge the step from “There is something which is Pegasus” to “Pegasus exists.” A common objection to Meinong is that the difficulty would reappear for negative subsistence statements such as “Pegasus does not subsist.” We would need a new explanation for how these statements could be true.
Even so, Meinong’s solution enjoyed an initial period of popularity. Its fortunes plummeted when Bertrand Russell (1872-1970) presented a brilliantly detailed alternative in his classic article “On Denoting.” According to Russell, “Pegasus” is a disguised description. “Pegasus exists” means that there is exactly one horse that has wings and is ridden by Bellerophon. This statement is false if there are two or more such horses or if there are no such horses. “Pegasus does not exist” specifies the second alternative and so means “Each thing is such that it is not a winged horse ridden by Bellerophon.” This analysis frees us from referring to nonexistent objects.
Russell was proud of the way his theory of definite descriptions solved paradoxes. He advised his fellow logicians to collect paradoxes because they serve the same role as experiments in science. Just as we can test a theory by how well it answers observational questions, we can also test a logical theory by how well it resolves deductive riddles.
The problem-solving power of Russell’s theory, coupled with Russell’s polemical skills, shrank Meinong to an amusing footnote. When I was a student, Meinong was still regarded as a marginal transitional figure. I was therefore surprised to see a book on Meinong mentioned on a morning television program. The film reviewer, Gene Shalit, was exhibiting books with stranger and stranger titles. The climax was Terence Parsons’ Nonexistent Objects. Shalit was incredulous that Parsons had written a whole book about things that do not exist.
Parmenides next considers whether things can come into existence or pass out of existence. He believes he has already shown that “nonexistent thing” is a contradiction in terms like “round square.” Nothing can be both round and square because no square can have a perimeter that is everywhere equidistant from its center. It follows that nothing can become a round square. Nor could anything change from being a round square to being a more respectable figure. Similarly, no thing could become a nonexistent object or start out as a nonexistent thing and then become existent. Parmenides concludes that anything that exists has no beginning and no end.
Could something not have a property? If “Pythagoras is not fat” is true, then there is either a state of affairs in which Pythagoras is fat or not. If there is a state of affairs in which Pythagoras is fat, then “Pythagoras is not fat” is not true. If there is no such a state of affairs, then there is no state of affairs that could be referred to by “Pythagoras is not fat.” Thus “x is not F” statements have the same problem as “x does not exist” statements.
One might suggest that a negative fact makes “Pythagoras is not fat” true. If there is a state of affairs consisting of Pythagoras not being fat, then “Pythagoras is not fat” could be made true by that fact. However, Parmenides would counter that reality is about what is the case rather than what is not the case. If you permit one negative fact, you open a floodgate to countless negative facts. These negative facts are hard to distinguish from one another. At this moment, there is no earthquake in Elea. Is that nonearthquake the same nonearthquake that is now transpiring in Ionia? There is no determinate answer to such a question. Reality must be definite.
If “Pythagoras is not fat” is meaningless, then we cannot make sense of Pythagoras changing from being fat to not being fat. Accordingly, Parmenides denies that any thing changes over time.
Can things change over space? According to geographical surveys, the island of Crete extends for 257 kilometers and then ends. But to have an ending, Crete would cease to be at a certain point in space. Ceasing to be is failing to exist. Parmenides concludes that no object can be limited in size.
Wouldn’t this unlimited size make for intolerable crowding? No, because Parmenides denies that there is more than one thing! If there were two distinct things, then there would be a statement that is true about one but not about the other. A statement such as “Pythagoras is not Anaximander” cannot be true because nothing can be a non-Anaximander. A non-Anaximander is a nonexistent thing.
For Parmenides, an argument is not a cab that can be dismissed when it has taken you as far as you wished to go. You must go all the way. Parmenides concludes that there is exactly one changeless thing. For all its unity and simplicity, this oneness is difficult to picture. Parmenides tends to envisage it as a big, round sphere. The sphere is without gaps or variations in density or movement.
If reality were literally a sphere, then we could distinguish between the surface of the sphere and its core. Parmenides has already argued against there being objects with different parts. So the great unity which is reality cannot be a sphere or any other familiar object. Much of what Parmenides positively says about reality can only be consistently interpreted as metaphor.
The natural objection to Parmenides is that his reasoning is refuted by experience. Our senses tell us that there are many things. These things come in various sizes. They are sometimes in motion. They undergo qualitative changes such as when milk sours.
