I have left the text of the first edition of this book practically unaltered. But I promised in the Preface that I would outline in an epilogue the changes I would make today if I were writing an entirely new book on the same subject. Here is that outline.

As thinking is primarily an activity, an art, the new book would probably not be called Thinking as a Science, but, perhaps, The Art of Thinking Scientif1cally, or, simply, The Art of Thinking.

There would be one or two major changes from the present book, at least in emphasis. I am more and more impressed, as I grow older, with how little the individual could accomplish in any direction whatever if he had to depend entirely on his own unaided efforts. He could not survive his first few years of life without the help of his parents or guardians. He could not think at all (or only at the level of a chimpanzee) if he did not inherit from the society and civilization in which he was born the priceless gift of an already created language. Without this he would not only be unable to reason logically, he would have nothing worthy to be called a "concept." He could not frame a sentence; he could not even name things. We think in words, even in conversations. Our language, concepts, and logic are part of the social inheritance of all of us.

This has several important corollaries. One of them is that before the individual can even dream of "thinking for himself," or solving a simple problem, he must first acquire at least an elementary knowledge of what mankind has already learned, discovered, or invented before him. Even if he receives what is called a good modern education, it will take him till the age of eighteen or more to acquire even the rudiments of what he needs to know.

So my new book would emphasize far more than my previous one the need of extensive reading and study before the reader can profitably launch on "thinking for himself" or arriving at "independent conclusions." That, of course, should always be his goal; but the road to that goal is long, hard, and often roundabout.

How to Study

My new book would therefore have a chapter on "How to Study." One of the topics considered in it would be the possibility of increasing one's reading speed, and the methods of achieving this. But my new book would emphasize what some of the teachers of the new "speed reading" methods unfortunately do not -- the necessity that the student learn to "change gears," i.e., to learn to read different matter at different speeds depending on its nature, importance, and difficulty, as well as on the reader's purpose in reading it.

One of the chief problems of study, in fact, is how often the student should reread a textbook or a particular passage of it, or how often he should go over substantially the same material in other books. In studying a foreign language, for example, the reader may have to come across the same word or phrase again and again before he is able to translate it on sight, and he may have to see or hear it many more times before he can use it unprompted in a sentence framed by himself.

Knowledge of a foreign language, in short, is not really knowledge until it has been thoroughly assimilated, or worked in. This is no doubt widely recognized. But what is much less widely recognized is that this is not merely true of a language but of practically any other subject. A doctor is seldom a good doctor when he has just graduated from medical school, even though he may already have been over much verbal material with dreary repetition. Not until he has served as an intern, or been in private practice a couple of years, and so gone still more over the same ground and again and again encountered the same or similar problems, is he likely to achieve a quick and confident recognition and interpretation of symptoms.

A student of algebra may be taught how to extract the square root of a polynominal, and may be intelligent enough to follow the demonstration the first time, but it will probably not be until he has extracted many square roots of many polynominals that he will really feel confident he knows how. The student of languages, as well as the student of math, or a doctor, or a pianist, soon finds himself slipping backward if he ceases to study or practice. Our memories are not what they should be. A little of our knowledge is constantly oozing away. Knowledge and skill cannot be retained, let alone increased, except by constant addition, renewal, and refreshment.

I might also in this "How to Study" chapter give some hints to the reader on how to set up a study program to teach himself a particular subject, but in this epilogue I am postponing that to a later point. I may say here, however, that there are already some excellent books or pamphlets on how to study. The reader should find a wide range of choice in a college bookshop.

Language and Thought

My new book would have a chapter on "Language and Thought." I pointed out earlier that without language we would hardly be able to think at all. As the great nineteenth-century philologist Max Mueller put it: To think is to speak low. To speak is to think aloud.

The corollary of this is tremendously important. A man with a scant vocabulary will almost certainly be a weak thinker. The richer and more copious one's vocabulary and the greater one's awareness of fine distinctions and subtle nuances of meaning, the more fertile and precise is likely to be one's thinking. Knowledge of things and knowledge of the words for them grow together. If you do not know the words, you can hardly know the thing. We are told that the Tasmanian method of counting is: "One, two, plenty." This points to a very significant truth. Man could not even count, certainly not beyond the number of fingers on his hands, until he had invented names and symbols for numbers. For in speaking of the need for language for thought, we must, of course, include symbols as an integral part of language. It is amazing how recent in human history are even the Arabic numerals, the denary system, and the elementary signs for addition, subtraction, multiplication, and division -- not to speak of the myriad symbols now constantly used in algebra, geometry, trigonometry, differential and integral calculus, vector analysis, and other branches of higher mathematics. A single tiny symbol or formula -- like that for zero, or pi, or a function, or the square root of minus one, or dy/d.~, or Einstein's famous E = mc² (energy equals the quantity of matter multiplied by the square of the speed of light) -- can condense, sum up, fix, and hold forever a discovery that it may have taken mankind centuries to arrive at.

