Assumption Quotes (58 quotes)
All silencing of discussion is an assumption of infallibility.
An author has always great difficulty in avoiding unnecessary and tedious detail on the one hand; while, on the other, he must notice such a number of facts as may convince a student, that he is not wandering in a wilderness of crude hypotheses or unsupported assumptions.
As lightning clears the air of impalpable vapours, so an incisive paradox frees the human intelligence from the lethargic influence of latent and unsuspected assumptions. Paradox is the slayer of Prejudice.
Definition of Mathematics.—It has now become apparent that the traditional field of mathematics in the province of discrete and continuous number can only be separated from the general abstract theory of classes and relations by a wavering and indeterminate line. Of course a discussion as to the mere application of a word easily degenerates into the most fruitless logomachy. It is open to any one to use any word in any sense. But on the assumption that “mathematics” is to denote a science well marked out by its subject matter and its methods from other topics of thought, and that at least it is to include all topics habitually assigned to it, there is now no option but to employ “mathematics” in the general sense of the “science concerned with the logical deduction of consequences from the general premisses of all reasoning.”
Education must be subversive if it is to be meaningful. By this I mean that it must challenge all the things we take for granted, examine all accepted assumptions, tamper with every sacred cow, and instil a desire to question and doubt.
For ourselves, we may take as a basic assumption, clear from a survey of particular cases, that natural things are some or all of them subject to change.
For terrestrial vertebrates, the climate in the usual meteorological sense of the term would appear to be a reasonable approximation of the conditions of temperature, humidity, radiation, and air movement in which terrestrial vertebrates live. But, in fact, it would be difficult to find any other lay assumption about ecology and natural history which has less general validity. … Most vertebrates are much smaller than man and his domestic animals, and the universe of these small creatures is one of cracks and crevices, holes in logs, dense underbrush, tunnels, and nests—a world where distances are measured in yards rather than miles and where the difference between sunshine and shadow may be the difference between life and death. Actually, climate in the usual sense of the term is little more than a crude index to the physical conditions in which most terrestrial animals live.
Given any domain of thought in which the fundamental objective is a knowledge that transcends mere induction or mere empiricism, it seems quite inevitable that its processes should be made to conform closely to the pattern of a system free of ambiguous terms, symbols, operations, deductions; a system whose implications and assumptions are unique and consistent; a system whose logic confounds not the necessary with the sufficient where these are distinct; a system whose materials are abstract elements interpretable as reality or unreality in any forms whatsoever provided only that these forms mirror a thought that is pure. To such a system is universally given the name MATHEMATICS.
How do we discover the individual laws of Physics, and what is their nature? It should be remarked, to begin with, that we have no right to assume that any physical law exists, or if they have existed up to now, that they will continue to exist in a similar manner in the future. It is perfectly conceivable that one fine day Nature should cause an unexpected event to occur which would baffle us all; and if this were to happen we would be powerless to make any objection, even if the result would be that, in spite of our endeavors, we should fail to introduce order into the resulting confusion. In such an event, the only course open to science would be to declare itself bankrupt. For this reason, science is compelled to begin by the general assumption that a general rule of law dominates throughout Nature.
I have always felt that astronomical hypotheses should not be regarded as articles of faith, but should only serve as a framework for astronomical calculations, so that it does not matter whether they were right or wrong, as long as the phenomena can be characterized precisely. For who could possibly be certain as to whether the uneven movement of the sun, if we follow the hypotheses of Ptolemy, can be explained by assuming an epicycle or eccentricity. Both assumptions are plausible. That’s why I would consider it quite desirable for you to tell something about that in the preface. In this way you would appease the Aristotelians and the theologians, whose opposition you dread.
I undertake my scientific research with the confident assumption that the earth follows the laws of nature which God established at creation. … My studies are performed with the confidence that God will not capriciously confound scientific results by “slipping in” a miracle.
