Philosophy

"It seems that scientists are often attracted to beautiful theories in the way that insects are attracted to flowers — not by logical deduction, but by something like a sense of smell."

"I may as well say at once that I do not distinguish between inference and deduction. What is called induction appears to me to be either disguised deduction or a mere method of making plausible guesses."

"Pure mathematics consists entirely of assertions to the effect that, if such and such a proposition is true of anything, then such and such another proposition is true of that thing. It is essential not to discuss whether the first proposition is really true, and not to mention what the anything is, of which it is supposed to be true. Both these points would belong to applied mathematics. We start, in pure mathematics, from certain rules of inference, by which we can infer that if one proposition is true, then so is some other proposition. These rules of inference constitute the major part of the principles of formal logic. We then take any hypothesis that seems amusing, and deduce its consequences. If our hypothesis is about anything, and not about some one or more particular things, then our deductions constitute mathematics. Thus mathematics may be defined as the subject in which we never know what we are talking about, nor whether what we are saying is true. People who have been puzzled by the beginnings of mathematics will, I hope, find comfort in this definition, and will probably agree that it is accurate."

"The influence of geometry upon philosophy and scientific method has been profound. Geometry, as established by the Greeks, starts with axioms which are (or are deemed to be) self-evident, and proceeds, by deductive reasoning, to arrive at theorems which are very far from self-evident. The axioms and theorems are held to be true of actual space, which is something given in experience. It thus appeared to be possible to discover things about the actual world by first noticing what is self-evident and then using deduction. This view influenced Plato and Kant, and most of the intermediate philosophers. ...The eighteenth century doctrine of natural rights is a search for Euclidean axioms in politics. The form of Newton's Principia, in spite of its admittedly empirical material, is entirely dominated by Euclid. Theology, in its exact scholastic forms, takes its style from the same source."

"The Greeks... discovered mathematics and the art of deductive reasoning. Geometry, in particular, is a Greek invention, without which modern science would have been impossible."

"Robert [Grosseteste] became much interested in science and scientific method … He was conscious of the dual approach by means of induction and deduction (resolution and composition); i.e., from the empirical knowledge one proceeds to probable general principles, and from these as premises one them derives conclusions which constitute verifications or falsifications of the principles. This approach to science was not that far removed from Aristotle ..."

"I cannot see why it is necessary that every deduction from algebra should be bound to certain conventions incident to an earlier stage of mathematical learning, even supposing them to have been consistently used up to the point in question. I should not care if any one thought this treatise unalgebraical, but should only ask whether the premises were admissible and the conclusions logical."

"Experience has convinced me that the proper way of teaching is to bring together that which is simple from all quarters, and, if I may use such a phrase, to draw upon the surface of the subject a proper mean between the line of closest connexion and the line of easiest deduction. This was the method followed by Euclid, who, fortunately for us, never dreamed of a geometry of triangles, as distinguished from a geometry of circles, or a separate application of the arithmetics of addition and subtraction; but made one help out the other as he best could."

"With the completion of Euclid's Elements... For the first time in history masses of isolated discoveries were unified and correlated by a single guided principle, that of rigid deduction from explicitly stated assumptions. ...Not until 1839, in the work of ...D. Hilbert, was the full impact of Euclid's methodology felt in all mathematics. Concurrently with the pragmatic demonstration of the postulational method in arithmetic, geometry, algebra, topology, the theory of point sets, and analysis which distinguished the first four decades of the twentieth century, the method became almost popular in theoretical physics in the 1930's through the work of P. A. M. Dirac. Earlier scientific essays in the method, notably by E. Mach in mechanics and A. Einstein in relativity, had shown that the postulational approach is not only clarifying but creative. Mathematicians and scientists of the conservative persuasion may feel that a science constrained by an explicitly formulated set of assumptions has lost some of its freedom... Experience shows that the only loss is denial of the privilege of making avoidable mistakes in reasoning. ...Objection to the method is neither more nor less than objection to mathematics. ...If the Pythagorean dream of a mathematized science is to be realized, all of the sciences must eventually submit to the discipline that geometry accepted from Euclid."

""I exist" does not follow from "there is a thought now." The fact that a thought occurs at a given moment does not entail that any other thought has occurred at any other moment, still less that there has occurred a series of thoughts sufficient to constitute a single self. As Hume conclusively showed, no one event intrinsically points to any other. We infer the existence of events which we are not actually observing, with the help of general principle. But these principles must be obtained inductively. By mere deduction from what is immediately given we cannot advance a single step beyond. And, consequently, any attempt to base a deductive system on propositions which describe what is immediately given is bound to be a failure."

