Five Thousand B.C. and Other Philosophical Fantasies Read online

  MORALIST: All right, have it your way; so you’re not superior to a tree. But why are you truthful? And please don’t answer my question again with the question, “Why does a tree grow?”

  LARRY: If you tell me why a tree grows, then perhaps I can tell you why I am truthful.

  MORALIST: I still don’t see the connection between the two! Why must I first tell you why a tree grows?

  LARRY: Because I have great difficulty understanding your use of the word why. I was hoping that if you told me why a tree grows then I could gather enough data on your use of this word to help me answer your question more satisfactorily.

  MORALIST: Oh, so our difficulty is semantical! In that case, I’ll use a different word. What is your reason for being truthful?

  LARRY: Does everything have to have a reason?

  MORALIST: Well of course!

  LARRY: Really now! Does a tree have a reason for growing?

  MORALIST: Of course not. At least, I don’t think so.

  LARRY: Then why should I have a reason for being truthful?

  MORALIST: Because you are not a tree!

  LARRY: So because I am not a tree, it follows that I should have a reason for being truthful?

  MORALIST: Oh heavens, you are only confusing matters! Look, a tree is not a conscious being; it has no free will and makes no choices. So one would hardly expect a tree to have a reason for growing, but one would expect you to have a reason for what you do!

  LARRY: I grant you that if I were not conscious then I would not possibly have a reason for anything I do. But it does not therefore follow that because I am conscious I must have a reason for everything I do. In particular, I have absolutely no reason for being truthful.

  MORALIST: No reason? None at all?

  LARRY: None whatsoever!

  MORALIST: Fantastic! In other words, you are in the same category as Kurt. You feel like being truthful and that is the only reason you are.

  LARRY: No, no, not at all! You totally miss my point! As Kurt told you, his feeling like being truthful is, for him, his reason for being truthful. But I have no reason at all!

  MORALIST: You mean that you don’t even feel like being truthful?

  LARRY: What a strange non sequitur! Of course I feel like being truthful; otherwise I wouldn’t be truthful.

  MORALIST: So I was right! That is your reason for being truthful.

  LARRY: I am sorry, but you are still confused. I both feel like being truthful and am truthful but there is no evidence that either of these two phenomena is the reason of the other.

  MORALIST: Look, I just can’t believe that you have no reason at all for being truthful! You must have a reason; you just don’t know what it is!

  LARRY: At this point, I am not sure just which of several possible meanings of the word reason you have in mind. When you ask the reason for my being truthful, are you asking for my motive or purpose in being truthful, or are you seeking the cause of my truthfulness? Or are you perhaps asking whether I am truthful out of some principle like virtue or duty or obedience to God or the desire to serve humanity or to be personally well off? Which of these meanings do you have in mind?

  MORALIST: Take your choice!

  LARRY: I would rather you choose.

  MORALIST: Very well then. Which of these principles you mentioned is relevant to your case?

  LARRY: None of them.

  MORALIST: Then what is the principle you follow?

  LARRY: None whatsoever. I am not truthful on principle.

  MORALIST: All right then, let’s go over to another of your suggested meanings, cause. What is the cause of your being truthful?

  LARRY: I have no idea.

  MORALIST: Aren’t you helpful!

  LARRY: I am trying to be.

  MORALIST: You certainly don’t seem to be trying! At any rate, let’s go on to the next possibility. What is your motive or purpose in being truthful?

  LARRY: I am not aware of any motive, and I certainly have no purpose in being truthful. Does a tree have any motive or purpose in growing?

  MORALIST: Why must you keep picking on that poor tree?

  LARRY: Why do you keep picking on me?

  MORALIST: I’m not picking on you! I’m trying to help you. I’m trying to help you to know yourself better.

  LARRY: Why on earth should I want to know myself better?

  MORALIST: Well, don’t you want to?

  LARRY: Of course not. Why should I want to do such a foolish thing?

  MORALIST: What’s so foolish about it? Recall Shakespeare’s saying, “Know thyself.”

  LARRY: I guess it’s all right for those who like that sort of thing.

  MORALIST: And did not Socrates say that the unexamined life is not worth living?

  LARRY: Isn’t that a bit on the arrogant side? Who is Socrates to decide which lives are worth living and which not? Does a tree examine its life?

  MORALIST: Socrates was talking about human beings, not trees!

  LARRY: What is the difference?

  MORALIST: Oh, so we’re back to that again! Look, I don’t have the time to spend with you playing these useless word games! Since you stubbornly deny that your truthfulness is to any purpose, then I think further conversation is futile.

  LARRY: Good grief, how you have misunderstood me! I never said that my being truthful is to no purpose!

  MORALIST: Of course you did! A short while back you distinctly said that you had no purpose in being truthful.

  LARRY: That is true. Indeed, I have no purpose in being truthful. But that does not mean that there is no purpose in my being truthful. Of course there is a purpose—I feel a very important one —but this purpose is not mine.