In all spheres of science, art, skill, and handicraft it is never doubted that, in order to master them, a considerable amount of trouble must be spent in learning and in being trained. As regards philosophy, on the contrary, there seems still an assumption prevalent that, though every one with eyes and fingers is not on that account in a position to make shoes if he only has leather and a last, yet everybody understands how to philosophize straight away, and pass judgment on philosophy, simply because he possesses the criterion for doing so in his natural reason.
In my opinion progress in science is usually made by dropping assumptions.
In recent years several new particles have been discovered which are currently assumed to be “elementary,” that is, essentially structureless. The probability that all such particles should be really elementary becomes less and less as their number increases. It is by no means certain that nucleons, mesons, electrons, neutrinos are all elementary particles.
In the Life of Darwin by his son, there is related an incident of how the great naturalist once studied long as to just what a certain spore was. Finally he said, “It is this, for if it isn’t, then what is it?” And all during his life he was never able to forget that he had been guilty of this unscientific attitude, for science is founded on certitude, not assumption.
In the modern interpretation of Mendelism, facts are being transformed into factors at a rapid rate. If one factor will not explain the facts, then two are involved; if two prove insufficient, three will sometimes work out. The superior jugglery sometimes necessary to account for the results may blind us, if taken too naively, to the common-place that the results are often so excellently 'explained' because the explanation was invented to explain them. We work backwards from the facts to the factors, and then, presto! explain the facts by the very factors that we invented to account for them. I am not unappreciative of the distinct advantages that this method has in handling the facts. I realize how valuable it has been to us to be able to marshal our results under a few simple assumptions, yet I cannot but fear that we are rapidly developing a sort of Mendelian ritual by which to explain the extraordinary facts of alternative inheritance. So long as we do not lose sight of the purely arbitrary and formal nature of our formulae, little harm will be done; and it is only fair to state that those who are doing the actual work of progress along Mendelian lines are aware of the hypothetical nature of the factor-assumption.
Indeed, not all attacks—especially the bitter and ridiculing kind leveled at Darwin—are offered in good faith, but for practical purposes it is good policy to assume that they are.
It is a constant struggle not to let the theory lead the science in the way that is most beneficial to one’s assumptions.
It was noted long ago that the front row of burlesque houses was occupied predominantly by bald-headed men. In fact, such a row became known as the bald-headed row. It might be assumed from this on statistical evidence that the continued close observation of chorus girls in tights caused loss of hair from the top of the head.
[Disputing a statistical study for the American Cancer Society showing smoking to be a cancer causative.]
[Disputing a statistical study for the American Cancer Society showing smoking to be a cancer causative.]
Mathematics is not arithmetic. Though mathematics may have arisen from the practices of counting and measuring it really deals with logical reasoning in which theorems—general and specific statements—can be deduced from the starting assumptions. It is, perhaps, the purest and most rigorous of intellectual activities, and is often thought of as queen of the sciences.
My practice as a scientist is atheistic. That is to say, when I set up an experiment I assume that no god, angel or devil is going to interfere with its course; and this assumption has been justified by such success as I have achieved in my professional career. I should therefore be intellectually dishonest if I were not also atheistic in the affairs of the world.
My story [Lord of the Rings] is not an allegory of Atomic power, but of Power (exerted for Domination). Nuclear physics can be used for that purpose. But they need not be. They need not be used at all. If there is any contemporary reference in my story at all it is to what seems to me the most widespread assumption of our time: that if a thing can be done, it must be done. This seems to me wholly false.
My “"thinking”" time was devoted mainly to activities that were essentially clerical or mechanical: searching, calculating, plotting, transforming, determining the logical or dynamic consequences of a set of assumptions or hypotheses, preparing the way for a decision or an insight. Moreover ... the operations that fill most of the time allegedly devoted to technical thinking are operations that can be performed more effectively by machines than by men.
No engineer can go upon a new work and not find something peculiar, that will demand his careful reflection, and the deliberate consideration of any advice that he may receive; and nothing so fully reveals his incapacity as a pretentious assumption of knowledge, claiming to understand everything.
