Truth, Knowledge, or Just Plain Bull: How to tell the difference

by Bernard M. Patten

  Clearly, Costello’s admission would in no way imply that Costello is not in New York City, where, incidentally, he was. Costello’s admission just means he recognized that he wasn’t in San Francisco or Chicago.

  “But I’m not a serpent, I tell you!” said Alice. “I’m a—I’m a—”[12]

  Part of the hesitation is based on Alice’s sudden realization that it is awfully hard to prove anything and even harder to prove a negative statement. For instance, is there any way in the world you can prove that you are not a communist? Someone can prove you are a communist by finding your card. But you can’t prove you are not a communist because p. 296 the absence of evidence is not evidence of absence. In the same way, you can’t prove you are not a child pornographer. But someone could prove you are a child pornographer by finding the stuff on your computer, assuming, of course, it wasn’t planted there. This is why it was so hard for Iraq to prove that it did not have weapons of mass destruction. Perhaps this is the reason for the presumption at law that you are innocent until proven guilty. It is up to the prosecutor to prove the guilt beyond a reasonable doubt. It is up to the United States to prove Iraq has those weapons. It is not up to Iraq to prove it doesn’t have them.

  So, sensing the difficulty of proving that she is not a serpent, Alice falls back on a positive assertion of what she is. Alice does this in the hope that that will be sufficient demonstration that, if she is a little girl, she can’t be a serpent, as there is no case on record of a little girl being a serpent, too.

  But in a larger sense, Alice asks herself, “Who in the world am I?” for she is, after all, the dreamer, and this is her dream. Ah, that’s the great puzzle, and it’s one of the greatest of philosophic puzzles—the problem of personal identity. The Pigeon explores the question further:

  “Well! What are you?” said the Pigeon. “I can see you’re trying to invent something!”

  “I—I’m a little girl,” said Alice, rather doubtfully, as she remembered the number of changes she had gone through, that day.

  “A likely story indeed!” said the Pigeon, in a tone of the deepest contempt. “I’ve seen a good many little girls in my time, but never one with such a neck as that! No, no! You’re a serpent; and there’s no use denying it. I suppose you’ll be telling me next that you never tasted an egg!”

  “I have tasted eggs, certainly,” said Alice, who was a very truthful child; “but little girls eat eggs quite as much as serpents do, you know.”[13]

  The Pigeon’s thinking is poor. Obviously, a little girl can have a long neck as well as a short neck. So neck size is no criterion of girlhood one way or the other. Neck size is irrelevant to the issue. Therefore, the Pigeon is wrong to conclude that Alice is not a little girl because of her neck length.

  Let’s examine the Pigeon’s syllogism through which the Pigeon reaches the conclusion that Alice is a serpent. In formal form, that syllogism might appear as:

  1. Serpents eat eggs.

  2. Alice eats eggs.

  3. Therefore, Alice is a serpent.

  p. 297 Recall that in syllogism, there are two assertions, called “premises,” and one conclusion that should follow from the premises. In syllogism, the predicate of the conclusion contains the major term, and the subject of the conclusion has the minor term. Thus is a serpent is the major term and Alice is the minor term. The major premise is that which has the major term, and the minor premise is that which has the minor term. Thus, Serpents eat eggs is the major premise, and Alice eats eggs is the minor premise. The term that is present in both the major and the minor premise is the middle one. Here the middle term is eats eggs.

  OK, so let’s examine, in a formal way and then in a informal way, the truth of the premises and the truth of the conclusion. Is the major premise true? Do serpents eat eggs?

  Answer: Yes.

  How about the minor premise? Is that true? Does Alice eat eggs?

  Answer: Yes. Probably.

  Alice admitted tasting eggs. While it is possible to taste eggs without eating them, it is unlikely that Alice tasted eggs without having eaten them. Alice may have equivocated here, put a little sugar on the dog eat dog, in order to assuage the Pigeon, who seems very keen on this egg-eating issue.

  But if the major and the minor premises are correct, why is the conclusion wrong, as we know it must be? Alice is not a serpent. She is a little girl.

  Answer: In formal logic, this syllogism is invalid (that is, wrong) because the middle term is not distributed at least once. That is, eating eggs, while done by all serpents, can also be done by other animals as well. Therefore, that Alice eats eggs doesn’t exclude the possibility that she is not a serpent. The major premise says Serpents eat eggs. It does not say that any animal that eats eggs is a serpent. Alice is quite right in her refutation of the Pigeon: “Little girls eat eggs quite as much as serpents do, you know.” That refutation should have stopped the argument dead. Instead of admitting defeat, the Pigeon answers, “I don’t believe it . . . but if they do, then they’re a kind of serpent: that’s all I can say.”[14]

  This is the Pigeon’s confession that the major premise has to be changed in order for the conclusion to be justified. If anyone who eats eggs is a serpent, then Alice is a serpent. But changing the major premise makes it false. Here’s the reason. The Pigeon’s new statement would look like this:

  1. Whatever eats eggs is a serpent.

  2. Alice eats eggs.

  3. Therefore, Alice is a serpent.

  p. 298 The previous problem of the undistributed middle term has been corrected. Now the middle term is distributed and encompasses all classes that eat eggs. In redistributing the middle term, the Pigeon did correct the problem of the undistributed middle term. But he now changed the major premise so that it is not true. In fact, he changed the major premise to an erroneous broadcast definition. “Whatever eats eggs is a serpent” is not true. Since it is a generalization, we can prove it not true by finding one exception. Since exceptions are legion, the premise is obviously false. Therefore, the Pigeon’s conclusion is false, for any conclusion based on a false premise is false.