"Between the workable empiricism of the early land measurers... of ancient Egypt and the geometry of the Greeks in the sixth century before Christ, there is a great chasm. ...and the chasm is bridged by deductive reasoning applied consciously and deliberately to the practical inductions of daily life. Without the strictest deductive proof from admitted assumptions, explicitly stated as such, mathematics does not exist. This does not deny that intuition, experiment, induction, and plain guessing are important elements in mathematical invention. It merely states the criterion by which the final product of all guessing, by whatever name it be dignified, is judged to be or not to be mathematics. It is not known where or when the distinction between inductive inference—the summation of raw experience—and deductive proof from a set of postulates was first made, but it was sharply recognized by the Greek mathematicians as early as 550 B.C."

"The long chains of simple and easy reasonings by means of which geometers are accustomed to reach the conclusions of their most difficult demonstrations, had led me to imagine that all things, to the knowledge of which man is competent, are mutually connected in the same way, and that there is nothing so far removed from us as to be beyond our reach, or so hidden that we cannot discover it, provided only we abstain from accepting the false for the true, and always preserve in our thoughts the order necessary for the deduction of one truth from another."

"It has fallen to the lot of one people, the ancient Greeks, to endow human thought with two outlooks on the universe neither of which has blurred appreciably in more than two thousand years. ...The first was the explicit recognition that proof by deductive reasoning offers a foundation for the structure of number and form. The second was the daring conjecture that nature can be understood by human beings through mathematics, and that mathematics is the language most adequate for idealizing the complexity of nature into appreciable simplicity. Both are attributed by persistent Greek tradition to Pythagoras in the sixth century before Christ. ...there is an equally persistent tradition that it was Thales... who first proved a theorem in geometry. But there seems to be no claim that Thales... proposed the inerrant tactic of definitions, postulates, deductive proof, theorem as a universal method in mathematics. ...in attributing any specific advance to Pythagoras himself, it must be remembered that the Pythagorean brotherhood was one of the world's earliest unpriestly cooperative scientific societies, if not the first, and that its members assigned the common work of all by mutual consent to their master."

"He is a despicable sage whose wisdom does not profit himself."

"The sage and the contemner of wealth most resemble God."

"En un descuido puede caer el mayor sabio, pero en dos no; y de paso, que no de asiento."

"Nothing better or happier can befall a man than to be in the proximity of one of those victorious ones, who, precisely because they have thought the most deeply, must love what is most alive and, as sages, incline in the end to the beautiful. They speak truly, they do not stammer, and do not chatter about what they have heard; they are active and live truly and not the uncanny masquerade men are accustomed to live: which is why, in their proximity, we for once feel human and natural for once, and feel like exclaiming with Goethe: “How glorious and precious is a living thing!”"

"I cannot understand how some people can live without communicating with the wisest people who ever lived on earth."

"The two operations of our understanding, intuition and deduction, on which alone we have said we must rely in the acquisition of knowledge."

"There are more fools than wise men, and even in a wise man there is more folly than wisdom."

"A man should learn to detect and watch that gleam of light which flashes across his mind from within more than the lustre of the firmament of bards and sages. Yet he dismisses without notice his own thought, because it is his."

"A questioner asks: If human nature is evil, then where do ritual and rightness come from? I reply: ritual and rightness are always created by the conscious activity of the sages."

"The two great conceptual revolutions of twentieth-century science, the overturning of classical physics by Werner Heisenberg and the overturning of the foundations of mathematics by Kurt Gödel, occurred within six years of each other within the narrow boundaries of German-speaking Europe. ...A study of the historical background of German intellectual life in the 1920s reveals strong links between them. Physicists and mathematicians were exposed simultaneously to external influences that pushed them along parallel paths. ...Two people who came early and strongly under the influence of Spengler's philosophy were the mathematician Hermann Weyl and the physicist Erwin Schrödinger. ...Weyle and Schrödinger agreed with Spengler that the coming revolution would sweep away the principle of physical causality. The erstwhile revolutionaries David Hilbert and Albert Einstein found themselves in the unaccustomed role of defenders of the status quo, Hilbert defending the primacy of formal logic in the foundations of mathematics, Einstein defending the primacy of causality in physics. In the short run, Hilbert and Einstein were defeated and the Spenglerian ideology of revolution triumphed, both in physics and in mathematics. Heisenberg discovered the true limits of causality in atomic processes, and Gödel discovered the limits of formal deduction and proof in mathematics. And, as often happens in the history of intellectual revolutions, the achievement of revolutionary goals destroyed the revolutionary ideology that gave them birth. The visions of Spengler, having served their purpose, rapidly became irrelevant."

