[Math Lair] The Search for Truth: Chapter IV: The Ancient Cambodians

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Chapter IV

The Ancient Cambodians

I. A Sensible Question

"What on earth have the ancient Cambodians got to do with the development of straight thinking?", someone may ask. Wait a moment, and you will see. They had a great deal to do with it; indeed their part was probably the most important of all. Egypt, Babylon, Greece, and our own epoch have made tremendous contributions, many of them well known to everybody. But the Cambodians appear to have been overlooked until about thirty years ago. While we wait for twelve centuries to slip by, as the thread follows some obscure route not yet traced from the Egypt of 1800 B.C. to the Greece of 600 B.C, we shall pass the time with the Cambodians.

This chapter might well have come at the beginning of the whole story. Its point perhaps will be clearer in the light of the following personal reminiscence concerning a man, now dead, to whom I owe my first real interest in the history and evolution of straight, clear thinking. If the reader will pardon the necessarily personal tone, he will be amply repaid when he reads certain words of the late William James, not hitherto printed or even written (to the best of my knowledge). To avoid any possible misunderstanding, the William James I mean was the American psychologist and philosopher who lived from 1842 to 1910, and who created the philosophical theory called pragmatism.

In 1906, when William James lectured on the Pacific Coast, I happened to be living in San Francisco. That was before the entrancing mistress of the Golden Gate had been purged by earthquake, purified by fire, and forgiven for her sins by reformers. Being out of touch at the time with anything that could be called thought-provoking, I used to welcome the weekly visits of a somewhat boisterous electrical engineer who was always bursting with crazy ideas which he loved to inflict on anyone who would listen. This energetic young man used to breeze into the city on Saturday afternoons to stay over the week-end and see all the sights he had no business seeing be­tween intervals of lucid philosophic discussion. He lived and worked somewhere in the sticks down the peninsula, so there was always lots he hadn't seen between one Sunday and the next. On account of his energy and general self-assertiveness his friends called him Bluebottle.

"Hey, old timer," he greeted me one Saturday noon when I met him at the station, "James is lecturing down there. Want to hear him? Say, you'd better. He's just what you need. Come on; we can just make the 1:15."

He dragged me off to catch a train back over the very route he had just travelled. By the time we reached the train it was already in motion, and we barely caught it. Out of breath and exasperated at the prospect of having to listen to a lecture instead of to Bluebottle, I managed at last to get in the only question for which I had wind enough.

"Who the hell's James?"

To my shame it was the first I had ever heard of the great philosopher. Bluebottle elaborated. By the time we reached our destination I was less enthusiastic about listening to the lecture than when we started. But Bluebottle chartered a horse and buggy and we started for the lecture hall. It may have been the jolting of that infernal rattletrap over the bumpy, unpaved road, or it may have been Bluebottle's noisy enthusiasm, or it may have been a combination of both of these and several other things, but anyway, when we reached the lecture hall I felt that I simply could not go in, and I very sensibly spent two and one-half hours in the adjoining lavatory while Blue­bottle did enough listening for both of us.

After the lecture, feeling completely recovered, I proposed that we return at once to San Francisco. Bluebottle wouldn't hear of it.

"Say, the lecture's only for the professors and the old women. He saves all the real stuff for the discussions."

"The discussions?" I repeated, going suddenly queasy again. "I don't think I'd better—."

"Aw, come on. You'll be all right. Say, let's take a hike out to the Blue Goose. That'll set you up in great shape, and we can be back in plenty of time. The discussion doesn't begin till eight. It meets in Jake Schnitzler's hangout. It's just like they do in Germany. The fellows all sit around and ask ques­tions—and everything."

That vague "everything," as I was to learn, did indeed account for a good deal, including much of Bluebottle's en­thusiasm. We got back, as Bluebottle had promised, in plenty of time. It was a quarter to eight. Bluebottle had had nothing to eat except an occasional pretzel since breakfast, and I also was beginning to want my dinner badly. My suggestion that we have at least a cup of stiff black coffee apiece and a sinker or two before venturing into the thick of a philosophical dis­cussion was dismissed with scorn.