No man who has not a decently skeptical mind can claim to be civilized. Euclid taught me that without assumptions there is no proof. Therefore, in any argument, examine the assumptions. Then, in the alleged proof, be alert for inexplicit assumptions. Euclid’s notorious oversights drove this lesson home. Thanks to him, I am (I hope!) immune to all propaganda, including that of mathematics itself.
On entering a temple we assume all signs of reverence. How much more reverent then should we be before the heavenly bodies, the stars, the very nature of God!
On the most usual assumption, the universe is homogeneous on the large scale, i.e. down to regions containing each an appreciable number of nebulae. The homogeneity assumption may then be put in the form: An observer situated in a nebula and moving with the nebula will observe the same properties of the universe as any other similarly situated observer at any time.
One point at which our magicians attempt their sleight-of-hand is when they slide quickly from the Hubble, redshift-distance relation to redshift-velocity of expansion. There are now five or six whole classes of objects that violate this absolutely basic assumption. It really gives away the game to realize how observations of these crucial objects have been banned from the telescope and how their discussion has met with desperate attempts at suppression.
Owing to his lack of knowledge, the ordinary man cannot attempt to resolve conflicting theories of conflicting advice into a single organized structure. He is likely to assume the information available to him is on the order of what we might think of as a few pieces of an enormous jigsaw puzzle. If a given piece fails to fit, it is not because it is fraudulent; more likely the contradictions and inconsistencies within his information are due to his lack of understanding and to the fact that he possesses only a few pieces of the puzzle. Differing statements about the nature of things, differing medical philosophies, different diagnoses and treatments—all of these are to be collected eagerly and be made a part of the individual's collection of puzzle pieces. Ultimately, after many lifetimes, the pieces will fit together and the individual will attain clear and certain knowledge.
Pure mathematics is a collection of hypothetical, deductive theories, each consisting of a definite system of primitive, undefined, concepts or symbols and primitive, unproved, but self-consistent assumptions (commonly called axioms) together with their logically deducible consequences following by rigidly deductive processes without appeal to intuition.
Rational thinking which is free from assumptions ends therefore in mysticism.
Science was false by being unpoetical. It assumed to explain a reptile or a mollusk, and isolated it—which is hunting for life in graveyards. Reptile or mollusk or man or angel only exists in system, in relation.
Science, though apparently transformed into pure knowledge, has yet never lost its character of being a craft; and that it is not the knowledge itself which can rightly be called science, but a special way of getting and of using knowledge. Namely, science is the getting of knowledge from experience on the assumption of uniformity in nature, and the use of such knowledge to guide the actions of men.
So I want to admit the assumption which the astronomer—and indeed any scientist—makes about the Universe he investigates. It is this: that the same physical causes give rise to the same physical results anywhere in the Universe, and at any time, past, present, and future. The fuller examination of this basic assumption, and much else besides, belongs to philosophy. The scientist, for his part, makes the assumption I have mentioned as an act of faith; and he feels confirmed in that faith by his increasing ability to build up a consistent and satisfying picture of the universe and its behavior.
The ancients devoted a lifetime to the study of arithmetic; it required days to extract a square root or to multiply two numbers together. Is there any harm in skipping all that, in letting the school boy learn multiplication sums, and in starting his more abstract reasoning at a more advanced point? Where would be the harm in letting the boy assume the truth of many propositions of the first four books of Euclid, letting him assume their truth partly by faith, partly by trial? Giving him the whole fifth book of Euclid by simple algebra? Letting him assume the sixth as axiomatic? Letting him, in fact, begin his severer studies where he is now in the habit of leaving off? We do much less orthodox things. Every here and there in one’s mathematical studies one makes exceedingly large assumptions, because the methodical study would be ridiculous even in the eyes of the most pedantic of teachers. I can imagine a whole year devoted to the philosophical study of many things that a student now takes in his stride without trouble. The present method of training the mind of a mathematical teacher causes it to strain at gnats and to swallow camels. Such gnats are most of the propositions of the sixth book of Euclid; propositions generally about incommensurables; the use of arithmetic in geometry; the parallelogram of forces, etc., decimals.