Words Sharpen Observation

A vocabulary increases and sharpens our observation, as sharp okservation in turn leads us to increase our vocabulary. The student of nature who is learning to recognize bushes and trees finds his observation increasingly sharpened as he is told how to identify respectively an oak, maple, elm, beech, pine, spruce, or hemlock. The name both fastens down the results of observation and tells him what distinguishing traits to look for. As a result of his knowledge, a countryman very seldom calls a specific tree simply a tree. The professional forester or nurseryman habitually makes even finer distinctions, such as that between red oaks, black oaks, and white oaks, or between Norway maples, Schwedler maples, and sugar maples.

Once again, when a student of nature has a leaf described to him, or wants to describe one, he finds himself immeasurably aided by a specialized vocabulary of description for certain characteristics of edge or form -- dentate, crenate, serrate, ovate, obovate, lanceolate, oblanceolate, sagittate, orbicular, and so on. The more names that are mastered, the more is observation sharpened.

This intimate interdependence of language and thought exists in all fields of knowledge, from the simple and concrete to the most abstruse and abstract.

The highest thrill of the amateur bird watcher comes when he identifies a new species for the first time. He usually does this by comparing the new bird he has just seen with the pictures or descriptions in a bird book. But to be able to do this he has to observe very sharply everything he can -- its size, shape, color, and markings, down to the minutest details, like the color and shape of its bill, its peculiarities of flight and song, and so forth.

When the bird student knows the name of the new species or its verbal description in a book he knows what to look for. His observation becomes keener not only for that time, but for the next time. By this process he finds his observation becoming ever more acute as his knowledge becomes fuller. The professional ornithologist, by a refinement of the same method, knows when he has discovered a species hitherto unrecognized by anyone. Whereupon he preserves his discovery, and makes it accessible to all, by giving the new species a name, accompanied by a full and precise pictorial and verbal description.

Identifying the Parts

Let us turn to still another field. The first thing the student of medicine is asked to do is to study anatomy. This means, at the beginning, to learn to recognize and name the hundreds of parts of the human body, from the anulus inguinalis profundus to the vesicula seminalis. It requires the dreary memorization of hundreds of names even to master what is called gross anatomy. When the student comes to some special part, like the nervous system (not to mention microscopic anatomy), he must learn hundreds of more names. And he must learn this special vocabulary if for no other reason than to know what his professors are talking about. Later on, as, say, a medical researcher, he must know this vocabulary not only to explain his findings in a medical journal, but to make them in the first place.

One of the things that used to puzzle me as a youth was why even the greatest painters and sculptors, like Leonardo da Vinci and Michelangelo, thought it necessary to study artistic anatomy. Their eyes were sharp enough: couldn't they have painted just what they saw? The answer, as I have now come to realize, is that by learning the names, position, and description of the muscles, tendons, and veins in the normal human body they knew what to look for and where to look for it, and their naturally acute vision was sharpened still more.

What is true for the supreme genius is true for those of us who are less gifted. In a charming introduction to his book on birds, John Kiernan tells the reader that he had never seen a white-breasted nuthatch until he saw, on a bird card, a picture of one going down a fence post headfirst. The next day he saw five different nuthatches at different places. They had always been around, but he had never before looked for them. He had been blind!

The reader has perhaps had the experience of looking at some object through binoculars or a magnifying glass and seeing details that he could not previously see with his naked eye; but on removing the glass he could still see them, because now he knew they were there. The Arabian Nights story, telling how Ali Baba could not open the door to the robbers' den until he had learned to say "open sesame," contains a profound moral. To be admitted to the realms of knowledge we must learn the right passwords.

Symbols of Communication

I remarked earlier that when I speak of "language" I do not have in mind merely words and sentences, but symbols, signs, and signals of all kinds used in human intercommunication. There are special symbols in every science; but I have particularly in mind numbers, notation, and other symbols of mathematics by which the results of mathematicians are made known to each other and without which, in fact, the mathematicians themselves could not even think mathematically. One authority, Tobias Dantzig, has written a book called Number: The Language of Science.

There are still further corollaries to be drawn from the inextricable interdependence of thought and language. He who seeks to be a clear and precise thinker must also seek to be a clear and precise writer. Good writing is the twin of good thinking. He who would learn to think should learn to write.

One of the most important steps, to repeat, is to enlarge one's vocabulary. The way most often consciously adopted for doing this is to study long lists of assorted words, usually polysyllabic. This may be better than nothing, but it is not the method to be preferred. It is generally more advisable to go from things and concepts to the names for them than to go from miscellaneous names to things and concepts. Vocabularies tend to grow with knowledge in general, and particularly with increasing knowledge of special subjects. Each science, discipline, art, sport, or branch of knowledge has its own special vocabulary, which is acquired with study or experience of that branch of knowledge or activity.

An abundant vocabulary is usually a by-product of wide knowledge. One good rule, both in thinking and writing, is never to use a word if you have only a vague and uncertain knowledge of its meaning. Look it up first in the dictionary to find its exact denotations and connotations -- not to speak of its correct pronunciation!