"Aw, c'm on. You'll be all right. There's always lots of rye bread and cheese and everything."

Again that mysterious "everything." Just as we reached the door of Jake's roomy quarters, Bluebottle blandly informed me that the membership of the discussion circle was very select, and that admission was by invitation only. I turned to flee, but Bluebottle grabbed me.

"Can't a fellow take a guest?" And he shoved me headfirst into the one and only philosophical discussion I have ever attended. But for him I would never have crashed the gate at that one. Not till years later did I learn that Bluebottle himself hadn't been invited.

The discussion was already in progress, but I failed to get the drift of the desultory questions, as Bluebottle was nudging and shoving me over to the dimly lit corner where the refresh­ment table loomed invitingly. Bluebottle had not exaggerated. It was just like Germany, with huge piles of all manner of sausages, bolognas, cheeses, cold pork chops, pretzels and stacks of rye bread and pumper­nickel massed around two brassbound ten-gallon kegs, the one of steam beer, the other of bock.

While Bluebottle saw to his own wants, I retired with my pork chop and hunk of rye behind a fleshy young truth seeker who was squatting like a Buddha on a Chinese rug, and who had just propounded an interminably involved question to the puzzled philosopher. James looked bored. I forget his answer, but I do remember that it deflated the windy young enquirer as if he had been adroitly pricked with a needle in his fleshiest part. That young man was silent thereafter. All the gas had been let out of him. And yet it had all been done kindly. There was no malice in James.

During this episode I had lost track of Bluebottle. I now saw him deftly unhorse a pallid young man with long dank black hair and plump himself down in the loser's chair, directly in front of James. It was the seat of honor, lower in dignity only than that of James himself, for the displaced young man was the leader of the discussion group. Bluebottle was brand­ishing an enormous stein of foaming bock. Between gulps he started the ball rolling.

"C'm on! What's the matter, you fellows? Why doesn't somebody ask Professor James a question? We may not have another chance like this in a hundred years. If nobody else asks anything, I've got one. What's the discussion about this evening, anyway?"

"Thought," James informed him tersely. "Thinking."

"Sure," Bluebottle apologized. "That's what the lecture was about, wasn't it? My mistake, Professor. Well, isn't anybody going to ask him a question?"

To the surprise of everyone, including the questioner himself, somebody did. And this is the question that came from some where in the general direction of the refreshment table: "Can thought think about thought?"

Bluebottle slowly lowered his stein and his jaw dropped. For probably the first time in his philosophic career he was astonished, nonplussed, and flabbergasted by a philosophical question. James, on the other hand, was instantly alert. His eyes lit up with glad recognition, as if he had come upon a life­long friend of his own secret musings in some public and un­expected place.

"Ah!" he exclaimed, leaning forward to catch a glimpse of the modest questioner shrinking behind the bock barrel. "That was a very sensible question."

"Excuse me, Professor James," Bluebottle interrupted, "but that was not a very sensible question." He paused to gather em­phasis. "It was a damned silly question."

I glanced up apprehensively at the ceiling. My fears, how. ever, were about eighty hours ahead of their schedule. But I believe to this day that it was Bluebottle's impious defiance of celestial philosophy which brought that ceiling down when it did come.

"In vino veritas?"¹ James quizzed, with a significant glance at the half-gallon stein in Bluebottle's purple fist.

"Wrong again, Professor," Bluebottle retorted with a grin. "In bocko beero double-Dutch veritas."²

James took it in good part. He insisted that Bluebottle prove his point if he had one. Bluebottle did nobly, and the debate lasted till 5 a.m. the following morning. His argument, strangely enough, I now see, might have inspired that unknown and forgotten Egyptian thinker, and possibly did inspire him, to a solution of the riddle of the pyramids. But, where the Egyptian was convinced by the argument and got something valuable out of it, namely a consistently workable formula for the volume of the pyramid, Bluebottle for his part could get nothing at all, and insisted that the whole of it was a tissue of verbalized, meaningless bosh. In short it was words, all words, and nothing but more words.