"Il ne manque cependant à l’oisiveté du sage qu’un meilleur nom, et que méditer, parler, lire, et être tranquille s’appelât travailler."

"Descartes was an eminent mathematician, and it would seem that the bent of his mind led him to overestimate the value of deductive reasoning from general principles, as much as Bacon had underestimated it."

"Aristo the Bald, a native of Chios and nicknamed the Siren, said that the chief good was to live in perfect indifference to all those things that are of an intermediate character between virtue and vice; making not the slightest difference between them, but regarding them all on a footing of equality. For that the wise man resembles a good actor; who, whether he is filling the part of Agamemnon or Thersites, will perform them both equally well."

"Ὁ δίκαιος ἀταρακτότατος, ὁ δ᾽ ἄδικος πλείστης ταραχῆς γέμων."

"Look into your own religion. There's constant reference to relativity. Your ancients, they were masters of understanding that there is no one ultimate rule book for all situations. The woman churning curd into butter, she has to pull one end of the rope, and let the other end go otherwise the rope will break. Contradictions and polarities are two ends of the same rope. You can pull one end and let the other end go."

"The ship wherein Theseus and the youth of Athens returned from Crete had thirty oars, and was preserved by the Athenians down even to the time of Demetrius Phalereus, for they took away the old planks as they decayed, putting in new and stronger timber in their places, in so much that this ship became a standing example among the philosophers, for the logical question of things that grow; one side holding that the ship remained the same, and the other contending that it was not the same."

"The idea of the building, the intention of it, its design, are all immutable and are the essence of the building. The intention of the original builders is what survives. The wood of which the design is constructed decays and is replaced when necessary. To be overly concerned with the original materials, which are merely sentimental souvenirs of the past, is to fail to see the living building itself."

"My view is that the contribution of human cells is going to be minimal, maybe 3 percent, maybe 5 percent. But what if they contributed to 100 percent of the brain? What if the embryo that develops is mostly human? It’s something that we don’t expect, but no one has done this experiment, so we can’t rule it out."

"... in an experiment, there are sort of two kinds of exercises. In one, you might collect more data and bring down your s. In another, you have a concern, what we call a , and you check it, whether it exists at all or not."

"To engage in experiments on heat was always one of my most agreeable employments."

"The scientific question is the logical hypothesis which from a known law further proceeds by analogy and induction, the answer gives the experiment, which is prescribed in the question itself."

"great difficulties are felt at first and these cannot be overcome except by starting from experiments .. and then be conceiving certain hypotheses ... But even so, very much hard work remains to be done and one needs not only great perspicacity but often a degree of good fortune.If we wanted to be straight, we would be (Tue 14 Dec 2004 02.55 GMT)"

"I became captivated by the edifices chemists had raised through experiment and imagination—but still I had a lurking question. Would it not be better if one could really “see” whether molecules as complicated as the sterols, or strychnine were just as experiment suggested."

"The modern concept of the vacuum of space, confirmed every day by experiment, is a relativistic ether. But we do not call it this because it is taboo."

"Why are the theories of physics so similar in their structure? There are a number of possibilities. The first is the limited imagination of physicists: when we see a new phenomenon, we try to fit it into the framework we already have—until we have made enough experiments, we don’t know that it doesn’t work. So when some fool physicist gives a lecture at UCLA in 1983 and says, “This is the way it works, and look how wonderfully similar the theories are,” it’s not because Nature is really similar; it’s because the physicists have only been able to think of the same damn thing, over and over again."

"An experiment without a control is an act of faith."

"A thinker sees his own actions as experiments and questions — as attempts to find out something. Success and failure are for him answers above all.."

"Play is experimenting with the accident."

"There is one feature I notice that is generally missing in cargo cult science. … It's a kind of scientific integrity, a principle of scientific thought that corresponds to a kind of utter honesty — a kind of leaning over backwards. For example, if you're doing an experiment, you should report everything that you think might make it invalid — not only what you think is right about it; other causes that could possibly explain your results; and things you thought of that you've eliminated by some other experiment, and how they worked — to make sure the other fellow can tell they have been eliminated. Details that could throw doubt on your interpretation must be given, if you know them. You must do the best you can — if you know anything at all wrong, or possibly wrong — to explain it. If you make a theory, for example, and advertise it, or put it out, then you must also put down all the facts that disagree with it, as well as those that agree with it. There is also a more subtle problem. When you have put a lot of ideas together to make an elaborate theory, you want to make sure, when explaining what it fits, that those things it fits are not just the things that gave you the idea for the theory; but that the finished theory makes something else come out right, in addition. In summary, the idea is to try to give all of the information to help others to judge the value of your contribution; not just the information that leads to judgement in one particular direction or another."

