Five Thousand B.C. and Other Philosophical Fantasies

by Raymond Smullyan

  Theorem C (Chaudhuri’s Theorem). Nothing is real.

  Chaudhuri derived his theorem from two ontological axioms. He referred to certain properties as Brahmanic properties. (I’m not sure what he meant by a Brahmanic property, but I suspect that he meant the same thing as the medieval Western ontologists meant by a perfection. ) Here are Chaudhuri’s ontological axioms.

  Axiom C1. Reality is Brahmanic.6

  Axiom C2. Given any Brahmanic property, if there is any real entity having the property, then there is also an unreal one having the property.

  From these two axioms, Chaudhuri’s theorem easily follows. We leave the proof to the reader.

  Appendix

  1

  Proof of Theorem 1. This is quite simple: Let E be the property of existence. By Axiom 1, E is a perfection. Obviously, anything having Property E has the property of existence (since E is the property of existence), and so by Axiom 2, there is something having Property E, that is, there is something having the property of existence.

  2

  We first prove Propositions 1 and 2.

  Proof of Proposition 1. This proposition is a trivial one and follows from Axiom 1 alone: Let g be any god; g has all perfections. By Axiom 1, the property of existence is a perfection. Therefore, g has the property of existence.

  Proof of Proposition 2. This proposition follows from Axioms 3 and 4: Let P be the class of all perfections. (There is such a class by Axiom 3.) Let G be the property of being a god. By the definition of a god, Property G is nothing more nor less than the property of having all the perfections in P. Then by Axiom 4, this Property G is a perfection.

  Proof of Theorem 2. Again, let G be the property of being a god. By Proposition 1, every entity having Property G has the property of existence (this is the same thing as saying that all gods have the property of existence). Also, by Proposition 2, the Property G is a perfection. Then by Axiom 2, there must be at least one entity having Property G, which means that there is at least one god.

  3

  Proof of Theorem 3. We have already proved that there is at least one god, so all that remains to prove is that there is at most one god.7

  Let g1 be any god. We will prove that given any god g2, it must be that g2 is identical with g1. Suppose that g2 is a god. Since g1 is a god, then by Axiom 5 the property of being identical to g1 is a perfection. But g2, being a god, has all perfections, so in particular, g2 has the perfection of being identical to g1. This proves that any gods g1, g2 must be identical, and hence there cannot be more than one god.

  4

  Proof of Theorem A. Let N be the property of nonexistence. It is obvious that nothing having Property N can also have the property of existence. Then by Postulate 2 there is no entity at all having Property N. In other words, there is no entity at all having the property of nonexistence. (This proof uses Postulate 2, but it does not require Postulate 1!)

  Proof of Theorem B. From Postulate 1 alone it follows that there cannot be any existing devil (which is already a relief!) because by definition every devil has all antiperfections, and nonexistence is an antiperfection (by Postulate 1), and so every devil has the property of nonexistence. So if there were a devil, it would have the property of nonexistence. But by Theorem A, there is no entity at all that can have the property of nonexistence. Hence, there is no devil.

  5

  Askanas’s Proof of Theorem B. Askanas’s proof is a bit more subtle! We recall that we now have Postulate 1 and Postulate 2’ available but not Postulate 2.

  Again let N be the property of nonexistence. Since we don’t have Postulate 2 available, we cannot conclude that no entity has Property N. However, by Postulate 1, the Property N is an antiperfection. Then by Postulate 2’, the Property N + is also an antiperfection. Now, nothing can possibly have Property N + (because such an entity would have both the Property N of nonexistence and the property of existence, and this is a contradiction). But since N + is an antiperfection, then if there were a devil, it would have to have Property N +. Therefore, there is no devil.

  Notes

  1

  Richard Wincor, Sherlock Holmes in Tibet (New York. Weybright and Talley, 1968).

  2

  Oscar Mandel, Chi Po and the Sorcerer: A Chinese Tale for Children and Philosophers (Tokyo: Charles E. Tuttle Co., 1964).