Not till many years later did I come across practically the same argument set forth in the serious writings of one of the toughest, closest German reasoners of the Nineteenth and Twentieth Centuries, Richard Dedekind (1931–1916). As this kind of reasoning will reappear frequently in our following of the thread, I shall give the gist of Bluebottle's argument as nearly as I can recall it.

Can thought think about thought? If it can, then a thought about a thought, or a think about a thought, or a thought about a think, or finally a think about a think, is another thought or another think, and "obviously" the successive thinks or thoughts will all be different from one another. From this it is quite easy to show that thoughts about thoughts can be con­tinued indefinitely; there is no end to the sequence, and there are in fact an infinity of them. At least we can conceive of there being an infinity of them; for if there were a last one, we could think about it (could we?) and get another one, different from all its predecessors. So the last would not really be the last, and we could go on at least one more. But from that one we could go on in the same way, and so on forever and ever, world with­out end, Amen. By a refinement of this sort of reasoning (Blue­bottle's clinching argument has been omitted) Dedekind dem­onstrated that the universe of human ideas (the Gedankenwelt, he called it) is infinite. We are indeed as the gods, drunk or sober.

Without admitting that he had done it, Bluebottle had in fact recaptured one of the fundamental distinctions between finite (countable) collections of things and infinite (uncount­able) collections: a part of an infinite collection can contain just as many things as the whole of the collection. The most familiar example is that of the infinite (unending) sequence I, 2, 3, 4, 5, .... of all the common whole numbers. Knock out every other number, say 1, 3, 5, ...., and there are just as many left as there were before. This example (or essentially this one; actually it had to do with the squares of the numbers, instead of every other one) was devised by Galileo to confound thick-headed Simplicius. A "proof" will be found in a later chapter; for the moment the reader (if it is new to him) may amuse himself by trying to refute the assertion about there being just as many left after the odd numbers have been de­leted. If a part of a collection can contain just as many things as the whole, what has become of our common sense and our everyday visual, tactual experience? This was Bluebottle's trouble. He could not reconcile his verbalized reasoning with his manual experiences. He could conceive of no possible way by which a human being could perform the infinity at acts necessary to knock all the odd numbers out of the whole sequence. In his obstinate refusal to admit the conceptual possibility, Bluebottle differed radically from most of the mathematicians who have created the kind of mathematics (the calculus, analysis) which is of the greatest use in the sciences and practical affairs. Without this flagrant violation (by reasoning) of common, material experience, modern mathematics, as it now exists, simply would not exist.

Bluebottle heartlessly repudiated his own brain-child. He disowned the lusty mite entirely, declaring that it was the illegitimate offspring of an unblessed union between a bologna sausage and a keg of bock. Nothing that James could bring up in the way of authority from Antipho, Bryso, and Democritus to Cantor, Weierstrass, and Dedekind could shake Bluebottle's obstinate and irreverent skepticism. If logical reasoning led to such conclusions then he, Bluebottle, would undertake to build a dynamo that would run forever on one puff of classical logic—hot air, he called it.

James did not accept the challenge, and after about nine hours of high philosophical argument, with frequent intermis­sions while the disputants took time out for refreshments, the charmed circle broke up at five o'clock on Sunday morning. As it was yet too early for church, all, including James, went home and went to bed. James had not yet uttered the memorable words which it is the main business of this chapter to record and, possibly, preserve for future generations of young philos­ophers and enquiring Bluebottles.

The sequel began arriving at thirteen minutes past five the following Wednesday morning, April 18, 1906. In common with thousands of others in San Francisco and all down the peninsula, I was jolted out of bed and half out of my wits by the great, reforming earthquake. My first dazed thought was that James and Bluebottle were at it again.

At seven o'clock that evening, while watching from a vantage point on Nob Hill with hundreds of others the purification by fire of what had been our homes and dens of iniquity, I barged into Bluebottle not far from where I lived. The good fellow had caught the last train up from the sticks which managed to get within walking distance of the city. He declared that he had come up solely to see if I was safe and, if not, to salvage my remains. As he was gorging on cold turkey, caviar and cham­pagne at the moment, I rather doubted his assertion, but held my peace and shared the turkey. Some generous hotel keeper, seeing his place about to go up in smoke, had told the boys to help themselves to what they could carry away before the militia could arrive to chase them out. Bluebottle had enough for a platoon, and he was inviting one and all to his banquet.

