equals 3/2.Ancient riddle sessions form the trunk of a tree with many branches: Hindu Vedic hymns, acrostic poetry, crossword puzzles. The Socratic method of questioning is another branch. A full understanding of what counts as solving a paradox requires an appreciation of the rules of the game Socrates defined.
The Delphic oracle said that no man is wiser than Socrates (ca. 470–399 B.C.). Socrates cited this as a license to question anyone who was reputed to be knowledgeable. If the esteemed individual had knowledge to impart, Socrates would help fulfill the oracle by becoming enlightened. If the wise man did not have knowledge, Socrates would help fulfill the oracle by showing that the examinee was no wiser than he.
Socrates approached the pundits of Athens as a student asking for instruction. In keeping with this humble status, Socrates appears to have written no treatises. What we know about Socrates comes chiefly from Plato’s dialogues. His early dialogues are presented as a fairly accurate intellectual biography of Socrates. But as Plato’s views mature, Socrates increasingly takes on the literary role of being a spokesman for Plato’s philosophy.
Socrates professed to know nothing except that he was ignorant. It was natural that he ask the questions. Socrates asks short questions: “What is courage?”, “What is piety?”, “What is justice?” Until the Meno, he focuses on moral issues. Socrates had studied physics. But he had concluded that inquiry into physical causes cannot yield reasons for acting or thinking in one way rather than another. Only reasons justify actions. Only through reasons can we be influenced by the future (writing for posterity) or by ideals (designing a garden with the dimensions of a Golden rectangle) or by what does not exist (searching for the Fountain of Youth).
When Socrates asks you a question, he wants to know what you think. It’s personal. You cannot satisfy him by reporting what the wise say. You cannot satisfy him by reporting what most people think. If your position is refuted, you will have discovered that your beliefs conflict with each other. The pain of contradiction will motivate you to revise your beliefs.
Socrates keeps the conversation simple. An uncluttered field of discussion helps him spot inconsistencies. If you begin a speech, Socrates cuts you off. If you change the topic, he herds you back. If you speak obscurely, he presses you to clarify.
If asked, “What is virtue?” you might answer that virtue is a trait such as fortitude, temperance, honesty. However, Socrates rejects answers that consist of examples. He wants a definition. The kind of answer that would satisfy him states the essence of a thing, such as “Clay is earth mixed with water,” and “A triangle is an enclosed three-sided figure.” Socrates is not interested in merely learning how people use a word or how a term is officially defined.
Socrates demands a definition that reflects a reality independent of our wills. When you define π as the ratio of a circle’s circumference to its diameter, you arbitrarily label an interesting concept. The arbitrariness of the label does not make the concept arbitrary. The concept concerns an objective relationship. Essential facts about π can be discovered but can never be invented or altered by a stipulation or vote.
In 1897, the Indiana House of Representatives considered House Bill No. 246 to establish a new value for π. The bill passed through the Committee on Canals and was recommended by the Committee on Education, plus the Committee on Temperance. A mathematician, Professor C. A. Waldo of Purdue University, happened to be at the capitol. He was surprised to hear a debate on π. After his intervention and some publicity from the Indianapolis Sentinel, the senators agreed to postpone consideration of the bill. It was never taken up again and so did not become law.
If House Bill No. 246 had passed, the senators may have succeeded in assigning the label π to another (much less interesting) concept. But the ratio originally designated by π would have still equalled 3.14159265 . . . Even in Indiana.
For a period, disciples of Pythagoras ruled the Greek settlement of Croton. But they could never have solved the problem of incommensurability by decreeing that equals 3/2.
Socrates believes that words refer to forms that exist independently of human practices. A form (or “universal”) is something held in common between separate things. The statement “Bucephalus and Dobbins are horses” is really about three things: Bucephalus, Dobbins, and horseness. Horseness would exist even if all the particular horses were destroyed. Forms have a higher degree of reality than the particular things that are related by that form.