Those following in the footsteps of Anaximander did not question the authority of experience. Even Heraclitus, who is the first to emphasize perceptual illusions, pictures experience as a teacher. Heraclitus thinks our senses show every thing is in constant flux. But there is a unity in the change. When Heraclitus says “You cannot step into the same river twice,” he only means that you cannot step twice into the same water of a river. There is one river but many distinct bodies of water flow through it. Heraclitus urges a balance between experience and reason. He says that the senses can instruct us only insofar as the intellect appraises their worth as witnesses.
Admittedly, the Pythagoreans did elevate the status of pure reasoning. But they viewed reason as a divine shortcut to results that can be triumphantly corroborated by the senses. Only with Parmenides do we see an attempt to completely veto the senses. Parmenides heartily agreed that his arguments conflicted with experience. But he insisted on the supremacy of the intellect over the senses.
Parmenides stresses the principle that one should follow the argument wherever it leads. Previous philosophers had assumed the senses place an important check on one’s reasoning. But they had trouble resisting Parmenides’ suggestion that reason is king. After all, the testimony of the senses must be judged by reason. What is the alternative? Any method that purports to be better than reason would have to be adopted and applied by reason. This gives reason an almost despotic dominion over all methods of inquiry.
Although Parmenides thinks the senses convey a grand illusion, he recognizes a practical necessity for dealing with this realm of appearances. To that end, he proposes a physical theory more or less in the tradition of Anaximander. He tidies up his predecessors by expunging references to voids and privations (such as the view that darkness is merely the absence of light). But even after purging nothingness from traditional physics, Parmenides only offers a theory that aims to be like the truth. His real truth is an uncompromising monism.
Some dismissed Parmenides as an equivocal trickster. The Greeks were aware of how negations can trip us up into absurdity. In the Odyssey Homer describes how a giant, one-eyed Cyclops, Polyphemos, inadvertently trapped Odysseus and his overly inquisitive crew in his cave. Polyphemos controlled the entrance with a huge rock that only he could move. After Polyphemos discovered that he had blocked the escape of Odysseus’s men, he ate two of them for dinner. The next morning Polyphemos had another pair for breakfast. Odysseus, “man of many wiles,” decided to ingratiate himself with the help of his large supply of strong wine. After Polyphemos devoured yet another pair of men, Odysseus offered him a cup of this delicious wine. Polyphemos eagerly accepted a second cup. Then another . . . In a contented stupor, Polyphemos asked Odysseus for his name so that he may receive a favor. Odysseus replied “Nobody.” The Cyclops’s reward to Nobody was a promise to eat him last. Polyphemos slipped off into sleep, gurgling up human remains as he slumbered. Odysseus and his remaining men then seized a stake and rammed it into Polyphemos’s single eye. The blinded monster gave a horrible cry that brought all the neighboring Cyclops running to his blockaded cave. They called, asking whether Polyphemos was crying out because some human was leading away his flocks or whether someone was killing him by treachery or violence. From the cave, the mighty Polyphemos bellowed “Nobody is killing me by treachery or violence!” Upon hearing this, his Cyclops neighbors returned to their own caves, advising Polyphemos to bear what the gods send in patience. Odysseus and his men then escaped, taunting the blinded Cyclops as they rowed away.
The monist Parmenides drew his own taunts. “If Parmenides is right, dog is man and heaven is earth.”
By Parmenides’ reasoning, there is at most one meaningful statement. For if there were two, then one statement would have a meaning that the other statement does not have.
Parmenides is pioneering a semantic solution to paradoxes. Instead of trying to answer the riddle, he characterizes “Does Pegasus exist?” as covert nonsense. If you think that the meaning of a name is its bearer and you think “Pegasus” has no bearer, then you think “Pegasus exists” and “Pegasus does not exist” are equally meaningless. Since the conclusion of an argument must be a proposition, neither of these statements can be the conclusion of an argument. If you also believe that paradoxes are conclusions or arguments, then you will be committed to denying that there is any paradox of negative existentials.
The riddle theory of paradox allows for the possibility of meaningless paradoxes. Riddles need only appear to be genuine questions; they can instead be meaningless utterances that look like questions. Pseudoquestions need only appear to have answers and so need only appear to have an overabundance of good answers. Each pseudoanswer can score well on standard criteria for ranking responses without genuinely expressing a proposition. They can be good in the way that counterfeit currency is good.
Parmenides appears to accept the point that there is only one meaningful statement And he does not shy away from the conflicts with common sense that his critics allege. Parmenides would gain nothing by playing down conflicts with common sense. Critics were therefore at a loss as to how to object to Parmenides. How can you accuse Parmenides of something more absurd than what he explicitly professed?