"Say," he began, and interrupted himself just long enough to rebuke a smug female who informed the feasters that they should stop their eating and drinking and merry making, for this was the judgment of a just, merciful, and wrathful God on the Scarlet Woman of the Seven Hills by the Golden Gate. "Say," he resumed when the woman departed with a face as red as a boiled beet, "I saw James just after the shake. He was in his right mind, but he wasn't as fully clothed as he thought he was. He was walking along with his head down and his hands behind his back. His shirt tail was hanging down over his pants, and he had forgotten to pull his suspenders over his shoulders. 'Morning, Professor,' I said. 'Your shirt tail's out.'

"James looked up and saw who I was, but didn't answer. He seemed sort of dazed. This was the time to give him the third degree and get the truth out of him, so I did.

"'Still think the same about philosophy as you did the other night?' I asked.

"He took a long time before answering. Then he came out with it.

"'Young man,' he said, 'it takes nature to put us in our proper places.'

"'Yes,' I said, 'but what about philosophy?'

"James came through. 'It is all just words, words, words,' he said."

*   *   *   *   *

Bluebottle passed away three years ago. Prohibition got him. He took to brewing his own stuff, and it was worse than his philosophy. I feel that I can never repay him for the unfailing source of pleasure he brought into my life. To him I owe my first real interest in the history and evolution of straight, clear thinking, and I take this opportunity of thanking his great spirit, wherever it may be.

2. Who Were the Cambodians?

Thirty years ago the interior of Cambodia, that exotic frag­ment of Indo-China, was less well known than it is today. To judge by the number of lecturers at large on the manners and customs, the religion and the ruined temples of the Cambo­dians, busses to the interior must be running every thirty minutes now. The magnificent ruins in the jungles these travel­lers rave about were built by some forgotten people of whom nothing very definite or credible seems to be known, so each lecturer is free to sell his own theory. The last one I sampled ascribed these ruins to the ancient Mormons (I did not know till then that there were any); the one before that proved that the Lost Tribes of Israel were responsible for the dilapidated temples and palaces, and the one before that connected them in some way that was difficult to follow with Atlantis and the lost Continent of Mu. The only thing on which all the theorists seem to agree is the grace and beauty of the Cambodian danc­ing girls. Until I see for myself, I shall take their word on that, too.

But all this does not tell us who was responsible for that mys­teriously vanished civilization of Cambodia, nor what part the jungle played in the evolution of human thought. For the latter at least we shall do better by consulting the strangely veracious record of l'Abbé Lemoine. This inquiring Frenchman, about thirty years ago, made his trepidant way into the jungle with only two native bearers. Others had seen some of the ruins be­fore he set eyes on them, but he was looking for more than fan­tastically carved piles of pinkish gray stone, and he found what he was seeking.

One stifling hot Sunday afternoon, attracted by a hullabaloo of shouts, yells, barks, shrieks, and screams, Lemoine cau­tiously squirmed his way up through the dense tropical brush on the gently sloping side of what he mistook at first for a small extinct crater. Reaching the top, he found himself staring down into a roughly elliptical amphitheatre, evidently of human ori­gin, for the depression was littered with fallen images and huge blocks of dressed stone, crowded almost to the brim with an excited, vociferating, gesticulating mob.

At first Lemoine thought he was witnessing some religious ceremony of the natives. The fact that it was Sunday gave his mind a subconscious flip in the wrong direction. But the longer he watched, the more puzzled he became. What on earth was all the fuss about? And why should rational beings make so much noise about nothing that was apparent to a disinterested observer? The discussion circle—for that was what it seemed to be—centered about a tall, dignified old fellow with a long wobbly nose and a shaggy white muff of a beard almost entirely en­circling his neck. It was the type of beard some of the Scotch deacons used to favor, leaving the chin and upper lip clean shaven and imparting a sort of grim, puritanical dignity to what otherwise might have been revealed as a very impressive and sensual pair of jowls. Lemoine named him Monsieur Lediacre. But although Lediacre howled and exhorted at the top of his voice, his audience paid but scant attention to him, being noisily engaged in five or six hundred individual exhorta­tions of its own. Their inattention seemed to make not the slightest difference to Lediacre.