After Socrates’ interlocutor proposes a definition, Socrates subjects it to searching examination. Frequently, the logic behind his questions does not emerge until Socrates rounds up his interlocutor’s concessions as premises for some unsuspected conclusion. On other occasions, Socrates asks for clarification simply because there seems to be a trivial counterexample to the definition. In any case, what begins as a leisurely tutorial develops into a debate. Socrates assumes an increasingly dominant role in the conversation. His “teacher” is eventually buffeted from absurdity to absurdity.
The Greeks loved to see the lofty cut down to size. The spectacle was all the more amusing because Socrates was a squat, pop-eyed, snub-nosed character wearing a shabby toga.
The method of inquiry Socrates favored, eristic, or as he preferred to call it “dialectic,” developed out of the formal debating games pioneered by Protagoras (though Socrates credits Zeno with its invention). An umpire arbitrarily assigns a proposition to be defended by one side against the questioning of the other. The interrogator wins if he forces the examinee into a contradiction. In especially restrictive formats, the respondent can only answer yes, no, or don’t know. The interrogator also had to operate within limits. For instance, there was a prohibition against asking for a premise that is equivalent to the issue in question. This is the origin of strangely labeled fallacies such as “begging the question.” The jargon was extended beyond the setting of debates to condemn informal reasoning such as Plato’s circular defense of tradition in the Timaeus: “[W]e must accept the traditions of the men of old time who affirm themselves to be the offspring of the gods—that is what they say—and they must surely have known their own ancestors. How can we doubt the word of the children of the gods?”
Protagoras grew rich by charging coaching fees. Some of the men Protagoras trained went on to become coaches themselves. This was the economic basis of the Sophist movement. The Sophists sparred with men of repute to gain notoriety for their debating skills. The Sophists would travel from place to place staging exhibitions to drum up business. Then as now, people will pay for advice on how to make friends and influence people. Highly successful Sophists could settle down in one city. Some even hired assistant teachers and founded small schools. Aristocrats viewed these vocational instructors as money-grubbers. Philosophers from that class, such as Plato, took pride in never stooping to accept money for teaching.
In reality, upwardly mobile Athenians had little alternative to paying for skills that were now important. Oratory was valued in their increasingly litigious society. At times, there were so many legal suits that the losers began to sue their neighbors just to pay the victors.
Lawyers sued lawyers. Law students sued their teachers. Teachers sued students: Euathlus had contracted to pay Protagoras for his lessons when he had won his first case. After completing his studies, Euathlus never went to court. Determined to collect his fee, Protagoras threatened to sue. He pointed out that if he sued Euathlus, then Euathlus would be obliged to pay either way. If Protagoras won the suit, then Euathlus would be obliged to pay because that is what the court ordered. If Protagoras lost, then Euathlus would have won his first case and so would have to pay in virtue of his contract.
However, Euathlus had learned his lessons well. Euathlus countered that if he won, then, in accordance with the court’s decision, he owes nothing to Protagoras. If Euathlus loses, then he has yet to win his first case and so is still under no obligation to pay.
The Sophists made a dramatic impact on Greek culture. Lawyers became favorite figures in plays. In The Clouds, Aristophanes portrays Socrates as an archetypal sophist. While receiving a tour of Sokrates’s decrepit thinkery, Strepsiades is puzzled by some students who are bent over double, faces to the ground, behinds to the sky. The guide explains that these students major in geography and minor in astronomy. The ridicule rankled Socrates’ followers because, in Plato’s dialogues, Socrates sharply contrasts himself with the Sophists. Socrates denies that he ever taught for money. He always presents himself as a pure seeker of the truth.
Socrates espouses no doctrines until the Meno. This dialogue begins much as the earlier dialogues. Meno is reputed to know much about virtue and attempts to enlighten Socrates by reviewing the various kinds of virtue. Socrates interrupts this survey and asks for the general principle that enables Meno to distinguish virtues from other traits. When Meno attempts to define virtue, he receives the usual treatment by Socrates. The befuddled Meno makes a rueful comparison:
Socrates, I used to hear before ever I met you that you do nothing but perplex yourself and other people. And now, it seems you are bewitching me—and drugging me and binding me completely with your spells, so that I have become saturated with perplexity. And if you will allow me to speak facetiously, you seem to me to resemble to a striking degree, both in appearance and in other respects, the flat electric ray that lives in the sea. For it numbs anyone who comes in contact with it, and you seem to have done something of the sort to me. For in truth, I feel a numbness both in my mind and on my lips, and I do not know what answer to make to you.