  3

  Raymond Smullyan, What ls the Name of This Book’ (Englewood Cliffs, N.J.: Prentice-Hall, 1977).

  4

  This is the same Inspector Craig of whom I wrote so much in The Lady Or The Tiger.’ (New York: Alfred A. Knopf, 1982).

  5

  Parenthetical remarks accompanying the axioms are mine.

  6

  If my aforementioned suspicion is correct, then except for terminology this axiom is the same as Van Dollard’s first axiom.

  7

  This, according to a famous quip of Alfred North Whitehead, is the creed of the Unitarians.

  5

  Concluding Pieces

  11

  Dream or Reality?

  To distinguish the real from the unreal, one must experience them both.

  S. Gorn’s Compendium

  of Rarely Used Clichés1

  SKEPTIC: You claim that you see a chair. How do you know that you see a chair?

  SUBJECT: I never said that I know that I see a chair; I merely said that I see a chair. I am not as sure that I know that I see a chair as I am that I see a chair. To me, seeing is more immediate than knowing.

  SKEPTIC: Suppose I prove to you that you don’t see a chair?

  SUBJECT: No proof can convince me since I already know that I do see a chair.

  SKEPTIC: Ah, I’ve caught you! You do claim you know you see a chair.

  SUBJECT: I never denied knowing it; I merely said that I am less sure that I know it than that I am seeing the chair.

  SKEPTIC: And you would still claim to see the chair even if I proved to you that you don’t?

  SUBJECT: Of course I would!

  SKEPTIC: Then you are being irrational.

  SUBJECT: Not really.

  SKEPTIC: Can you prove that you are seeing a chair?

  SUBJECT: Of course not! Or rather, I should ask, “Prove it from what premises?”

  SKEPTIC: Can you at least prove that it is probable?

  SUBJECT: Probable? I don’t even know what it means to say that it is probable that I am seeing a chair. What I say is that I am seeing a chair.

  SKEPTIC: But how do you know that you are seeing a chair?

  SUBJECT: You asked me that before. Let me say this: First of all, I am not completely clear that I understand the meaning of how I know anymore than how I see. But to the extent that I do understand it, I can honestly say that I do not know how I know that I see a chair.

  SKEPTIC: So you don’t know how you know you see a chair, and you admit you can’t prove you see a chair, yet you stubbornly maintain that you see a chair.

  SUBJECT: Of course!

  SKEPTIC: Then you are being dogmatic!

  SUBJECT: Perhaps.

  SKEPTIC: But do you really want to be dogmatic? Just think of what dogma leads to! Think of fascism, communism, and the Spanish Inquisition.

  SUBJECT: Oh, come on now; these are examples of intolerance, not just dogmatism!

  SKEPTIC: But what is the difference between dogmatism and intolerance?

  SUBJECT: The present case is as good an illustration as any. One might label my dogged belief that I see a chair dogmatic (though I am not sure this would be correct), but surely no one in his right mind would label this belief of mine an act of intolerance!

  SKEPTIC: The reason that I cannot accept your statement that you see a chair is that I doubt the existence of chairs. I think, however, that one can translate your statement into another form whose truth I would accept. I think that what you are really trying to say is that you are having a certain visual sensation—the so-called sensation of seeing a chair.

  SUBJECT: If it makes you happy to transla
te it into those terms, by all means do so! I would not think of saying it this way. It may be also true—in fact, it probably is true—that I am having this so-called sensation. But again, as I see it, the notion of sensation is a far more sophisticated concept than just seeing and leads to a considerable number of philosophical problems and ambiguities. To a phenomenalist or idealist, a sensation is an immediate element of experience. To a materialistic realist, a sensation is a certain brain state or cerebral phenomenon, which seems to me to be something completely different. At any rate, the sort of statements that I most immediately understand are things like, “I see a chair,” “I see a table,” and so forth. I understand statements involving terms like sensation mainly to the extent to which I can translate them into such primitive statements.