"We've learned from experience that the truth will come out. Other experimenters will repeat your experiment and find out whether you were wrong or right. Nature's phenomena will agree or they'll disagree with your theory. And, although you may gain some temporary fame and excitement, you will not gain a good reputation as a scientist if you haven't tried to be very careful in this kind of work. And it's this type of integrity, this kind of care not to fool yourself, that is missing to a large extent in much of the research in cargo cult science."

"All experiments in psychology are not of this [cargo cult] type, however. For example there have been many experiments running rats through all kinds of mazes, and so on — with little clear result. But in 1937 a man named Young did a very interesting one. He had a long corridor with doors all along one side where the rats came in, and doors along the other side where the food was. He wanted to see if he could train rats to go to the third door down from wherever he started them off. No. The rats went immediately to the door where the food had been the time before.The question was, how did the rats know, because the corridor was so beautifully built and so uniform, that this was the same door as before? Obviously there was something about the door that was different from the other doors. So he painted the doors very carefully, arranging the textures on the faces of the doors exactly the same. Still the rats could tell. Then he thought maybe they were smelling the food, so he used chemicals to change the smell after each run. Still the rats could tell. Then he realized the rats might be able to tell by seeing the lights and the arrangement in the laboratory like any commonsense person. So he covered the corridor, and still the rats could tell.He finally found that they could tell by the way the floor sounded when they ran over it. And he could only fix that by putting his corridor in sand. So he covered one after another of all possible clues and finally was able to fool the rats so that they had to learn to go to the third door. If he relaxed any of his conditions, the rats could tell.Now, from a scientific standpoint, that is an A-number-one experiment. That is the experiment that makes rat-running experiments sensible, because it uncovers the clues that the rat is really using — not what you think it's using. And that is the experiment that tells exactly what conditions you have to use in order to be careful and control everything in an experiment with rat-running.I looked into the subsequent history of this research. The next experiment, and the one after that, never referred to Mr. Young. They never used any of his criteria of putting the corridor on sand, or of being very careful. They just went right on running rats in the same old way, and paid no attention to the great discoveries of Mr. Young, and his papers are not referred to, because he didn't discover anything about rats. In fact, he discovered all the things you have to do to discover something about rats. But not paying attention to experiments like that is a characteristic of cargo cult science."

"Science … is to be regarded as a series of interconnected conceptual schemes which arose originally from experimentation or careful observation and were fruitful of new experiments."

"Mere numbers cannot bring out... the intimate essence of the experiment. This conviction comes naturally when one watches a subject at work ... What things can happen! What reflections, what remarks, what feelings, or, on the other hand, what blind automatism, what absence of ideas!... The experimenter judges what may be going on in (the subject’s) mind, and certainly feels difficulty in expressing all the oscillations of a thought in a simple, brutal number, which can have only a deceptive precision. How, in fact, could it sum up what would need several pages of description!"

"The history of these experiments is not a proud one. The Nazis specialised in them, with a view to eradicating homosexuality."

"I wish that people would be persuaded that psychological experiments, especially those on the complex functions, are not improved (by large studies); the statistical method gives only mediocre results; some recent examples demonstrate that. The American authors, who love to do things big, often publish experiments that have been conducted on hundreds and thousands of people; they instinctively obey the prejudice that the persuasiveness of a work is proportional to the number of observations. This is only an illusion."

"I do feel strongly that this is nonsense! … So perhaps I could entertain future historians by saying I think all this superstring stuff is crazy and is in the wrong direction. … I don’t like it that they’re not calculating anything. … why are the masses of the various particles such as quarks what they are? All these numbers … have no explanations in these string theories – absolutely none! … I don’t like that they don’t check their ideas. I don’t like that for anything that disagrees with an experiment, they cook up an explanation—a fix-up to say, “Well, it might be true.” For example, the theory requires ten dimensions. Well, maybe there’s a way of wrapping up six of the dimensions. Yes, that’s all possible mathematically, but why not seven? When they write their equation, the equation should decide how many of these things get wrapped up, not the desire to agree with experiment. In other words, there’s no reason whatsoever in superstring theory that it isn’t eight out of the ten dimensions that get wrapped up and that the result is only two dimensions, which would be completely in disagreement with experience. So the fact that it might disagree with experience is very tenuous, it doesn’t produce anything."

"we are engaged in a grim experiment never before attempted. We are subjecting whole populations to exposure to chemicals which animal experiments have proved to be extremely poisonous and in many cases cumulative in their effect. These exposures now begin at or before birth and-unless we change our methods-will continue through the lifetime of those now living. No one knows what the result will be, because we have no previous experience to guide us."