Writing Improves Thinking

The reader who seeks to write well and think well should aim first at the essential qualities -- coherence, clarity, precision, simplicity, and brevity. Euphony and rhythm are of course also desirable, but they are like the final rubbing on a fine piece of furniture -- finishing touches justified only if the piece has been soundly made.

As a method of procedure, the apprentice writer may often find it advisable first of all to root out his faults. He should try to acquire the Five Virtues of Coherence, Clarity, Precision, Simplicity, and Brevity by vigilant abstention from the Five Vices of Incoherence, Obscurity, Vagueness, Pedantry, and Circumlocution.

For those who ask why writing is important to the thinker, one reply would be that it may be of crucial importance when the thinker wishes to present the results of his thinking to his professional colleagues or directly to the public. Newton and Leibnitz each invented the calculus independently, and Newton's discovery was earlier. But it was the calculus as presented by Leibnitz that other mathematicians began to use, mainly because Leibnitz devised a better notation.

The Abbé J. G. Mendel's biological experiments and theories on heredity, propounded in 1866, were of epoch-making importance, comparable to Darwin's theory of evolution published in The Oriqin of Species in 1859. Darwin's book brought him instant world fame, but neither Mendel nor his contribution received any recognition until 1900, thirty-four years after he had published his results and sixteen years after his death. Recognition came only when other botanists independently obtained results similar to Mendel's and in searching the literature found that both the experimental data and the general theory had been published by him a third of a century before. Mendel's original paper had reached the principal libraries in Europe and America. But it was so sparely and obscurely written that even eminent botanists at the time failed to grasp its implications.

A book on the art of thinking is not the place to dwell in detail on the art of writing. The most illuminating discussion of its length written on the subject is still Herbert Spencer's essay on The Philosophy of Style published in 1871. (Unfortunately, its own style is somewhat stilted and pompous.) A helpful little manual is The Elements of Style by William Strunk, Jr., first published in 1918 and then republished with a delightful introduction and added chapter by Strunk's former student, E. B. White, in 1959.

Every professional writer ought to have, in addition to at least one good dictionary, four style books in his study: The King's English, by H. W. Fowler and F. G. Fowler, A Dictionary of Modern English Usage, by H. W. Fowler, Usage and Abusage, by Eric Partridge, and Modern American Usage, by Wilson Follett.

A Notebook or Journal

And every serious thinker, especially if he hopes to be a professional writer, should keep a notebook or a journal. I pointed out, in the first edition of this book, that good ideas are often elusive and must be captured in flight -- in other words, that it is excellent practice always to have a pencil and pad handy, so as to jot down a good thought the moment after it lights up your mind. The complacent assumption that once a bright idea or happy phrase occurs to you it is a permanent acquisition, to be called upon only when needed, too often proves false. Even Nietzsche, one of the great seminal minds of the nineteenth century, found that: "A thought comes when it wishes, not when I wish."

When we write out our ideas, we are at the same time testing, developing, arranging, crystallizing, and completing them. We imagine ourselves not only making these ideas clear to others, but making them seem as important to others as they do to ourselves. So we try to make what was vague in our minds precise and definite; what was implicit, explicit; what was disconnected, unified; what was fragmentary, whole. We frame a generalization, then try to make it as plausible as we can; we try to think of concrete illustrations of it. And as we do this, we also expose it to ourselves -- and sometimes, alas, find that it is empty, untenable, or sheer nonsense.

A lot of ideas that cannot be tested by formal experiments can be at least partly tested by writing them out. A great teacher of my acquaintance, when a student bothered him once too often by persisting in some silly proposal of his own on a subject, would suggest that the student write a paper on his idea and bring it in at the next seminar. The student seldom did so; perhaps because he was mentally lazy, but more likely because, when he attempted to write it out and to prove its validity, he found it to be hopelessly vague or a self-contradiction.

Writing Aids Concentration

One incidental advantage of the habit of writing out one's ideas is that it promotes concentration as almost no other practice does. As one who has written daily newspaper editorials or weekly magazine columns for many years, I can testify that nothing forces one to pull one's thoughts together more than deciding on a topic, sitting before the typewriter, feeding in a clean sheet of paper, and then trying to frame one's exact theme, title, and opening paragraph.

Francis Bacon summed it up with unsurpassable conciseness:  "Reading maketh a full man, conference a ready man, and writing an exact man."

If the reader wants to know what the best and most stimulating notebooks and journals are like, I suggest, for a starting assortment:  The Meditations of Marcus Aurelius, Pascal's Pensées, The Heart of Emerson's Journals, Samuel Butler's Note-books, and Charles Horton Cooley's Lift and the Student. All of these, of course, can be sampled rather than read through; they are admirable bedside books.

How to Solve a Problem

In the first edition, I remarked that all thinking is problem-solving. My new book would contain a special chapter on "How to Solve a Problem."

It would begin, perhaps, by raising the problem: how to recognize a problem when you see it. The better informed, more intelligent, and more intellectually curious you are, the more problems you will become aware of. In his Voyage of the Beagle, Darwin describes how the savages, at one harbor in which the Beagle anchored, immensely admired the small boats in which his party landed, but paid no attention whatever to the big ship. They took it for granted, like a fact of nature. It was too far out of their experience.