The only response to Parmenides is an identification of an essential misstep in his reasoning. Since his premises are nonempirical, he can be refuted only on the basis of linguistics and logic. Neither of these fields existed in Parmenides’ era, so little of merit could be said in response to Parmenides’ revolutionary style of philosophical argument. No one could capitalize on the analogies that the Greeks perceived between Parmenides’ reasoning and linguistic tricks such as Odysseus’s use of “Nobody.”
Contemporary philosophers and linguists agree that Odysseus’s ruse turns on an equivocation between using “Nobody” as a name and using it as a quantifier (a quantifier indicates how much: some, most, all). On the surface, names are the easiest words to understand because their meaning is whatever bears the name. All human beings have a strong tendency to apply the name model of meaning to all words, even when they cannot think of any reasonable referent. We should not picture “nobody” as naming anything at all. “Nobody” draws its meaning from how it functions in a whole sentence; it does not draw its meaning from what it names.
People have no more insight into how they speak than into how they see. For instance, parents try to teach their babies how to speak by asking them lots of questions. But interrogatives are the most sophisticated grammatical constructions, always mastered at the end of the child’s linguistic maturation. Similarly, “Paradoxes are riddles” may seem too simple to be true. But actually I have helped myself to a rich explanatory entity. Questions are far more versatile and subtle than arguments or sets or any other entity that philosophers have used to define paradox. My objections to their definitions will almost always complain of them being too narrow.
In his day, Parmenides was invincible. The ancient Greeks were at an embryonic stage of linguistic self-consciousness, struggling to draw basic grammatical distinctions such as between verb and noun. They were not in a position to tackle “nobody.”
Revolutionary progress in linguistics has not precluded persistent myths about the nature of language. In the early twentieth century, Germans were responsible for great advances in our understanding of language. However, they also had a weakness for the view that philosophizing is possible, if not only in German, then only in German and Greek! This linguistic nationalism is manifest as late as 1953 in Martin Heidegger’s Introduction to Metaphysics.
Ironically, Greek is especially prone to equivocation on issues of being. English is nearly as bad. The word is is ambiguous between the is of predication as in “Cicero is eloquent” and the is of identity as in “Cicero is Tully.” This is the basis for the deductive graffiti found in university lavatories: Homer is blind. Love is blind. Therefore, Homer is love. These premises treat the is of predication as if it were the is of identity.
There is also a rather peripheral existential sense of is. When people say “I am” is the shortest complete sentence of English, they intend the existential sense. In Greek, the existential sense is more central and so it is easier to slide to the existential sense from other senses of the Greek counterpart of is.
Finally, I should mention the is of mention. This is used to describe the word for a thing rather than the thing, as in: Athena loves Zeus. Zeus is a four-letter word. Therefore, Athena loves a four-letter word. The second premise involves the is of mention but the argument is valid only if is receives the identity reading.
Diogenes Laertius attributes the following sophistry to Chrysippus: “If you say something, it passes through your lips: now you say wagon, consequently a wagon passes through your lips.” Sometimes there is genuine uncertainty about whether a word is being used or mentioned. Is uncopyrightable being used or mentioned in the sentence “The only 15 letter word that can be spelled without repeating a letter is uncopyrightable”? Normally, the difference between words and things seems too obvious to actually be confused. Yet the tendency to extend the properties of words to things and vice versa is culturally universal. The Egyptians believed they could survive after death by preserving their names after death. Accordingly, the controversial Egyptian leader Hatshepsut (the first female pharaoh) had her name written all over monuments in the Valley of the Kings. When she died, her bitter stepson Thutmose III masterminded a massive erasing campaign. By rubbing out “Hatshepsut,” he hoped to rub out Hatshepsut.
Such different concepts are marked by the little word is! Bertrand Russell characterized the ambiguity of is as a disgrace to the human race.
People judge the subtly of words by their size. They scoff at the suggestion that big issues can turn on little words. Recent political history illustrates this size principle. In 1997, Paula Jones was pursuing a sexual harassment case against President Bill Clinton. Various women were questioned about any sexual relationships with the president. Monica Lewinsky signed an affidavit saying that in her case, there is absolutely no sex of any kind in any manner, shape, or form, with President Clinton. Clinton’s attorney Robert Bennett quoted Lewinsky’s affidavit as part of his defense against Jones’s allegations. The president later conceded he had improper contact with Lewinsky (although no contact that fit the definition of sexual relations imposed on Clinton for the purpose of his testimony). On August 17, 1998, Solomon Wisenberg cross-examined the President. He asked President Clinton whether he agreed that Lewinsky’s statement was completely false.