(Plato’s Meno 80 A)
Meno then acts on the maxim that the best defense is a good offense. He challenges Socrates with a dilemma: if you know the answer to the question you are asking, then nothing can be learned by asking. If you do not know the answer, then you cannot recognize a correct answer even if it is given to you. Therefore, one cannot learn anything by asking questions.
The natural solution to Meno’s paradox of inquiry is that the inquirer has an intermediate amount of knowledge—enough to recognize a correct answer but not enough to answer on one’s own. Consider a student confronted with a multiple choice question: “Whom did Socrates save in the campaign against Potidaeu? (a) Alcibiades (b) Xantippe (c) Euclides (d) Pericles.” The student knows that at the battle of Delium a general with a name starting with A saved Socrates after Socrates had saved his life in the campaign against Potideau. From this shard of knowledge and the knowledge that exactly one of the test alternatives is correct, the student deduces that Socrates saved Alcibiades in the campaign against Potideau. Meno’s paradox can be solved for cases in which the inquirer has some pieces of knowledge that he can bring together to identify the correct answer.
This solution does not apply to situations in which the inquirer has no knowledge with which to start. For instance, newborn babies seem perfectly ignorant. If an infant boy begins as a “blank slate,” he has no clues to exploit.
Extreme skeptics deny that adults know any more than babies know. If these skeptics were to follow through by ending their questioning, then these self-professed know-nothings would be free of the inconsistency. But Socrates is trying to end his total ignorance by asking questions.
Socrates salvages the Socratic method by scaling back Socratic ignorance. He concedes that there is a sense of know in which people know much—indeed everything! He demonstrates this sense by shepherding Meno’s slave boy into the deduction of a geometrical truth. Although the slave boy has never been exposed to geometry, Socrates facilitates the boy’s recognition of the theorem by asking him questions. The boy sometimes responds incorrectly but soon spots his mistake when Socrates draws attention to the consequences of his answers. Socrates concludes that the slave boy had dormant knowledge of the theorem before he was questioned. Instead of teaching him anything new, Socrates merely revives the boy’s knowledge.
Where did the slave boy’s knowledge come from? Socrates infers that the boy is remembering facts that he explicitly knew in a state before he was ever born. The boy had the knowledge because he dwelt among the forms. This knowledge was forgotten during the trauma of birth. But he recovered the knowledge when Socrates prompted the boy’s memory.
Socrates generalizes: We never learn anything new. We relearn what we formerly knew by encountering objects that serve as reminders. The form of a horse comes back to mind when we see particular horses. A particular horse is an imperfect reflection of the form for horse and so is not the sort of thing that could give us knowledge of horses on its own.
Socrates denies that any one can teach any one anything. (Maybe this is why he will not teach for money!) All Socrates can do is prompt memories. Socrates’ mother, Phaenarete, was a midwife and Socrates regards himself as continuing the family business: “The only difference is that my patients are men, not women, and my concern is not with the body but with the soul that is in travail of birth. And the highest point of my art is the power to prove by every test whether the offspring of a young man’s thought is a false phantom or instinct with life and truth.” (Plato’s Theaetetus 150) The midwife does not produce the child on her own. Similarly, Socrates merely helps others reanimate knowledge that they must have first acquired in an earlier state of existence.
Mental midwifery is hazardous work. Most people do not question the ordinary world of appearances. They resent the suggestion that there is a further reality behind this realm of appearances. In Plato’s Republic, Socrates dramatizes the perils of philosophy with the allegory of the cave. Men are shackled together in a way that keeps them facing a cave wall. Behind and above them is a fire and a walled walkway. The barrier conceals servants who stroll by with figurines above their heads. These figurines cast shadows on the cave wall. This shadow play is the only reality for the prisoners, who have never seen things under normal conditions. Shadows assume the status of objects (fig. 5.1).