  SKEPTIC: But would it not be a more secure basis for philosophy to start out assuming only the things one really knows, like one’s own sensations? No one but you can know whether you have a sensation or not. So if you say you have a given sensation, it cannot be reasonably denied. But you have absolutely no basis for claiming to know that the sensation is of something.

  SUBJECT: This whole way of starting out philosopy is, to my mind, the worst one possible. To start out with one’s sensations (or sense data) as the primary known realities! Children, who to my mind are the best philosophers, don’t do anything like that. They talk about objects, not sensations of objects. Once you start out with sensations as the given, then you get involved in the whole nightmare of worrying about the very problem you raised: Are there objects corresponding to these sensations, or are there just free-floating sensations, so to speak? Then the problem arises as to what these objects are really like: How do they resemble our sensations of them, how do they cause the sensations of them, and for that matter what real evidence do we have for their very existence? Is our evidence probabilistic, or must we accept objects as an act of “animal faith”? Kant thought it a scandal of philosophy that the existence of external objects had never been satisfactorily proved. But to me, the search for a proof is utterly ridiculous. I directly perceive the objects; what more could I want? I don’t perceive sensations at all. At least, the things I perceive I don’t call sensations but objects, like this chair. I can assure you that if I did not perceive this chair directly, then absolutely no proof for its existence would carry the slightest conviction with me. I honestly regard it as pathological to require proofs of things one already knows.

  An important consideration has just occurred to me. There is another way—a totally different way—of understanding the statement, “I see a chair,” than the one I had in mind, that is, the way it would be understood by a physicist qua physicist, which is a statement about the physical world, made within the framework of physics. This secondary interpretation, which to my utter amazement is regarded as primary by some philosophers, states that my body is now facing the chair, I am awake with open eyes, light rays are reflected from the chair that form an image on my retina, causing physiological changes in my optic nerve, brain, and so forth. If this “physicalistic” interpretation of my statement is what you understood, then I can well understand your labeling my sureness of it an unfounded dogma—indeed, I would agree! I believe that this secondary interpretation also holds, but I cannot possibly know it in the absolute sense that I know the other. Indeed, I know this only secondhand, that is, on the testimony of scientists. I have never seen my brain or optic nerve and only know of them from authorities I trust. Incidentally, my objections to analyzing the statement, “I see a chair,” into objects and relationships does not apply to the “physicalistic” interpretation; indeed, this interpretation does put together things like human bodies, chairs, light rays, optic nerves, brains, and so forth. Although I also clearly understand this secondary interpretation, it is a far more involved business than the primary interpretation, and I am able to understand this secondary interpretation only by analyzing it ultimately in terms of experience statements in their primary sense.

  SKEPTIC: Since you make this sharp dichotomy between what you call the primary and secondary interpretations of experience statements and claim such an important difference between them, how in discourse do you make clear which meaning you have in mind?

  SUBJECT: With philosophers—particularly so-called materialists—this is usually the most difficult thing in the world! With most people —especially with children—there is no difficulty whatsoever since they usually understand experience sentences only in the primary sense. Of course, primitive people—as well as all people who lived before the rise of science and so knew nothing about optic nerves and brains—can understand such statements only in the primary sense.

  The situation seems to me well-nigh tragic. People in their childhood understand only the primary interpretation of experience statements. But at some stage of their development, particularly those who study science, they become aware of the secondary interpretation. They learn that one sees a chair when and only when one’s physical brain is in a certain state. This is an exciting realization. But unfortunately certain people—those who become materialists—tend to identify the two meanings and cannot subsequently separate them. It may be possible that they even forget after awhile the primary meaning altogether, but I think this in fact unlikely. If they did, it almost would be too frightening to imagine. It would be as if someone like Albericht traded love for gold, and after living in the world of gold for awhile totally forgot what love was even like except in the purely operational sense of understanding how people behave when they are in love. But as I said, I doubt that my fears have any real basis. To use an analogy, a blind physicist knows what the word red means only in the secondary sense; a sighted child, knowing no physics, knows the word in the primary sense. I doubt very much if a sighted adult who became blind could ever in his lifetime actually forget what red meant in the primary sense.