  Therefore, the Pigeon is still wrong. Truth has once again triumphed: Alice is not a serpent. By sheer strength of correct thinking, we have proven that Alice is not a serpent. Furthermore, we know Alice is a little girl. No little girl has ever been a serpent. That is a fact. Therefore, the Pigeon is wrong. He is arguing contrary to fact, which always puts one in a bad position vis-à-vis the truth.

  By the way, can you guess why the Pigeon is so hung up on the serpent thing? Deep-seated fears and anxieties are often at the heart of poor thinking, of which the Pigeon’s is a typical example. Undoubtedly, at sometime in the past, the Pigeon had had eggs eaten by a serpent. Whenever pigeons (or people) persist in being irrational, suspect a deep, underlying psychological basis adversely working from their heart’s core on their perspective capacity, leading them away from truth and toward error.

  At this moment the door of the house opened, and a large plate came skimming out, straight at the Footman’s head; it just grazed his nose, and broke to pieces against one of the trees behind him. The Footman continued in the same tone, exactly as if nothing had happened.

  “How am I to get in?” asked Alice again in a louder tone.

  “Are you to get in at all?” said the Footman. “That’s the first question, you know.”[15]

  It was the first question. No doubt, only Alice did not like to be told so. Alice’s question assumed she would get in. Alice was begging the question, and the Footman called her on it.

  “It’s really dreadful,” she muttered to herself, “the way all the creatures argue. It’s enough to drive one crazy!”[16]

  p. 299 We feel your pain, Alice. But, oh, dear, what do you expect from characters in a book written by an Oxford don whose main mission in his professional life was to teach logic!

  “Would you tell me, please, which way I ought to go from here?”

  “That depends a
good deal on where you want to get to,” said the Cat.

  “I don’t much care where—” said Alice.

  “Then it doesn’t matter which way you go,” said the Cat.

  “—so long as I get somewhere,” Alice added as an explanation.

  “Oh, you’re sure to do that,” said the Cat, “if you only walk long enough.”[17]

  These eminently logical remarks by the Cheshire Cat are among the most quoted passages in the Alice books. The deep meaning here involves that relation of science to ethics. The Cat’s answer expresses very precisely the eternal cleavage between science and ethics. Science cannot tell us where to go, but after this decision is made on other grounds (social, political, environmental, ethical, aesthetic, etc.), it can tell us the best way to get there.

  An echo of the Cheshire Cat talk is heard in Jack Kerouac’s novel On the Road:

  “We gotta go and never stop going till we get there.”

  “Where we going, man?”

  “I don’t know but we gotta go.”[18]

  A passage in the Talmud is similar: “If you don’t know where you are going, any road will take you there.”

  Because the Cheshire Cat has been eminently logical in this one instance, that doesn’t mean it will be logical in another:

  “In that direction,” the Cat said, waving its right paw round, “lives a Hatter; and in that direction,” waving the other paw, “lives a March Hare. Visit either you like: they’re both mad.”[19]

  (Misinformation is common, especially in directions given by locals to strangers. The March Hare lives on the left and the Hatter on the right, but, as they are both together at the tea party, they cannot now be visited at their respective homes. The Cat’s body language is ambiguous because waving the paws “round” does not indicate a definite direction in the way p. 300 pointing would. But the Cat’s speech and behavior are consistent with the theme of this part of AAW, which is navigational insouciance.)

  “But I don’t want to go among mad people,” Alice remarked.

  “Oh, you ca’n’t help that,” said the Cat: “we’re all mad here. I’m mad. You’re mad.”

  “How do you know I’m mad?” said Alice.[20]

  Wonderful! Alice is asking for evidence. She knows that all she needs is one counterexample to prove the Cheshire Cat’s generalization “we’re all mad here” wrong. If Alice can show she is not mad—or, better still, if the Cat can’t prove she is—then the Cat’s statement will have been proven false. Let’s review what we covered before and see how the clever Cheshire Cat handles Alice’s challenge.

  “You must be,” said the Cat, “or you wouldn’t have come here.”[21]

  In a sense, this is, as we discussed previously, an excellent example of circular reasoning. It is a tautology. But in a larger sense, the Cat knows whereof he speaks, given that he and Alice are in a dream.