Feebleminded barbarians, no doubt. But most of us civilized laymen daily switch on the lights, or turn on our television set, without the slightest curiosity regarding the cause of the miraculous result.

A question akin to this, which my chapter would raise, is "What is the problem?" Our modern social reformers are constantly preoccupied, for example, with the problem of poverty. But poverty is the original condition of man, from which he has sought to escape by the sweat of his brow, by work, production, and saving. It was when Adam Smith asked himself not what causes the poverty but what causes the wealth of nations that real progress on the problem began to be made. For centuries, in the same way, doctors took health for granted and assumed that the only problem is what causes disease. It was not until surgeons tried to transplant kidneys, hearts, and other organs that they became acutely troubled by the problem of what causes immunity. There is always the possibility of learning more by asking ourselves the opposite question. There are hundreds of books on How to Play Chess. Znosko Borowsky created a mild sensation by writing one called How Not to Play Chess.

Rules for Discovery

I suspect that my chapter on problem-solving would be heavily obligated to a little book by George Polya, first published in 1945, called How to Solve It.

Polya's book is devoted primarily to the problem of solving problems in mathematics; but it is applicable over the whole field of invention, discovery, and independent thinking.

"A great discovery," the author tells us in the preface, "solves a great problem but there is a grain of discovery in the solution of any problem." Your problem may be modest, but if it challenges your curiosity and brings into play your inventive faculties, and if you solve it by your own means, you may experience the tension and enjoy the triumph of discovery. Such experiences at a susceptible age may create a taste for mental work and leave their imprint on mind and character for a lifetime.

Polya has all sorts of instructive things to say about what questions to ask -- What is the unknown? -- about the uses of analogy, about "decomposing" and "recomposing" problems, about Descartes' rules for invention, about the indispensability of good symbols and good notation for mathematical thinking. He tells how, overnight or after a longer interval, our subconscious mind will often solve problems for us, but warns that "conscious effort and tension seem to be necessary to set the subconscious work going -- otherwise everything would be too easy."

Polya calls his whole book an effort to teach Heuristic: "The aim of heuristic is to study the methods and rules of discovery and invention...." The most famous attempts to build up a system of heuristic are due to Descartes and to Leibnitz, both great mathematicians and philosophers.

Polya's own illustrations and application are confined entirely to mathematics, for which his own enthusiasm is contagious. The reader, he says, should at least try to find out whether he has a taste for mathematics, and he may find out that "a mathematics problem may be as much fun as a crossword puzzle, or that vigorous mental work may be an exercise as desirable as a fast game of tennis. Having tasted the pleasure in mathematics he will not forget it easily and then there is a good chance that mathematics will become something for him: a hobby, or a tool of his profession, or his profession, or a great ambition."

Specialization, Perseverance, Analogy

My new book would contain a chapter on The Dilemma of Specialization. The dilemma is this. In the modern world knowledge has been growing so fast and so enormously, in almost every field, that the probabilities are immensely against anybody, no matter how innately clever, being able to make a contribution in any one field unless he devotes all his time to it for years. If he tries to be the Rounded Universal Man, like Leonardo da Vinci, or to take all knowledge for his province, like Francis Bacon, he is most likely to become a mere dilettante and dabbler. But if he becomes too specialized, he is apt to become narrow and lopsided, ignorant on every subject but his own, and perhaps dull and sterile even on that because he lacks perspective and vision and has missed the cross-fertilization of ideas that can come from knowing something of other subjects.

I do not know the way out of this dilemma, or the exact compromise, but I hope to find it by the time I write my new book.

My new book, like the present one, will have a chapter on concentration, but it is more likely to be called "Concentration and Perseverance," -- for it will put far more emphasis on patience, plodding, perspiration, pertinacity, determination, effort, work -- on again and again returning to an obstinate problem until it is solved. Scientists talk much nowadays of "serendipity" -- the faculty of making desirable discoveries by accident. An example often cited is how Sir Alexander Fleming discovered penicillin because one of his laboratory technicians had carelessly left the top off a dish in which a virulent infectious organism, staphylococcus, was growing; a number of fungi had floated into the open dish, overgrown the bacteria -- and killed it. The accident led Fleming to his discovery. But these "accidents" only seem to bear fruit when they happen to alert indefatigable scientists who have already been working for years on a project. As Pasteur put it: "Chance favors the prepared mind."

In my new book I would treat Analogy less cavalierly than I did earlier in this one, and perhaps have a separate chapter with that title. I did mention analogy in my first edition as a constructive method of making discoveries, but then went on to talk almost exclusively about its dangers and pitfalls. A. Wolf, in his Textbook of Logic (1938), emphasizes its achievements:

"One need only think of the most important discoveries in the history of science, in order to realize the enormous value of analogy. Our conception of the solar system (the helio-centric theory) owes a great deal to the analogy of the miniature system of Jupiter and the Medicean satellites. Some of the most important discoveries in modern mathematics are due to the analogy, discovered by Descartes, between algebra and geometry. The wave-theory of sound was suggested by the observation of water-waves; and the undulatory theory of light was suggested by the analogous air-waves which transmit sound. The theory of natural selection by the struggle for existence was suggested to Darwin by his knowledge of the artificial selection by which breeders have produced the many varieties of domestic animals. And so forth."