  MORALIST: Now I don’t understand you at all!

  LARRY: Isn’t that amazing; you understand the matter perfectly with a tree but not with a human! That so beautifully reveals how differently you think of the two. You grant that a tree has no reason or purpose in growing since you say that a tree is not a conscious entity. Yet that does not mean that the growing of a tree serves no purpose. Now you will say that since I, unlike a tree, am a conscious entity, I not only serve purposes but have my own purposes, and indeed I often do. When I came here tonight, I had the definite purpose of speaking with you all. But that does not mean that everything I do I necessarily do for a purpose. In particular, my being truthful serves absolutely no purpose of mine. But I do not doubt that it serves a very important purpose. You see now why I compare my being truthful to the growing of a tree?

  MORALIST: Yes, now for the first time I begin to get an inkling of what you are saying. I don’t think I would agree with your point of view, but I do find it of interest, and I wish we had more time to go into details, but the evening is getting well on, and we should not neglect our final speaker, Simplicus. Actually, I planned this occasion primarily in Simplicus’s honor as a tribute to a great and truthful man, one who is probably more truthful than all of us. All of us here tell nothing but the truth, but Simplicus also always tells the whole truth. Therefore, he should be most competent to analyze the real purpose of truthfulness. And so we ask you, Simplicus, what is your reason for being truthful?

  SIMPLICUS: Me? Truthful? I had no idea that I was.

  2

  A Puzzle

  Before leaving the subject of truth telling, I would like to tell you one of my favorite logic puzzles.

  Suppose there are two identical twin brothers, one who always lies and the other who always tells the truth. Now, the truth teller is also totally accurate in all his beliefs; all true propositions he believes to be true and all false propositions he believes to be false The lying brother is totally inaccurate in his beliefs; all true propositions he believes to be false, and all false propositions he believes to be true. The interesting thing is that each brother will give the same answer to the same question. For example, suppose you ask whether two plus two equals four. The accurate truth teller knows that it is and will truthfully answer yes. The inaccurate
liar will believe that two plus two does not equal four (since he is inaccurate) and will then lie and say that it does; he will also answer yes.

  The situation is reminiscent of an incident I read about in a textbook on abnormal psychology: The doctors in a mental institution were thinking of releasing a certain schizophrenic patient. They decided to give him a test under a lie detector. One of the questions they asked him was, “Are you Napoleon?” He replied, “No.” The machine showed that he was lying!

  Getting back to the twin brothers, two logicians were having an argument about the following question: Suppose one were to meet one of the two brothers alone. Would it be possible by asking him any number of yes-no questions to find out which one he is? One logician said, “No, it would not be possible because whatever answers you got to your questions, the other brother would have given the same answers.” The second logician claimed that it was possible to find out. The second logician was right, and the puzzle has two parts: (1) How many questions are necessary?; and (2) more interesting yet, What was wrong with the first logician’s argument? (Readers who enjoy doing logic puzzles might wish to try solving this one on their own before reading further.)

  To determine which brother you are addressing, one question is enough; just ask him if he is the accurate truth teller. If he is, he will know that he is (since he is accurate) and truthfully will answer yes. If he is the inaccurate liar, he will believe that he is the accurate truth teller (since he is inaccurate in his beliefs), but then he will lie and say no. So the accurate truth teller will answer yes and the inaccurate liar no to this question.

  Now what was wrong with the first logician’s argument; don’t the two brothers give the same answer to the same question? They do, but the whole point is that if I ask one person, “Are you the accurate truth teller?” and then ask another, “Are you the accurate truth teller?” I am really asking two different questions since the indentical word you has a different reference in each case.

  2

  On Things in General

  3

  Miscellaneous Fragments

  1

  Self-annihilating Sentences. Over a period of many years, the computer scientist Dr. Saul Gorn has compiled a delightful collection of sentences that somehow manage to defeat themselves. He has titled this collection “S. Gorn’s Compendium of Rarely Used Cliches.” With his kind permission, I reproduce a few choice items (with one or two minor modifications).

  1. Before I begin speaking, there is something I would like to say.

  2. I am a firm believer in optimism because without optimism, what else is there?

  3. Half the lies they tell about me are true.

  4. Every Tom, Dick, and Harry is called John.

  5. Having lost sight of our goal, we must redouble our efforts!

  6. I’ll see to it that your project deserves to be funded.

  7. I’ve given you an unlimited budget, and you have already exceeded it!

  8. A preposition must never be used to end a sentence with.

  9. This species has always been extinct.

  10. Authorized parking forbidden!

  11. If you’re not prejudiced, you just don’t understand!

  12. Inflation is an economic device whereby each person earns more than the next.

  13. Superstition brings bad luck.

  14. That’s a real step forward into the unknown.

  15. You’ve outdone yourself as usual.

  16. Every once in a while it never stops raining.

  17. Monism is the theory that anything less than everything is nothing.

  18. A formalist is one who cannot understand a theory unless it is meaningless.

  2

  Saul Gorn once told me his theory of asceticism: “It is well known that the longer one postpones a pleasure, the greater the pleasure is when one finally gets it. Therefore, if one postpones it forever, the pleasure should be infinite.”

