Certainly it is permitted to anyone to put forward whatever hypotheses he wishes, and to develop the logical consequences contained in those hypotheses. But in order that this work merit the name of Geometry, it is necessary that these hypotheses or postulates express the result of the more simple and elementary observations of physical figures.
Given any rule, however "fundamental" or "necessary" for science, there are always circumstances when it is advisable not only to ignore the rule, but to adopt its opposite. For example, there are circumstances when it is advisable to introduce, elaborate and defend ad hoc hypotheses, or hypotheses which contradict well-established and generally accepted experimental results, or hypotheses whose content is smaller than the content of the existing and empirically adequate alternative, or self-inconsistent hypotheses, and so on.
The growth of our knowledge is the result of a process closely resembling what Darwin called 'natural selection'; that is, the natural selection of hypotheses: our knowledge consists, at every moment, of those hypotheses which have shown their (comparative) fitness by surviving so far in their struggle for existence, a competitive struggle which eliminates those hypotheses which are unfit.
I have not been able to discover the cause of those properties of gravity from phenomena, and I frame no hypotheses; for whatever is not deduced from the phenomena is to be called a hypothesis, and hypotheses, whether metaphysical or physical, whether of occult qualities or mechanical, have no place in experimental philosophy.
We shall do better to abandon the whole attempt to learn the truthunless we can trust to the human mind's having such a powerof guessing right that before very many hypotheses shall have been tried, intelligent guessing may be expected to lead us to one which will support all tests, leaving the vast majority of possible hypotheses unexamined.
Charles Sanders Peirce
There are many hypotheses in physics of almost comparable brillance and elegance that have been rejected because they did not survive such a confrontation with experiment. In my view, the human condition would be greatly improved if such confrontations and willingness to reject hypotheses were a regular part of our social, political, economic, religious and cultural lives.
Are not all Hypotheses erroneous, in which Light is supposed to consist in Pression or Motion, propagated through a fluid Medium? For in all these Hypotheses the Phaenomena of Light have been hitherto explain'd by supposing that they arise from new Modifications of the Rays; which is an erroneous Supposition.
The past slips from our grasp. It leaves us only scattered things. The bond that united them eludes us. Our imagination usually fills in the void by making use of preconceived theories...Archaeology, then, does not supply us with certitudes, but rather with vague hypotheses. And in the shade of these hypotheses some artists are content to dream, considering them less as scientific facts than as sources of inspiration.
All interpretations made by a scientist are hypotheses, and all hypotheses are tentative. They must forever be tested and they must be revised if found to be unsatisfactory. Hence, a change of mind in a scientist, and particularly in a great scientist, is not only not a sign of weakness but rather evidence for continuing attention to the respective problem and an ability to test the hypothesis again and again.
The best and safest way of philosophising seems to be, first to enquire diligently into the properties of things, and to establish those properties by experiences [experiments] and then to proceed slowly to hypotheses for the explanation of them. For hypotheses should be employed only in explaining the properties of things, but not assumed in determining them; unless so far as they may furnish experiments.
The hypotheses which we accept ought to explain phenomena which we have observed. But they ought to do more than this; our hypotheses ought to foretell phenomena which have not yet been observed; ... because if the rule prevails, it includes all cases; and will determine them all, if we can only calculate its real consequences. Hence it will predict the results of new combinations, as well as explain the appearances which have occurred in old ones. And that it does this with certainty and correctness, is one mode in which the hypothesis is to be verified as right and useful.
...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.
It reveals to me the causes of many natural phenomena that are entirely incomprehensible in the light of the generally accepted hypotheses. To refute the latter I collected many proofs, but I do not publish them ... I would dare to publish my speculations if there were people men like you.
For it is the duty of an astronomer to compose the history of the celestial motions or hypotheses about them. Since he cannot in any certain way attain to the true causes, he will adopt whatever suppositions enable the motions to be computed correctly from the principles of geometry for the future as well as for the past.
The knowledge of Natural-History, being Observation of Matters of Fact, is more certain than most others, and in my slender Opinion, less subject to Mistakes than Reasonings, Hypotheses, and Deductions are; ... These are things we are sure of, so far as our Senses are not fallible; and which, in probability, have been ever since the Creation, and will remain to the End of the World, in the same Condition we now find them.