Like the first edition of the present volume, my new book would contain chapters on "Subjects Worth Thinking About" and on "Books on Thinking."

Subjects Worth Thinking About

But the former chapter, instead of containing a list of important but very miscellaneous problems, would call the reader's attention to some of the innumerable sciences or disciplines in which he could enjoyably and profitably interest himself -- agriculture, astronomy, atomic physics, biology, building, chemistry, crystallography, electricty, engineering, fossils, gardening, geography, geology, mathematics, medicine, metallurgy, meteorology, minerology, pathology, physics, physiology, and zoology. These are all physical sciences. I name so many here because my first edition rather neglected them in its emphasis on social questions. But, of course, in my new book the reader would still be invited to consider the attractions of the social disciplines -- political science, jurisprudence, economics, ethics, psychology, anthropology, or archeology.

In choosing subjects to think about or problems to solve, I must confess a personal preference for those that are useful. I admire disinterested curiosity and the achievements of "pure science" and "pure research" as much as anyone; but I cannot share the snobbery of those who seem able to express their esteem of pure science only by disparaging its practical applications. Both are admirable; and they are mutually dependent. The partisans of pure science chronically talk as if there were only a one-way dependency, and as if inventors were men of a lower order than pure scientists. They never tire of reminding us how the inventions of Marconi in wireless telegraphy and de Forest in radio were dependent on the previous theoretical discoveries of Clerk Maxwell and Hertz. All very true. But how far would pure research have been able to go in a hundred fields if it had not been for the invention, say, of the microscope? Or, for that matter, of the printing press?

As Karl R. Popper has pointed out, in his Poverty of Historicism (1957), one need not espouse a narrow pragmatism in order to appreciate Kant's saying: "To yield to every whim of curiosity, and to allow our passion for inquiry to be restrained by nothing but the limits of our ability, this shows an eagerness of mind not unbecoming to scholarship. But it is wisdom that has the merit of selecting, from among the innumerable problems which present themselves, those whose solution is important to mankind."

The Study of Economics

The reader of my new book would receive some guidance in how to take up a subject new to him, and there would be some specific illustrations. Suppose, for example, that he wanted to take up economics in a systematic way. He would be advised to begin with some short elementary text. An excellent one for the beginner today would be, say, Essentials of Economics, a book of only one hundred pages by Faustino Ballvé (Irvington-on-Hudson, N. Y.: Foundation for Economic Education). A collection of essays, Planning for Freedom, by Ludwig von Mises, is less systematic but enormously stimulating. (I would be less than mercenary if I failed to mention here also my own Economics in One Lesson.) The next step would be to read a book of intermediate length. One of the best is A Humane Economy by the late Wilhelm Roepke (Regnery).

The student would now be ready to tackle one of the most comprehensive and advanced books on the subject, of which I will mention only three. Human Action: A Treatise on Economics by Ludwig von Mises (Regnery, 907 pages) extends the logical unity and precision of economics beyond any other work. Some readers seem to find this excessively difficult. For these I can strongly recommend Man, Economy, and State, by Murray N. Rothbard (D. Van Nostrand, two volumes, 987 pages) which is equally comprehensive, and along Miscsian lines, but in which the reader may find the arrangement and exposition easier to follow. Finally, I would include in this triad an older book, Philip Wicksteed's The Common Sense of Political Economy (1910, new edition 1933, two volumes, 871 pages), as remarkable for the ease and lucidity of its style as for the penetration and power of its reasoning.

When the reader has finished even one of the books in this advanced triad, perhaps after a couple of introductory volumes, he will be prepared to choose his own further reading in economics, and may browse among the great writers and thinkers who created the science -- Hume, Adam Smith, Ricardo, Mill, Jevons, Menger, Böhm-Bawerk, Wicksell, Marshall, John Bates Clark -- an enviable feast. Adam Smith's Wealth of Nations, though published in 1776, can still be ardently recommended no less for its literary seductiveness than for the brilliant light it still can throw even on the economic life of today.

General Rules for Exploring Any New or Strange Subject

Of course, my book could only include such specific recommendations on one or two subjects. For others there would have to be general rules. One would be to ask an expert in the subject. Another would be to consult the article on the subject in an encyclopedia and to see whether that included, as it ought to, a good list of references. A third rule would be to consult such a book as Good Reading, a paperback pulished by The New American Library. This is a volume sponsored by the College English Association and prepared by the Committee on College Reading. I happen to have the 19th printing which came out in 1964, but revisions have been appearing every year or two. The volume lists selected books on every conceivable subject -- history, fiction, poetry, drama, biography, essays, philosophy, religion, and all the leading arts and sciences. There is also an instructive list of "100 Significant Books."