  SKEPTIC: Isn’t it unfortunate that the same words and phrases have these two very different senses and that our language doesn’t have separate phrases for the two meanings?

  SUBJECT: Extremely unfortunate! This is precisely one of the things that leads to so much confusion in philosophy!

  SKEPTIC: Is there no way that you can explain your distinction of primary and secondary meanings of experience statements to, say, a hard-boiled materialist?

  SUBJECT: They are obviously aware that I think that there are two meanings. The secondary meaning they already understand (at least I think they do). As for the primary meaning, those who are polite say, “I have no idea what you could possibly mean”; those who are more crass say, “You don’t mean anything at all; you are just using meaningless words, you are simply talking nonsense!”

  SKEPTIC: Could you give me an example?

  SUBJECT: Yes. One way I can explain that my primary meaning of, “I see a chair,” is totally different from the secondary meaning is this: Under the secondary meaning, it would be a total contradiction in terms to say that I might see a chair after my bodily death. But under the primary meaning, there is no contradiction at all. Whether I will see chairs after my death is (to my mind) simply an unknown fact, but it is inconceivable to me that the notion is contradictory. I am thinking of Schlick, who maintained that in principle there is no reason why he should not witness his own funeral. Ayer, on the other hand, held this notion to be self-contradictory. Clearly, Schlick was thinking of witnessing in what I term the primary sense, Ayer in the secondary sense. Obviously, Ayer would not accept my argument at all; he would not agree that his difference with Schlick showed that there are two senses of the phrase I see or I witness. He would deny that what I call the primary sense has any meaning at all.

  SKEPTIC: Tell me, would you commit yourself to saying that you know that you see a chair?

  SUBJECT: Yes, I would.

  SKEPTIC: You realize, of course, that this commits you to saying that you know that you are now not dreaming.

  SUBJECT: Not at all!

  SKEPTIC: What!


  SUBJECT: I said, “Not at all.” I regard it as perfectly possible that right now I am dreaming.

  SKEPTIC: Good God! Surely if you are dreaming right now, then you don’t still maintain that you now see a chair!

  SUBJECT: I most certainly do! In a million years, I would not dream of making my assertion that I see a chair dependent on the fact that I’m not dreaming.

  SKEPTIC: But if you are now dreaming, then the chair you claim to see doesn’t even exist!

  SUBJECT: It most certainly does exist; I see it! It is one of the objects I am now dreaming about (assuming that I am actually dreaming).

  SKEPTIC: But surely you don’t maintain that the objects you dreamed about, say, last night, really exist!

  SUBJECT: They may not exist now, but they sure as hell existed last night; I saw them!

  SKEPTIC: No, no; you are putting it the wrong way! It’s not that last night you really saw dream objects; it’s that last night you dreamed that you saw real objects, but in fact you were wrong!

  SUBJECT: Not at all; last night I really saw objects.

  SKEPTIC: Would you call these objects real or not?

  SUBJECT: This brings us to the heart of the matter. Look, I don’t use such words as real, unreal, dream, nondream, real world, unreal world in an absolute sense but only in a relative sense. Let me explain.

  What do I mean when I say that right now I may be dreaming? This should be explained first. Well, last night I went to sleep and then saw all sorts of objects. This morning I woke up, and where are all these objects? They are nowhere to be found in the world I now experience. So I tend to declare them unreal and the state I was in last night a “dream state,” or the world I experienced last night a dream world. When I say that I may be dreaming now, all I mean is that I am open to the possibility that at some future time I may be in a state in which I regard my present state as I did my state last night. In other words, the experience of having gone from one state into another, in which the former state seemed to be unreal, has happened to me many times, and I cannot see why it cannot happen to me again with regard to the very state I am in now. It could be that in the next day or hour I could again have the experience I call waking up and regard my present state as unreal. In fact, I don’t expect this to happen the next hour, day, week, month, or several years. But when my body dies, I am less sure that I will not enter a state relative to which my present state is a dream. And this state in turn may prove to be unreal relative to some future state, and so forth ad infinitum.