All of a sudden the truth dawned on Lemoine. So interested had he been in trying to follow the trend of Lediacre's dis­course, that he had failed to observe the most significant detail of the old fellow's personal appearance. Lediacre had a long prehensile tail. Quickly confirming this observation by a glance round the amphitheatre, Lemoine grasped the truth in a flash: they one and all were gibbons, apes, baboons, or others of that interesting and numerous tribe of our cousins. Their tails gave them away.

The discussion continued for six hours. Convinced as he watched and listened that Lediacre was using words and reason­ing, Lemoine tried to make out what the old chap was agonizing to get across to his disrespectful audience. Certain simple pat­terns of sounds were reiterated again and again, and not only that, but whole phrases and stanzas were rhythmically re­peated with rough regularity, like the surge and ebb of a scathing denunciation when the speaker is thoroughly steamed up, or the majestic lift and dip of a dire incantation soaring and gliding into inspired prophecy.

The lesser speechifying going on all around the amphitheatre also engaged Lemoine's horrified attention. These barbarous apes were deliberately—it seemed to the perturbed Frenchman—parodying a stormy session in his own national Chamber of Deputies. A closer attention, however, to what they were say­ing acquitted the apes of bad taste. In addition to talking they were also reasoning; there could be no doubt of that. And they were merely disagreeing with Lediacre, putting forth five hun­dred theories to his one. If the words of their exhorter were good, their own more numerous words were that much better. Lemoine reports that his mind tottered on the brink of void skepticism that sweltering Sunday afternoon. Many times, he confesses, he though he detected the simple, unmistakable pattern of the Aristotelian logic in the pattering chatter of the apes: "All men are descended from Us; Aristotle is a man; therefore Aristotle is descended from Us." Being a learned man, he also caught fragments of the Hegelian dialectic, but what it meant not even old Lediacre seemed to know. "What is truth?" Lemoine asked himself, not once but many times as he stewed in the sticky heat, an unwilling martyr to hordes of winged stingers and biters. "What is it?" he kept asking himself. "Or is it anything more than a more or less reflex action of the muscles of breathing and swallowing? Possibly the viscera also have something to do with it in some purely mechanical way?"

Lemoine drew back from this black abyss of intellectual ni­hilism barely in time to preserve what the biters and stingers had left of his sanity. "I reflected," he says, "that truth is more than words; that there is an eternal and indestructible ideal within and above the everlasting pattern of the laws of logic and reason themselves, and that ideal is truth. Now, the knowledge and perception of truth is a wholly human privilege. Truth is not of us; it is outside of us, but we, in our slow gropings toward the unattainable perfection of the ideal, are permitted now and then to catch glimpses from afar of the blazing bril­liance of the transcendent reality, which, were we closer, would blind us and halt our search forever. Now the apes are not human. They can have no such conception of truth as has been revealed to us by the philosophers and sages, nor in fact can they have any whatever conception of truth. This conception ii is which distinguishes man from the lower animals."

Lemoine saved himself. A possible flaw in his reasoning was pointed out years later by a distinguished evolutionist. It is true, this eminent scientist declared, that apes are not human. But can Lemoine prove that humans are not apes? If not that much, what is his evidence that both of us, apes and humans, are not descended from a common stock? These difficult ques­tions are out of our province, so I shall leave them with the suggestion that the most ancient Cambodians of all—the "common stock" of the distinguished evolutionists—may have more to do with our patient search for truth than all the Egyptians, Greeks, and Babylonians who ever lived.