One last general piece of advice. No practice excels that of browsing along a library shelf containing books on the subject that has awakened your interest, and sampling them.

If I may be permitted a personal note, it seems to me, looking back, that the hours of purest happiness in my own youth were spent in just this way. I would avidly sample one book after another, and when the bell rang, and the library closed for the night, and I was forced to leave, I would leave in a state of mental intoxication, with my new-found knowledge and ideas whirling in my head. I would speculate eagerly on what solutions the authors I had read had come to in the passages I hadn't had time to finish. I think now that these unpremeditated efforts to anticipate an author's conclusions stimulated my thinking far more than any continuous uninterrupted reading would have done. In fact, when I came back to one of these same books the next evening, I most often felt let down. The night before, the author had seemed on the verge of some marvelous breakthrough, opening new vistas to the soul, and now he seemed to fizzle out in a truism.

Books on Thinking

The final chapter in my new book, like the final chapter in the first edition of this one, would be about "Books on Thinking."

My new references would supplement, rather than displace, those in my first edition. For example, I cited there only two "classics" on the art of thinking -- John Locke's Conduct of the Understanding, and Arthur Schopenhauer's Thinking for Oneself. I should also have included the three classics mentioned in my present preface: Bacon's Novum Organum, Descartes' Rules for the Direction of the Mind, and Spinoza's Improvement of the Understanding. My new bibliography would of course also include a handful of good books written specifically on the art of thinking since the original edition of Thinking as a Science appeared. One of these would surely be The Art of Thought, by Graham Wallace (1926). Another would be Thinking to Some Purpose, by the late British logician L. Susan Stebbing. Her chief emphasis is on how to detect illogicalities in other people's thinking and how to avoid them in our own.

In addition, my new bibliography would refer the reader to passages, paragraphs, and even single sentences, widely scattered through the works of many authors, that throw light on the art of thinking. Some of these can be found in the biographies or autobiographies of great thinkers. My first edition cited material of this nature from the autobiographies of John Stuart Mill and Herbert Spencer. But there are illuminating passages in many writers less well known.

I quote here a few lines, for example, from Charles Horton Cooley's admirable notebook, Life and the Student (1927):

Let our struggle be with facts, with life, rather than with other writers. We cannot have the spirit of truth and the spirit of controversy at the same time. A writer whose aim is to be unlike others is liable to a subservience of contradiction. That is, he after all gets his cue from them, takes the other end of the same rope. Originality raises new questions.

Though it starts apparently in contradiction, the advice of Morris R. Cohen in the preface to his Reason and Nature (1931) reinforces that of Cooley:

The philosopher whose primary interest is to attain as much truth as possible must put aside as a snare the effort at originality. Indeed, it seems to me that the modern penchant for novelty in philosophy is symptomatic of restlessness or low intellectual vitality. ... The principle of polarity calls attention to the fact that the traditional dilemmas, on which people have for a long time taken opposite stands, generally rest on difficulties rather than real contradictions, and that positive gains in philosophy can be made not by simply trying to prove that one side or the other is the truth, but by trying to get at the difficulty and determining in what respect and to what extent each side is justified. This may deprive our results of sweep and popular glamour, but will achieve the more permanent satisfaction of truth.

Lessons in Logic

The art of thinking, like engineering or medicine, is based on several distinct sciences. One of these is psychology. I referred in the first edition of this book to John Dewey's How We Think which is still useful. But great experimental as well as theoretical progress has been made since Dewey's book was published. The reader could bring himself abreast of this by consulting the article on Thinking and Problem Solving, Psychology of in the 1965 edition of the Encyclopedia Britannica. The article itself includes an extensive list of books for further reading.

Logic, the study of the general conditions of valid inference, is of course the chief established science on which the art of thinking must be based. My recommendation for initial reading in my first edition was Stanley Jevons' Elementary Lessons in Logic. Because Jevons was an excellent writer as well as a first-rate thinker, this can still be read with pleasure and profit. But today I would prefer to recommend as an introductory volume A. Wolf's Textbook of Logic (first edition 1930, but often republished). More advanced, but still not too difficult, is L. Susan Stebbing's Modern Introduction to Logic (1940). Still more advanced, longer, and more difficult is An Introduction to Logic and Scientific Method, by Morris R. Cohen and Ernest Nagel (1934).

Scientific method is closely connected with logic. In fact, it is usual for modern books on logic (and this is true of the three just mentioned -- the last explicitly in its title) to treat traditional logic in the first half of the book as "formal" or "deductive" logic, and then to devote the second half to "inductive logic" and to "scientific method" in general. This second subject includes discussions of such subjects as circumstantial evidence, the evolutionary and comparative methods, the simpler inductive methods (Mill's "five canons), the statistical method, the deductive-inductive method, probability, laws of nature, scientific explanation, and so on. Long established as a standard work in this field is F. W. Westaway's Scientific Method (1919), but the literature is now very extensive.