  3

  Many years ago, Saul Gorn and I were having supper at the Automat. Just as Saul finished, a waiter snatched away his plate. “Ah!” exclaimed Saul. “I finished just in time!”

  4

  On another occasion, Saul and I were with a group of friends. Saul asked us whether we wanted to go to a certain place. We finally decided not to go. Saul looked at us and said, “Then how do you expect to get there?”

  5

  Saul once told me that he was teaching a class in which two students were always talking to each other. Finally, Saul said, “It’s pointless for you to keep talking because if you do, I’ll have to talk louder, and then neither of you will be able to hear what the other one is saying.”

  6

  This reminds me of an incident that occurred when I was giving an examination to an undergraduate class. At the beginning of the exam, I said to the class, “Will you give me your word of honor that you won’t cheat if I give you mine that I won’t report you in case you do?”

  7

  I am a firm believer that in studying mathematics one should never forget one’s common sense. Many years ago, I was teaching an elementary algebra course. On one exam, I had a standard-type question that involved finding the ages of a mother, father, and child. After the students read the question, I said, “On this problem, I’ll give you one hint.” All eyes eagerly turned to me. I continued, “If the child should turn out to be older than either of the parents, then you’ve done something wrong.”

  8

  On another occasion, I had to present the Pythagorean Theorem to a class in geometry. I drew a right triangle on the board with squares on the hypotenuse and legs and said, “Obviously, the square on the hypotenuse has a larger area than either of the other two squares. Now suppose these three squares were made of beaten gold, and you were offered either the one large square or the two small squares. Which would you choose?”

  Interestingly enough, about half the class opted for the one large square and half for the two small ones. A lively argument began. Both groups were equally amazed when told that it would make no difference.

  9

  At one university where I taught, we were thinking of hiring a certain candidate. We invited him up for a talk. Sometime after the talk, the chairman asked him how he liked teaching. He replied, “I’ve never done any, but I don’t think I’d like it.”

  At a departmental meeting a few days later, we were discussing why the candidate said that. “Oh,” suggested one of the department members, “he probably dislikes lying even more than teaching!”

  10

  A Question of Semantics. At a seminar that he was giving, the late philosopher Alan Ross Anderson told the following fascinating incident: Anderson was working for the navy during World War II with a group deciphering Japanese code. They had great difficulty deciphering one word (represented by a number) that kept coming in repeatedly. It was soon apparent that the word was an adjective applying to people and nations (“This nation is , but that nation is not .”). After much data were received, they finally decoded it as pro-Japanese. At the end of the war, the code book was captured, and the true meaning of the word was sincere.

  11

  The philosopher Nual Belnap, Jr., who collaborated with Alan Ross Anderson on a fundamental work in the field known as relevance logic, recently introduced me at a talk at Carnegie-Mellon University. He said, “In this introduction, I promised myself three things: First, to be brief. Second, not to be facetious. Third, not to refer to this introduction.”

  12

  Someone once told me that he believed that logicians reason more accurately than other people; they make fewer mistakes.

  “Logicians do not make fewer mistakes,” I replied quite emphatically, “and if I’m wrong about that, then here am I, a logician, who has just made a mistake.”

  13

  Recently, someone asked me if I believed in astrology. He seemed somewhat puzzled when I explained that the reason that I don’t is that I’m a Gemini.

  14

  Beca
use I have been a magician for many years, people have often asked me whether I ever have sawn a woman in half. I reply, “Oh, yes; I’ve sawn over seventy women in half in my lifetime, and I’m learning the second half of the trick now.”

  15

  I performed magic most intensively when I was a student at the University of Chicago. I never did much stage magic; I was a closeup magician who entertained small groups at private parties and more often at the tables of various supper clubs. The following recollection is about my funniest.

  At one table where I was performing, there was a man who was about the most blase character I have ever met. He just sat there smoking his pipe, saying not a word, and nothing I could do got the slightest rise out of him. I made my tricks more and more startling, all to no avail. After about twenty-five minutes of increasing effort, I finally did my most spectacular effect, at which he took his pipe out of his mouth, slammed the table with his fist, and angrily shouted, “It’s a trick!”

  16

  In those days, I particularly delighted in playing tricks on the philosopher Rudolf Carnap; he was the perfect audience! (Most scientists and mathematicians are; they are so honest themselves that they have great difficulty in seeing through the deceptions of others.) After one particular trick, Carnap said, “Nohhhh! I didn’t think that could happen in any possible world, let alone this one!”