Fig. 5.1
Through regular traffic with the shadows, the prisoners become adept at predicting the patterns. What would happen if one of the unwitting prisoners were released from his shackles and permitted to turn around? Would he not be shocked by the scene behind him? Suppose he ventured out of the cave. He would ascend clumsily up unfamiliar steps. He would emerge into sunlight that would leave him painfully dazzled. If he overcame the impulse to withdraw back into the familiar darkness, he would eventually acclimate to the real world of objects. He would be delighted by the colors and richness of reality. He would marvel at the sun that illuminates everything and is the source and sustenance of all there is.
Eventually the liberated man would feel obliged to rescue his friends back in the cave. Reluctantly, he would return to the cave in the hope of freeing them from illusion. Since he would now be used to sunlit conditions, his descent back to the cave would be as clumsy as his earlier ascent. As he resumes his seat with his friends, they will notice that he has lost his knack for predicting the behavior of the shadows. When he tells them that the shadows are mere effects of real objects blocking light, his companions will be amazed by his impudence. If he persists in denigrating their learning as mere familiarity with an illusion, then they may even slay him for his heresy.
The allegory of the cave portends Socrates’ own arrest and execution for heresy and corrupting the young men of Athens.
Socrates was unconventionally religious in his obedience to his “daimon”—a personal voice that warned against certain actions. Such introspectiveness was alien to Greek religious thinking.
Socrates interpreted the charge of corrupting the youth as an attack on his activities as “the gadfly of Athens.” Most of his speech before the court was a defense of the Socratic method. Socrates eloquently made the case for inquiry unfettered by tradition or deference to authorities.
After Socrates was convicted, the prosecution proposed the death penalty. The custom was for defendants to suggest an alternative punishment. The jury chose between the two. Socrates proposed that the state provide him free room and board at the Prytaneum, a kind of state hotel used to reward those who had been of extraordinary service to the state. The jury chose its only consistent sentence: death.
Socrates disagreed with the verdict but accepted it. He had willingly accepted the benefits bestowed by the state. He had thereby consented to its laws and was obliged to follow the dictates of its judiciary.
Friends (and some foes) hoped Socrates would escape from prison and go into exile. He had practiced civil disobedience in the past. Socrates had said he would not obey a judicial order to cease philosophizing. (Apology 29 C-D) He had earlier disobeyed an edict that required citizens to expose enemies of the state. If civil disobedience was permissible then, why not now? Everybody knew Socrates had many influential allies in the Athenian aristocracy. Socrates’ friend Crito actually did make arrangements for Socrates to escape. He beseeched Socrates to cooperate. Socrates replied:
Dear Crito, your zeal is invaluable, if a right one; but if wrong, the greater the zeal the greater the danger; and therefore we ought to consider whether I shall or shall not do as you say. For I am and always have been one of those natures who must be guided by reason, whatever the reason may be which upon reflection appears to me to be the best; and now that this chance has befallen me, I cannot repudiate my own words: the principles which I have hitherto honored and revered I still honour, and unless we can at once find other and better principles, I am certain not to agree with you; no, not even if the power of the multiple could inflict many more imprisonments, confiscations, deaths, frightening us like children with hobgoblin terrors.
(Crito 46-47)
Those under a death sentence were expected to take their own lives rather than put others through the ordeal of executing them. Accordingly, Socrates asked his jailer for hemlock and instructions on its use. The jailer explained that the poison is taken like a cup of medicine. You drink it down and circulate it through your body by walking about. When you feel your legs stiffen, you know that death is imminent. Socrates was bemused by the medical analogy. Ironic to the end, his last words were to the effect that he owed a debt to the god of medicine: “Crito, we ought to offer a cock to Asclepius. See to it, and don’t forget.”