I would be lying, however, if I claimed that I could always formulate worthwhile hypotheses on the basis of my theoretical framework. Sometimes there were no reflexive processes to be found; sometimes I failed to find them; and, what was the most painful of all, sometimes I got them wrong. One way or another, I often invested without a worthwhile hypothesis and my activities were not very different from a random walk.
But don't despise error. When touched by genius, when led by chance, the most superior truth can come into being from even the most foolish error. The important inventions which have been brought about in every realm of science from false hypotheses number in the hundreds, indeed in the thousands.
But anyone who is practically acquainted with scientific work is aware that those who refuse to go beyond fact, rarely get as far as fact; and anyone who has studied the history of science knows that almost every great step therein has been made by the 'anticipation of Nature, ' that is, by the invention of hypotheses, which, though verifiable, often had very little foundation to start with.
Thomas Henry Huxley
I feel that, in a sense, the writer knows nothing any longer. He has no moral stance. He offers the reader the contents of his own head, a set of options and imaginative alternatives. His role is that of a scientist, whether on safari or in his laboratory, faced with an unknown terrain or subject. All he can do is to devise various hypotheses and test them against the facts.
J. G. Ballard
Twice in my life I have spent two weary and scientifically profitless years seeking evidence to corroborate dearly loved hypotheses that later proved to be groundless; times such as these are hard for scientists-days of leaden gray skies bringing with them a miserable sense of oppression and inadequacy.
There is no reason why an extraphysical general principle is necessarily to be avoided, since such principles could conceivably serve as useful working hypotheses. For the history of scientific research is full of examples in which it was very fruitful indeed to assume that certain objects or elements might be real, long before any procedures were known which would permit them to be observed directly.
Whether statistics be an art or a science... or a scientific art, we concern ourselves little. It is the basis of social and political dynamics, and affords the only secure ground on which the truth or falsehood of the theories and hypotheses of that complicated science can be brought to the test.
When you believe you have found an important scientific fact, and are feverishly curious to publish it, constrain yourself for days, weeks, years sometimes, fight yourself, try and ruin your own experiments, and only proclaim your discovery after having exhausted all contrary hypotheses. But when, after so many efforts you have at last arrived at a certainty, your joy is one of the greatest which can be felt by a human soul.
The men and women of England who abolished slavery, created the educational system, or gave women the vote were not acting on the hypotheses of what the voters wanted. They were afire with faith in what people ought to want and in the end they persuaded their lethargic compatriots to give them enough support to warrant a change.
The major religions on the Earth contradict each other left and right. You can't all be correct. And what if all of you are wrong? It's a possibility, you know. You must care about the truth, right? Well, the way to winnow through all the differing contentions is to be skeptical. I'm not any more skeptical about your religious beliefs than I am about every new scientific idea I hear about. But in my line of work, they're called hypotheses, not inspiration and not revelation.
Is the world ruled by strict laws or not? This question I regard as metaphysical. The laws we find are always hypotheses; which means that they may always be superseded, and that they may possibly be deduced from probability estimates. Yet denying causality would be the same as attempting to persuade the theorist to give up his search; and that such an attempt cannot be backed by anything like a proof...
If we respect students abilities to define their own experiences, to generate their own hypotheses, and to discover new ways of categorizing the world, we might not be so quick to evaluate the adequacy of their answers. We might, instead, begin listening to their questions. Out of the questions of students come some of the most creative ideas and discoveries.
Watson augments human decision-making because it isn't governed by human boundaries. It draws together all this information and forms hypotheses, millions of them, and then tests them with all the data it can find. It learns over time what data is reliable, and that's part of its learning process.
What the scientists have always found by physical experiment was an a priori orderliness of nature, or Universe always operating at an elegance level that made the discovering scientist's working hypotheses seem crude by comparison. The discovered reality made the scientists exploratory work seem relatively disorderly.
R. Buckminster Fuller
Her professors were astonished by her leaps of thought, by the finesse and elegance of her insights. She arrived at hypotheses by sheer intuition and with what eventually one of her mentors described as an almost alarming speed; she was like a dancer, he said, out in the cosmos springing weightlessly from star to star. Drones, merely brilliant, crawled along behind with laborious proofs that supported her assertions.