Lemoine was not a psychologist. His specialty was the first-hand study of our cousins by cautious observation of their conferences and amours in the privacy of their jungles. That is why he immersed himself in the sticky humidity of Cambodia. His psychological theories therefore can be passed over in silence. However, we cannot leave them where he did, so we shall recall a modern scientific version of this difficulty of truth versus mere words, by quoting the considered verdict of a leading psychologist on this ticklish question. Anyone wishing to look into the matter more fully may read the chapter on Talking and Thinking in Behaviorism (1924), by John B. Watson, thunder of that theory in psychology. The italics are Watson's.

"The behaviorism advances the view that what the psychologists have hitherto called thought is nothing but talking to ourselves..... The terms 'thinking' should cover all word behavior of whatever kind that goes on subvocally."

This brief extract of course gives no adequate idea of Wat­son's theory, but possibly it is enough to suggest that Lemoine saved himself by talking to himself. The theory also gives Pilate a very neat answer when fully developed. But we must leave that to Doctor Watson, and return to Lemoine.

Lemoine relates how the discussion circle adjourned. Old Lediacre had been gesticulating at the blazing sun from time to time all through his harangue, but no ape had paid any atten­tion to his excited gestures. They repented bitterly when it was too late.

As so often in the tropics, the stilling, steaming heat brewed a devil of a thunderstorm almost in the twinkling of an eye, certainly in less than half an hour after the first cloud drifted athwart the sun. The debates had been raging for six hours. That first fleeting shadow caused a momentary hush. Then the chatter burst out with renewed fury, and poor old Lediacre looked strangely crestfallen as the sun shone out again.

But not for long was he downcast. Out of an almost clear sky the first rapier of lightning flickered and played above the jungle, seeking its mark. The accompanying crack of thunder was as sharp as a rifle shot. Panic swept the amphitheatre, but the apes were too paralysed to bolt for cover. Only when the angry clouds swooped down upon the multitude and began dumping tons of tepid water on its philosophical enthusiasm did it come to its senses. Being only proto-human, the apes had no umbrellas. In a biting, scratching, precipitate mob they scrambled up and boiled out of the amphitheatre, seeking refuge from the fury of the brutal elements, their merciful God only knows where. It required no earthquake to end that particular discussion.

In the last flash of lightning before he, too, fled, Lemoine saw the venerable Lediacre still holding his ground in the de­serted amphitheatre, and still ranting. The astonished French­man could not make out whether the valiant old ape was defying the lightning to do its damndest, or whether he was merely and more humanly yelling "I told you so!" In either event he was talking to himself.

3. The Search for Truth

As we leave Cambodia and go on to Greece, it will be well to have clearly in mind the sharp distinction between two kinds of truth-seeking which splits seekers of "truth" into two irrec­oncilable factions. Lemoine, we have just seen, was tempted for a moment to believe that "Truth" is a mere noise without meaning. The "Truth" which philosophers have been seeking for centuries is non-existent in any superhuman, absolute sense. "Truth," on this view, is no more existent than Apollo was, and all talk about "Truth" is meaningless chatter. There is no such thing. This is one view of the whole question.

As we come to them a little later, we shall see that at least some of the Greeks did not hold this view: for them "Truth" appears to have had some sort of mystic "existence" over and above any human effort to manufacture it. Similar remarks apply to what are commonly called "eternal verities" and "absolute truths." Are there such things, or are these again meaningless collocations of words? Both views have been held. Some have claimed that there are "eternal verities"; others have denied that the words "eternal verities" have any meaning whatever.

Between these extremes is the more temperate ground held by those who seek to understand what such a statement as "this is a true proposition" means—if anything.

Most of the Greeks who believed in the existence of truth as something superhuman in one way or another were past masters at the game of deductive reasoning. With them the search for truth became a purely verbal gymnastic. To call their efforts to discover truth mere profitless hairsplitting and child­ish quibbling would be to misuse a description that had better be reserved for the far subtler performances of the metaphysical theologians of the Middle Ages. Perhaps the description is, after all, incorrect or not quite just. Nevertheless it seems to be a fact that the greater truth-seekers among the Greeks pre­ferred to seek truth with their heads rather than with their hands. Their faith in the power of words to reveal the truth seems to have been unshakable. They belonged to what may be called the verbal faction of truth-seekers. It does not appear to have occurred to them that there could be another faction worthy of serious opposition. Possibly there was none such in their day.