A brilliant and penetrating book, for those who have the intellectual background, capacity, and ambition to read it, is The Logic of Scientific Discovery by Karl R. Popper (1961 edition).

Digression on Mathematics

It was one of the shortcomings of my first edition that it did not contain any explicit discussion of the enormously important field of mathematics. Yet at least an elementary knowledge of mathematics is essential for solving most of our daily practical problems as well as for most scientific thinking. We need arithmetic to buy and sell, to count our change, to read the time or the temperature, or to perform a hundred other daily operations. Mathematics has been called the "queen" and even the "mother of sciences," because every science has its mathematical aspect. The accelerative development of mathematics in the last century has been both cause and consequence of the tremendous progress in the same period in the whole realm of the sciences, physical and social.

And -- what was strangely not recognized until the last century -- there is an inextricable connection between logic and mathematics. Mathematics may be called the quantification of logic. Mathematical logicians consider it a branch of logic. A formidable literature has grown up in the last few decades on "mathematical logic," "the algebra of logic," and "symbolic logic."

I do not mean to discourage or frighten the nonmathematical reader at this point by any implication that unless he masters higher mathematics and symbolic logic he cannot hope to contribute anything to science, philosophy, or the higher realms of thought. Great contributions to science and other knowledge will be made in the future, as they have been made in the past, by persons innocent of mathematics beyond simple arithmetic. But I do want to suggest that, other things being equal, the more you know of mathematics the more you will be likely to accomplish in science or original thought.

And mathematics can be fun. Few things can give greater enjoyment than mathematical problems, in fact, to those who relish mental exercise for its own sake.

The reader may be, like myself, one who grew up with a deep aversion to mathematics. This was chiefly, I am now convinced, because of the way it was then taught. Algebra was thrown at most of us who are now over 40 simply as something that had to be learned if we didn't want to flunk. I never remember any teacher telling me anything about the engrossing history of algebra, or even explaining why algebra was necessary in solving any problem except the artificial ones that were specially invented for the textbooks. The course in algebra seemed to me mainly a malicious contrivance to cut down the time I could give to handball.

But now, I can assure any reader who doesn't know, all is changed. There are now so many fascinating introductions to mathematics (at least for adults) that it seems almost invidious to name only a handful. For a short introduction covering the whole field, I would especially recommend David Bergamini's Mathematics (1963) in the admirable Life Science Library series. Mathematician's Delight by W. W. Sawyer (1943) is a charming introduction available in paperback. Two single volumes that teach the actual operations of the conventional part of the field are Mathematics for the Practical Man by George Howe (1957), and Lancelot Hogben's best-selling Mathematics for the Million(1937) -- if you don't mind its belligerent Marxism. There is an excellent five-volume set on Mathematics for Self-Study (1931, 1962) by I. E. Thompson, covering in separate volumes arithmetic, algebra, geometry, trigonometry, and calculus. Finally there are the magnificent four volumes of The World ofMathematics edited by James R. Newman (1956).

Science, Philosophy, and Logic

I am still talking, the reader will remember, about studies that are directly likely to help him in the art of thinking -- though the discussion inevitably splashes over into the domain of the chapter on "Subjects Worth Thinking About."

To continue with aids to the art of thinking: The reader will get both knowledge and stimulation from reading histories of science, lives of great scientists and inventors and discussions of their methods, histories of engineering, and histories of inventions and discoveries. Again I can mention only a few books. Two more from the handsomely illustrated Life Science Library series: The Engineer, by C. C. Furnas, Joe McCarthy and others (1966), and The Scientist, by Henry Margenau, David Bergamini, and the editors of Life (1964). The latter book will introduce the reader to a wide variety of sciences. In the realm of technology the reader may consult anything from the five- volume History of Technology (1954-58), edited by C. Singer to the Popular History of American Invention (1924), edited by W. Kaempffert.

Of course I should include philosophy also among the subjects whose study would contribute directly to the stimulation and improvement of one's thinking. But my list of recommendations has already grown so long that I shall here mention only two. The first is Bertrand Russell's brilliant History of Western Philosophy (1945). The second is An Introduction to Philosophical Analysis (second edition, 1967), by John Hospers. This text will bring the reader abreast of the kind of problems that professional philosophers now discuss.

At this point some reader may ask, earnestly or skeptically: But if I do some or all of this reading, will it really make me a better thinker than if I devote my leisure wholly to detective stories or golf? To this I can confidently reply: Yes. But to the further question: How much will it help me?, I can not reply with any confidence at all. The answer depends on the native intelligence of the individual reader, the nature of his gifts and interests, and a score of other factors.

Improving the Prospects

Is it really necessary to study formal logic, for example? Tristram Shandy, Lawrence Sterne's hero, commenting on the gap between his father's argumentative powers and his ignorance of formal logic, says:  "It was a matter of just wonder with my worthy tutor, and two or three fellows of that learned society, that a man who knew not so much as the names of his tools, should be able to work after that fashion with them." In 1685, in the great hall of Dublin University, the young Jonathan Swift, having failed once before to take his bachelor's degree on account of his ignorance of logic, came up again without having condescended to read logic. He was asked how he could reason well without rules, and replied that he did reason pretty well without them. Reluctantly, though as the outcome proves, justifiably, his examiners gave him the degree. On the reverse side of the coin we may cite examples of even great professional logicians, like John Stuart Mill, sometimes falling into logical howlers.