The assumption of an absolute determinism is the essential foundation of every scientific enquiry.
The assumption we have made … is that marriages and the union of gametes occur at random. The validity of this assumption may now be examined. “Random mating” obviously does not mean promiscuity; it simply means, as already explained above, that in the choice of mates for marriage there is neither preference for nor aversion to the union of persons similar or dissimilar with respect to a given trait or gene. Not all gentlemen prefer blondes or brunettes. Since so few people know what their blood type is, it is even safer to say that the chances of mates being similar or dissimilar in blood type are determined simply by the incidence of these blood types in a given Mendelian population.
[Co-author with Theodosius Dobzhansky]
[Co-author with Theodosius Dobzhansky]
The assumptions of population thinking are diametrically opposed to those of the typologist. The populationist stresses the uniqueness of everything in the organic world. What is true for the human species,–that no two individuals are alike, is equally true for all other species of animals and plants ... All organisms and organic phenomena are composed of unique features and can be described collectively only in statistical terms. Individuals, or any kind of organic entities, form populations of which we can determine the arithmetic mean and the statistics of variation. Averages are merely statistical abstractions, only the individuals of which the populations are composed have reality. The ultimate conclusions of the population thinker and of the typologist are precisely the opposite. For the typologist, the type (eidos) is real and the variation. an illusion, while for the populationist the type (average) is an abstraction and only the variation is real. No two ways of looking at nature could be more different.
The framing of hypotheses is, for the enquirer after truth, not the end, but the beginning of his work. Each of his systems is invented, not that he may admire it and follow it into all its consistent consequences, but that he may make it the occasion of a course of active experiment and observation. And if the results of this process contradict his fundamental assumptions, however ingenious, however symmetrical, however elegant his system may be, he rejects it without hesitation. He allows no natural yearning for the offspring of his own mind to draw him aside from the higher duty of loyalty to his sovereign, Truth, to her he not only gives his affections and his wishes, but strenuous labour and scrupulous minuteness of attention.
The history of mathematics, as of any science, is to some extent the story of the continual replacement of one set of misconceptions by another. This is of course no cause for despair, for the newly instated assumptions very often possess the merit of being closer approximations to truth than those that they replace.
The ingenious but nevertheless somewhat artificial assumptions of [Bohr’s model of the atom], … are replaced by a much more natural assumption in de Broglie’s wave phenomena. The wave phenomenon forms the real “body” of the atom. It replaces the individual punctiform electrons, which in Bohr’s model swarm around the nucleus.
The living human being seems to consist of nothing more than matter and energy. Spirit is merely an assumption.
The most important thing for us to recall may be, that the crucial quality of science is to encourage, not discourage, the testing of assumptions. That is the only ethic that will eventually start us on our way to a new and much deeper level of understanding.
The next time you make an assumption, see what happens when you do the opposite.
The universality of parasitism as an offshoot of the predatory habit negatives the position taken by man that it is a pathological phenomenon or a deviation from the normal processes of nature. The pathological manifestations are only incidents in a developing parasitism. As human beings intent on maintaining man's domination over nature we may regard parasitism as pathological insofar as it becomes a drain upon human resources. In our efforts to protect ourselves we may make every kind of sacrifice to limit, reduce, and even eliminate parasitism as a factor in human life. Science attempts to define the terms on which this policy of elimination may or may not succeed. We must first of all thoroughly understand the problem, put ourselves in possession of all the facts in order to estimate the cost. Too often it has been assumed that parasitism was abnormal and that it needed only a slight force to reestablish what was believed to be a normal equilibrium without parasitism. On the contrary, biology teaches us that parasitism is a normal phenomenon and if we accept this view we shall be more ready to pay the price of freedom as a permanent and ever recurring levy of nature for immunity from a condition to which all life is subject. The greatest victory of man over nature in the physical realm would undoubtedly be his own delivery from the heavy encumbrance of parasitism with which all life is burdened.