How can you communicate your thoughts or demonstrate your hypotheses by conventional means when all the values and standards that you want to challenge are built into those means? Science and new technology today like to declare that they encourage 'lateral thinking,' new ways of seeing and putting data together - but all systems have an inbuilt resistance to what has not been programmed into them through the premises on which their rules are based.
The number of hypotheses and theories about climate change are numerous. Quite naturally they have caught the public attention, as any proof of past climactic change points to the possibility of future climate change, which inevitably will have significant implications for global economics.
I do not pretend to be able to prove that there is no God. I equally cannot prove that Satan is a fiction. The Christian god may exist; so may the gods of Olympus, or of ancient Egypt, or of Babylon. But no one of these hypotheses is more probable than any other: they lie outside the region of even probable knowledge, and therefore there is no reason to consider any of them.
My scientist friends have come up with things like 'principles of uncertainty' and dark holes. They're willing to live inside imagined hypotheses and theories. But many religious folks insist on answers that are always true. We love closure, resolution and clarity, while thinking that we are people of 'faith'! How strange that the very word 'faith' has come to mean its exact opposite.
You will reply that reality hasn't the slightest need to be of interest. And I'll answer you that reality may avoid the obligation to be interesting, but that hypotheses may not. In the hypothesis you have postulated, chance intervenes largely. Here lies a dead rabbi; I should prefer a purely rabbinical explanation; not the imaginary mischances of an imaginary robber.
Jorge Luis Borges
What is called for is an exquisite balance between two conflicting needs: the most skeptical scrutiny of all hypotheses that are served up to us and at the same time a great openness to new ideas. If you are only skeptical, then no new ideas make it through to you. On the other hand, if you are open to the point of gullibility and have not an ounce of skeptical sense in you, then you cannot distinguish useful ideas from the worthless ones.
The discovery of the telephone has made us acquainted with many strange phenomena. It has enabled us, amongst other things, to establish beyond a doubt the fact that electric currents actually traverse the earth's crust. The theory that the earth acts as a great reservoir for electricity may be placed in the physicist's waste-paper basket, with phlogiston, the materiality of light, and other old-time hypotheses.
William Henry Preece
In order to create something new, to invent a new product or idea, you need to anticipate where things are headed. That requires a mixture of certain habits of mind. You need to foster imagination, thoroughly understand the origins of past ideas, learn from others' mistakes, talk to lots of people about ideas and test your hypotheses against people both alive and dead.
It is clear that the building of models is not a purely mechanical process but requires skill of a high order - not merely mathematical skill but a sensitivity to the relative importance of different factors and a critical, almost an artistic, faculty in the selection of behaviour equations which are reasonable, tentative hypotheses in explaining the behaviour of actual economies.
Kenneth E. Boulding
Measurement has too often been the leitmotif of many investigations rather than the experimental examination of hypotheses. Mounds of data are collected, which are statistically decorous and methodologically unimpeachable, but conclusions are often trivial and rarely useful in decision making. This results from an overly rigorous control of an insignificant variable and a widespread deficiency in the framing of pertinent questions. Investigators seem to have settled for what is measurable instead of measuring what they would really like to know.
An essential aspect of creativity is not being afraid to fail. Scientists made a great invention by calling their activities hypotheses and experiments. They made it permissible to fail repeatedly until in the end they got the results they wanted. In politics or government, if you made a hypothesis and it didn't work out, you had your head cut off.
Science sometimes improves hypotheses and sometimes disproves them. But proof would be another matter and perhaps never occurs except in the realms of totally abstract tautology. We can sometimes say that if such and such abstract suppositions or postulates are given, then such and such abstract suppositions or postulates are given, then such and such must follow absolutely. But the truth about what can be perceived or arrived at by induction from perception is something else again.
The rules and principles of case law have never been treated as final truths but as working hypotheses, continually retested in those great laboratories of the law, the courts of justice. Every new case is an experiment, and if the accepted rule which seems applicable yields a result which is felt to be unjust, the rule is reconsidered.
Benjamin N. Cardozo