The only reply I can think of to these examples is that though ignorance of logic may not prevent correct reasoning, or knowledge of it guarantee correct thinking, that knowledge nonetheless helps. The probability is that in the long run a man who has studied formal logic will reason better, and make fewer errors, than if he had not.  Remembering the technical names and descriptions of the more common fallacies, for example, will help him to detect such fallacies in the reasoning of others and avoid them in his own.

I have much less doubt about the usefulness of mathematics. True, even a prolonged study of higher mathematics will not make a man into an original or even effective thinker if he lacks the innate qualities. But a study of mathematics is of great importance in training a man to think mathematically about a problem or a subject.

On the negative side the importance of mathematical study is overwhelming. Without a knowledge of at least elementary arithmetic none of us would be competent to manage his daily affairs. Without a knowledge of double entry bookkeeping and cost accounting, a business firm would never know just how much money it was making or losing. And without a knowledge of higher mathematics, few modern physical scientists could hope to make contributions to their subjects, or even understand what had already been discovered. Morris R. Cohen tells us that in dealing with experimental physics, the lack of advanced mathematical knowledge discomforted the acute and powerful mind of Hobbes.

Even if the case for the usefulness of mathematics were not so overwhelming, its study could still be infinitely rewarding. In a famous 15-page essay, The Study of Mathematics, included in his Mysticism and Logic (1918), Bertrand Russell writes:

Mathematics, rightly viewed, possesses not only truth, but supreme beauty ... sublimely pure, and capable of a stern perfection such as only the greatest art can show....

For the health of the moral life, for ennobling the tone of an age or a nation, the austerer virtues have a strange power, exceeding the power of those not informed and purified by thought. Of these austerer virtues the love of truth is the chief, and in mathematics, more than elsewhere, the love of truth may find encouragement for waning faith. Every great study is not only an end in itself, but also a means of creating and sustaining a lofty habit of mind; and this purpose should be kept always in view throughout the teaching and learning of mathematics.

But I ought not to try to proselytize for any one subject, among the hundreds, indeed (as encyclopedias and great libraries remind us) the thousands, that compete for the interest of the inquiring mind. Some of the world's most brilliant intellects have had no gift for mathematics. Most of us, moreover, have neither the surplus time nor energy to divert from the interests that already preoccupy our attention. And most of us, also, will feel less frustrated if we devote ourselves to less abstract and abstruse subjects which are nonetheless rewarding and absorbing. Not everyone can be a Newton or a Darwin, but everyone, by a little effort and persistence, can improve his intellectual attainments and satisfactions -- and his enjoyment of life.

I would like to end this epilogue where I began, and to repeat that if I were writing a new book on the art of thinking I would emphasize, as I failed to do in my first edition, that no man can hope to do original work or even profitable thinking in any science or branch of knowledge until he has gone to the trouble to learn what has already been discovered in that branch of knowledge. He must know the previous state of the question. Then he will see whether he can make any contribution of his own. When the great Isaac Newton was asked how he had been able to make such tremendous contributions to human knowledge and thought, and to see so much farther than other men, he answered modestly: "I stood on the shoulders of giants." In other words, he was able to build on what his predecessors had discovered.

We who live today are in one respect in a more enviable position than any other generation in history. We stand on the shoulders of giants, like Newton and his successors, who stood on the shoulders of other giants before them. A thousand professional mathematicians today, though they have nothing approaching his genius, know more mathematics than Newton, who invented the calculus. And they know it because Newton, Leibnitz, the Bernoullis, Euler, Lagrange, Gauss, Riemann, Hamilton, and a hundred lesser figures have taught them. So an intelligent college student today is in a position to learn more about calculus than Newton, more about economics than Adam Smith, more about evolution than Darwin.

The present generation has been privileged beyond all others in acquiring this great intellectual heritage. It is a cardinal sin for any individual to neglect to acquire at least some small part of it for himself.  It is more than a sin; it is a folly. It is a failure to take advantage of one of the greatest sources of human enjoyment.

For we may say of thought in general what Tarrasch said of chess:  Thinking, like Love, like Music, has the power to make men happy.

The way to this happiness is what I have tried to show in this book.

Notes

*  When he was 21, Henry Hazlitt's first book had been published under the title Thinking as a Science. It was written, he explains, because "I primarily wanted to teach myself how to think more efficiently, independently, and, if possible, originally. I had already sensed that he who teaches, learns." When the book was republished 53 years later, in 1969, by Nash Publishing Corporation, Los Angeles, California, instead of extensively revising the original text, the author prepared an Epilogue, which was published in the August 1970 issue of The Freeman, and is reproduced here.

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