The use of every organ has been discovered by starting from the assumption that it must have been some use.
The validity of all the Inductive Methods depends on the assumption that every event, or the beginning of every phenomenon, must have some cause; some antecedent, upon the existence of which it is invariably and unconditionally consequent.
The world always makes the assumption that the exposure of an error is identical with the discovery of truth that the error and truth are simply opposite. They are nothing of the sort. What the world turns to, when it is cured on one error, is usually simply another error, and maybe one worse than the first one.
Thus, be it understood, to demonstrate a theorem, it is neither necessary nor even advantageous to know what it means. The geometer might be replaced by the logic piano imagined by Stanley Jevons; or, if you choose, a machine might be imagined where the assumptions were put in at one end, while the theorems came out at the other, like the legendary Chicago machine where the pigs go in alive and come out transformed into hams and sausages. No more than these machines need the mathematician know what he does.
We can invent as many theories we like, and any one of them can be made to fit the facts. But that theory is always preferred which makes the fewest number of assumptions.
We must never assume that which is incapable of proof.
What intellectual phenomenon can be older, or more oft repeated, than the story of a large research program that impaled itself upon a false central assumption accepted by all practitioners? Do we regard all people who worked within such traditions as dishonorable fools? What of the scientists who assumed that the continents were stable, that the hereditary material was protein, or that all other galaxies lay within the Milky Way? These false and abandoned efforts were pursued with passion by brilliant and honorable scientists. How many current efforts, now commanding millions of research dollars and the full attention of many of our best scientists, will later be exposed as full failures based on false premises?
When you are criticizing the philosophy of an epoch do not chiefly direct your attention to these intellectual positions which its exponents feel it necessary to defend. There will be some fundamental assumption which adherents of all the various systems of the epoch unconsciously presuppose.
While we maintain the unity of the human species, we at the same time repel the depressing assumption of superior and inferior races of men. There are nations more susceptible of cultivation, more highly civilized, more enobled by mental cultivation than others, but none in themselves nobler than others. All are in like degree designed for freedom; a freedom which, in the ruder conditions of society, belongs only to the individual, but which, in social states enjoying political institutions, appertains as a right to the whole body of the community.
[Richard P.] Feynman's cryptic remark, “no one is that much smarter ...,” to me, implies something Feynman kept emphasizing: that the key to his achievements was not anything “magical” but the right attitude, the focus on nature's reality, the focus on asking the right questions, the willingness to try (and to discard) unconventional answers, the sensitive ear for phoniness, self-deception, bombast, and conventional but unproven assumptions.
[Science] is not perfect. It can be misused. It is only a tool. But it is by far the best tool we have, self-correcting, ongoing, applicable to everything. It has two rules. First: there are no sacred truths; all assumptions must be critically examined; arguments from authority are worthless. Second: whatever is inconsistent with the facts must be discarded or revised. ... The obvious is sometimes false; the unexpected is sometimes true.
[The] erroneous assumption is to the effect that the aim of public education is to fill the young of the species with knowledge and awaken their intelligence, and so make them fit to discharge the duties of citizenship in an enlightened and independent manner. Nothing could be further from the truth. The aim of public education is not to spread enlightenment at all; it is simply to reduce as many individuals as possible to the same safe level, to breed and train a standardised citizenry, to put down dissent and originality.
[The] structural theory is of extreme simplicity. It assumes that the molecule is held together by links between one atom and the next: that every kind of atom can form a definite small number of such links: that these can be single, double or triple: that the groups may take up any position possible by rotation round the line of a single but not round that of a double link: finally that with all the elements of the first short period [of the periodic table], and with many others as well, the angles between the valencies are approximately those formed by joining the centre of a regular tetrahedron to its angular points. No assumption whatever is made as to the mechanism of the linkage. Through the whole development of organic chemistry this theory has always proved capable of providing a different structure for every different compound that can be isolated. Among the hundreds of thousands of known substances, there are never more isomeric forms than the theory permits.