| Clinton: | It depends on what the meaning of the word “is” is. If the—if he—if “is” means is and never has |
| been, that is not—that is one thing. If it means there is none, that was a completely true statement . . . | |
| Wisenberg: | I just want to make sure I understand Mr. President. Do you mean today that because you were not engaging in sexual activity with Ms. Lewinsky during the deposition that the statement of Mr. Bennett might be literally true? |
| Clinton: | No, sir. I mean that at the time of the deposition, it had been—that was well beyond any point of improper contact between me and Ms. Lewinsky. So that anyone generally speaking in the present tense, saying there is not an improper relationship, would be telling the truth if that person said there was not, in the present tense; the present tense encompassing many months. That what I meant by that . . . |
Journalists cited this section of the testimony as an illustration of Clinton’s sophistry. But Clinton is right about the flexibility of the present tense. Part of the philosophical puzzle about “Is it now, now?” turns on the fact that the present can be narrowed to an arbitrarily thin slice of time. As with many philosophical riddles, the answer to “Is it now, now?” is “It depends.” If the riddler indexes now to the interval in which the whole sentence is uttered, then it is now, now. If the riddler restricts now to the time that the word now is uttered, then it is not now, now. We can resist the riddler’s insinuation that there is a mistake in our normal usage of now by noting that now works like an accordion. We are free to compress now and we are free to stretch n -o -w.
Clinton is right that a period of months is commonly sufficient to cover the present tense. Of course, “There is no sex” is still misleading because there had been relevant “improper contact.” The point of the affidavit was to provide evidence that the president was not engaged in a pattern of sexual impropriety. The improper contact had been recent enough to support Paula Jones’s allegation. But in the adversarial setting of legal examination, witnesses are not obliged to prevent listeners from inferring falsehoods. That is the job of the lawyer asking the questions.
Am I being too soft on Clinton? I confess to an experience that has inclined me to keep out of his way. When Clinton was elected in 1992, a reporter learned that the official photographs of the president are taken prior to the inauguration—before the oath of office is administered, while he is not yet president. He wondered whether these really were photographs of the president. The reporter phoned the chairman of the New York University philosophy department—which was me. I told the reporter not to worry about it. The inaugural photographs really were photographs of President Clinton. Think of it this way. A photograph of Clinton does not need to be a photograph of the full spatial extent of his body. Just a representative part of his body will do. The same applies for temporal parts; a photograph of one stage of Clinton is a photograph of Clinton. Even a baby picture of Clinton is a picture of President Clinton. The reporter perked up at the mention of temporal parts. So I waxed on about Albert Einstein’s pioneering work in modeling time as a fourth dimension. In this “block universe,” Clinton is a space-time worm extending from his birth to his death, much as the Long Island Expressway extends from the western end of Long Island to its eastern extreme. The reporter thanked me. I felt I had nipped the problem in the bud.
Later I heard back from a dissatisfied publicity officer. Why was the chairman of the philosophy department calling the president of the United States a “space-time worm”? When I obtained a copy of the newspaper, I was chagrined to learn that the philosophical community had been credited with the discovery of a new enigma about the inaugural photographs. We heirs of the glorious Greek tradition were whiling away our days in debates about the Great Inaugural Photograph Issue (apparently taking a break from our usual controversy about how many angels can dance on the head of a pin).
The reporter cast a shadow over my ambitions as an academic administrator. I knew how one of my fellow admirers of Parmenides must have felt. Pericles had been an effective Athenian statesman. Then he quarreled with his eldest son, Xanthippus. His angry son
thought himself so ill used and disobliged, that he openly reviled his father; telling first, by way of ridicule, stories about his conversations at home, and the discourses he had with the sophists and scholars that came to his house. As for instance, how one who was a practiser of the five games of skill, having with a dart or javelin unawares against his will struck and killed Epitimus the Pharsalian, his father spent a whole day with Protagoras in a serious dispute, whether the javelin, or the man that threw it, or the masters of the games who appointed these sports, were to be accounted the cause of this mischance. (Plutarch 1880, 122)
Although Pericles was Athens’s most famous democrat, his aristocratic background and his penchant for philosophical abstraction kept him under suspicion; most philosophers were aristocrats opposed to democracy. Fortunately, philosophers were also regarded as impractical dreamers and so tolerated. Even so, Pericles’ political opponents trumped up charges of impiety against his teacher Anaxagoras. Anaxagoras had to be rescued from prison (probably by Pericles) and resettled in Lampsacus. He founded a school there. When Anaxagoras died, the citizens of Lampsacus erected in the marketplace an altar dedicated to Mind and Truth.
Parmenides also enjoyed a good reputation—despite all the ridicule. He was esteemed by his fellow citizens and attracted loyal students. It is to his most famous pupil that we next turn.