However, as we are interested in "truth" as it is today, no less than in what it was the day before yesterday, it must be mentioned that there is another way of approaching Pilate's question "What is truth?" This other way is closer to the science of the laboratory than the verbal approach ever got. The verbalists are preëminently talkers; their Opponents, the operationalists, are doers. Although the following description of the operational approach contains a few technical allusions by way of illustration, the spirit of the operational method can be easily grasped without haggling over these details. The quotation is from a recent article by P. W. Bridgman (Scripta Mathematica, volume 2, 1934, p. 1). The italics are mine.

"We begin by an examination of the simple application which Einstein made of the [operational] method in handling two physical concepts which his analysis showed occurred in connection with all phenomena covered by his special theory of relativity, the concepts, namely, of length and simultaneity. What Einstein did in effect was to demand that the meaning of these concepts, which purport to apply to concrete physical situa­tions should be sought in the concrete physical operations in­volved in the physical application. More definitely, the meaning of length is to be sought in those operations by which the length of concrete physical objects is determined, and the meaning of simultaneity is sought in those physical operations by which it is determined whether two physical events are simultaneous or not. Contrasted with this was the earlier procedure, in which the length of an object was defined as the difference of the co-ordinates [mathematical labels] in absolute space of its terminal points and the simultaneity of two events meant the equality of their absolute times. Both absolute space and absolute time were metaphysical concepts, purposely and selfconsciously divorced from physical reality, as may be seen in the explicit definitions of Newton. The mere formulation of the two methods is sufficient to establish the superiority of the new and to make under­standable its success in avoiding the erroneous conclusions of the old with regard to physical fact. For if any physical situation is described only in terms of concepts which themselves are de­fined in terms of physical processes actually per­formed, the whole description reduces ultimately to a description of an actual physical experience, and as such must have the validity of all direct observation of physical fact, which for our purposes is to he accepted as ultimate. It is especially to be noticed that our concepts, being thus framed in terms of operations actually performed in physical experience, must lead,at any stage of physical inquiry, to conclusions in which room is left for future refinements within the uncertainties and approximations of our present physical operations."

No Cambodian would ever subscribe to subversive doctrine like that. No loophole is left for the infinite with its endless chains of interminable processes beyond all possibility of actual performance. Bluebottle, I know, would have been a thorough-going operationalist had he lived. No ancient Greek could ever become an operationalist, even if he were to live forever. Operationalism is the antithesis of verbalism; the one is direct and modern; the other, evasive and antique.

We alluded in an earlier chapter to Einstein's radical ad­vance—an advance an ancient Greek might easily have made, had he "reasoned" operationally instead of verbally—and the above quotation brings out the fundamental change in Him stein's approach which made possible that advance. Modern physics (in the quantum theory) has repeated the process, again with astonishing success. Does not all this indicate that perhaps the verbal search after "truth" was foredoomed to sterility? Possibly it is in this very matter of a mistaken ap­proach that will be found the secret of a greater failure—the failure on the part of the great Greeks and their successors to realize that the so-called "laws of thought" of Aristotle are not the unique, necessary pattern of all consistent thinking. That discovery was well within their range; it does not depend upon elaborate technicalities slowly developed through centuries of trial and error, as do some of our concrete modern scientific achievements.

Without prejudicing the issue, I think it can be anticipated that we shall find Pilate's "What is truth?" to be devoid of meaning. However, everyone must form his own opinion. Whatever may be the upshot in regard to Pilate, there can be no doubt whatever that the theories of science (for example, that of the gigantic radioactive atom mentioned in a previous chapter) are generated solely by the verbal method of truth-seeking, whereas the concrete facts of science (in the sense in­dicated by Bridgman) are brought out by the operational method. Let us continue with the verbal, deductive method.

¹ "The truth will out when you're drunk."

² "The double-Dutch truth fairly oozes from you when you've got a skinful of bock beer."