  Psychiatrists tell us the type of thinking in a dream (primary process thinking) is close to if not identical with the thinking of psychotics. Lewis Carroll’s diary in February 9, 1856, raises the same query: “When we are dreaming and, as often happens, have a dim consciousness of the fact, and try to wake, do we not say and do things which in waking life would be insane? May we not then sometimes define insanity as an inability to distinguish which is the waking and which the sleeping life? We often dream without the least suspicion of unreality.”[22]

  Socrates addresses the same problem in Plato’s Theaetetus:

  Theaetetus: I certainly cannot undertake to argue that madmen or dreamers think truly, when they imagine, some of them that they are gods, and others that they can fly, and are flying in their sleep.

  Socrates: Do you see another question that can be raised about these phenomena, notably about dreaming and waking?

  Theaetetus: What question?

  Modern psychiatry would hold that primary process thinking in dreams is normal. But the failure to distinguish the real from the unreal while awake is the characteristic ego disintegrative sign of psychosis. That consideration aside, let’s look at the Cheshire Cat’s logic:

  p. 301 Item: We’re all mad here. (unsupported assertion)

  Item: I’m mad. You’re mad. (unsupported assertions consistent with the first item. But more than that, these later assertions are actually subaltern claims that follow directly from the first item. If we are all mad here, then two people who are here [that is, those included in the category encompassed by the first item] are also mad. In a way, the interrelation of the claims of item one and item two point out the usual relation of subaltern claims. The subaltern is implicit and follows directly from the larger categorical claim. Thus, if all S are P, some S must also be P, many S must be P, few S must be P, this particular S that I see washed up on the beach must be P, and so forth.)

  Item: Because you’re here, you must be mad. (Unsupported conclusion)

  “And I wish you wouldn’t keep appearing and vanishing so suddenly: you make one quite giddy!”[23]

  Alice resorts to an ad hominem argument to give herself time to think of a good reply to the Cat’s circular reasoning. Her statement is an attack on the Cat’s behavior and has nothing whatsoever to do with the issue under discussion, which was whether they are all mad. Diversionary arguments, whether our own or Alice’s, are irrelevant.

  “All right,” said the Cat; and this time it vanished quite slowly, beginning with the end of the tail, and ending with the grin, which remained some time after the rest of it had gone.[24]

  Notice that the Cat unfairly selects part of Alice’s request and gives that part of the request undue emphasis and importance. His changing slowly is not what Alice really wanted. Alice wanted him to stop changing and remain constant. But of course she opened herself up to the Cheshire Cat’s interpretation by not stating precisely what she wanted. Usually, it’s a good idea to say exactly what you want and mean exactly what you say. Usually, it’s a good idea to not say what you don’t want to say and not say what you don’t mean.

  p. 302 “Well! I’ve often seen a cat without a grin,” thought Alice, “but a grin without a cat! It’s the most curious thing I ever saw in all my life.”[25]

  This shows us that if a statement is true, the converse of that statement is not necessarily true. This same point is hammered in further along during the tea party, where “mean what I say” is not the same as “say what I mean,” and “I see what I eat” is not the same as “I eat what I see,” and “I like what I get” is not the same as “I get what I like.”

  “You might just as well say,” added the Dormouse, which seemed to be talking in its sleep, “that I breathe when I sleep is the same thing as I sleep when I breathe!”

  “It is the same thing with you,” said the Hatter, and here the conversation dropped.[26]

  Sometimes the example comes right out of Carroll’s lesson book: “All apples are red, but it does not follow that any red thing is an apple.” This emphasis on the nonequivalence of converses is important and relates to syllogisms and to if-then statements of the form:

  If A (and then) B.

  The “if” statement is called the antecedent, and the “then” statement is the consequence. In more formal logic, this might look like:

  If A then B.

  A.

  Therefore, B.

  In practical form, an if-then statement might look like this:

  If you take cyanide, then you die.

  You take cyanide.

  You die.

  As a logician, Carroll knew how important it was to understand that converses are not necessarily true. That is why he gives so many examples to prove the point. In fact, disregard of these ideas leads to some common errors in thinking. For instance:

  p. 303 If you take cyanide, then you die.

  You do not take cyanide.

  Therefore, you do not die.

  Or:

  If A then B.

  Not A.

  Therefore, not B.

  The confusion here is that cyanide i
s a sufficient cause of death by itself. It interferes with the cytochrome respiratory chain so effectively that the transfer of electrons to oxygen is prevented and metabolism stops dead. But that does not mean that because you don’t take cyanide you will live forever. There are many other causes of death besides cyanide. Cyanide is just one of a large class of poisons that will cause death, and the large class of poisons causing death is part of an even larger class of things (eating too much pie, getting run over by a steamroller, choking on a filet mignon, cancer, stroke, Marchifava-Bignami disease, heart attack, etc.) that can cause death. Not taking cyanide will not prevent one of those other causes from eventually taking its toll. In formal logic, this error is called negating the antecedent.

  Here’s another problem that arises from a similarly defective reasoning:

  If you take cyanide, then you die.

  You die.

  Therefore, you took cyanide.

  Or: