"The processes of nature lie so deep, that, after all the pains we can take, much, perhaps, will remain undiscovered beyond the reach of human art or skill. But this is no reason why we should give ourselves up to the belief of fictions, be they ever so ingenious, instead of hearkening to the unerring voice of nature […]" (Colin Maclaurin, "An Account of Sir Isaac Newton’s Philosophical Discoveries", 1748)
"Man must cling to the belief that the incomprehensible is comprehensible. Else he would give up investigating. " (Johann Wolfgang von Goethe, "Maxims and Reflections", 1829)
"By degree of probability we really mean, or ought to mean, degree of belief [...] Probability then, refers to and implies belief, more or less, and belief is but another name for imperfect knowledge, or it may be, expresses the mind in a state of imperfect knowledge." (Augustus De Morgan, "Formal Logic: Or, The Calculus of Inference, Necessary and Probable", 1847)
"Science for the past is a description, for the future a belief." (Karl Pearson, "The Grammar of Science", 1892)
"For the truly scientific man, the hypothesis is destined solely to enable him to get the facts of nature in some definite order, an order which shall make apparent their connection with the great order and harmony which is believed to be present in the universe." (James M Baldwin, "The Processes of Life Revealed by the Microscope: A Plea for Physiological Histology", Science N.S. Vol. 2 (34), 1895)
"Induction applied to the physical sciences is always uncertain, because it rests on the belief in a general order of the universe, an order outside of us." (Henri Poincaré, "Science and Hypothesis", 1901)
"It [science] involves an intelligent and persistent endeavor to revise current beliefs so as to weed out what is erroneous, to add to their accuracy, and, above all, to give them such shape that the dependencies of the various facts upon one another may be as obvious as possible." (John Dewey, "Democracy and Education", 1916)
"Science herself consults her heart when she lays it down that the infinite ascertainment of fact and correction of false belief are the supreme goods for man." (William James, "Selected Papers on Philosophy", 1918)
"The question whether any branch of science can ever become purely deductive is easily answered. It cannot. If science deals with the external world, as we believe it does, and not merely with the relations of propositions then no branch of science can ever be purely deductive. Deductive reasoning by itself can never tell us about facts. The use of deduction in science is to serve as a calculus to make our observations go further, not to take the place of observation." (Arthur D Ritchie, "Scientific Method: An Inquiry into the Character and Validity of Natural Laws", 1923)
"There is scarcely a scientific axiom that is not nowadays denied by somebody. And at the same time almost any nonsensical theory that may be put forward in the name of science would be almost sure to find believers and disciples." (Max Planck, "Where is Science Going?", 1932)
"The belief in science has replaced in large measure, the belief in God. Even where religion was regarded as compatible with science, it was modified by the mentality of the believer in scientific truth." (Hans Reichenbach, "The Rise of Scientific Philosophy", 1951)
"The important distinction between science and those other systematizations [i.e., art, philosophy, and theology] is that science is self-testing and self-correcting. Here the essential point of science is respect for objective fact. What is correctly observed must be believed [...] the competent scientist does quite the opposite of the popular stereotype of setting out to prove a theory; he seeks to disprove it. (George G Simpson, "Notes on the Nature of Science", 1962)
"Science, indeed, tells us a very great deal less about the universe than we have been accustomed to suppose, and there is no reason to believe that all we can ever know must be couched in terms of its thin and largely arbitrary abstractions." (John W N Sullivan, "Art and Reality", 1964)
"[…] the social scientist who lacks a mathematical mind and regards a mathematical formula as a magic recipe, rather than as the formulation of a supposition, does not hold forth much promise. A mathematical formula is never more than a precise statement. It must not be made into a Procrustean bed - and that is what one is driven to by the desire to quantify at any cost. It is utterly implausible that a mathematical formula should make the future known to us, and those who think it can, would once have believed in witchcraft. The chief merit of mathematicization is that it compels us to become conscious of what we are assuming." (Bertrand de Jouvenel, "The Art of Conjecture", 1967)
"In science we always know much less than we believe we do." (Erwin Chargaff, "Uncertainties Great, Is the Gain Worth the Risk?", Chemical and Engineering News, 1977)
"The so-called exact sciences often are not as exact as is commonly believed. How often they infer the existence of a hat from the emergence of a rabbit!" (Erwin Chargaff, "Voices in the Labyrinth: Nature, Man and Science", 1977)
"I find it more difficult, but also much more fun, to get the right answer by indirect reasoning and before all the evidence is in. It’s what a theoretician does in science. But the conclusions drawn in this way are obviously more risky than those drawn by direct measurement, and most scientists withhold judgment until there is more direct evidence available. The principal function of such detective work - apart from entertaining the theoretician - is probably to so annoy and enrage the observationalists that they are forced, in a fury of disbelief, to perform the critical measurements." (Carl Sagan, "The Cosmic Connection: An Extraterrestrial Perspective", 1975)
"Many people believe that reasoning, and therefore science, is a different activity from imagining. But this is a fallacy […] Reasoning is constructed with movable images just as certainly as poetry is." (Jacob Bronowski, "Visionary Eye", 1978)
"All advances of scientific understanding, at every level, begin with a speculative adventure, an imaginative preconception of what might be true - a preconception that always, and necessarily, goes a little way (sometimes a long way) beyond anything which we have logical or factual authority to believe in. It is the invention of a possible world, or of a tiny fraction of that world. The conjecture is then exposed to criticism to find out whether or not that imagined world is anything like the real one. Scientific reasoning is therefore at all levels an interaction between two episodes of thought - a dialogue between two voices, the one imaginative and the other critical; a dialogue, as I have put it, between the possible and the actual, between proposal and disposal, conjecture and criticism, between what might be true and what is in fact the case. (Sir Peter B Medawar, "Pluto’s Republic: Incorporating the Art of the Soluble and Induction Intuition in Scientific Thought", 1982)
"The purpose of scientific enquiry is not to compile an inventory of factual information, nor to build up a totalitarian world picture of Natural Laws in which every event that is not compulsory is forbidden. We should think of it rather as a logically articulated structure of justifiable beliefs about nature. It begins as a story about a Possible World - a story which we invent and criticize and modify as we go along, so that it winds by being, as nearly as we can make it, a story about real life." (Sir Peter B Medawar, "Pluto’s Republic: Incorporating the Art of the Soluble and Induction Intuition in Scientific Thought", 1982)
"The scientific method is a potentiation of common sense, exercised with a specially firm determination not to persist in error if any exertion of hand or mind can deliver us from it. Like other exploratory processes, it can be resolved into a dialogue between fact and fancy, the actual and the possible; between what could be true and what is in fact the case. The purpose of scientific enquiry is not to compile an inventory of factual information, nor to build up a totalitarian world picture of Natural Laws in which every event that is not compulsory is forbidden. We should think of it rather as a logically articulated structure of justifiable beliefs about nature. It begins as a story about a Possible World - a story which we invent and criticise and modify as we go along, so that it ends by being, as nearly as we can make it, a story about real life." (Sir Peter B Medawar, "Pluto’s Republic: Incorporating the Art of the Soluble and Induction Intuition in Scientific Thought", 1982)
"The degree of confirmation assigned to any given hypothesis is sensitive to properties of the entire belief system [...] simplicity, plausibility, and conservatism are properties that theories have in virtue of their relation to the whole structure of scientific beliefs taken collectively. A measure of conservatism or simplicity would be a metric over global properties of belief systems." (Jerry Fodor, "Modularity of Mind", 1983)
"There are those who try to generalize, synthesize, and build models, and there are those who believe nothing and constantly call for more data. The tension between these two groups is a healthy one; science develops mainly because of the model builders, yet they need the second group to keep them honest." (Andrew Miall,"Principles of Sedimentary Basin Analysis", 1984)
"To a considerable degree science consists in originating the maximum amount of information with the minimum expenditure of energy. Beauty is the cleanness of line in such formulations along with symmetry, surprise, and congruence with other prevailing beliefs." (Edward O Wilson, "Biophilia", 1984)
"Modern philosophy of science has gone far beyond the naive belief that science reveals the truth. Even if it could, we would have no means of proving it. Certainty seems unattainable. All scientific statements remain open to doubt. […] We cannot reach the absolute at least as far as science is concerned; we have to content ourselves with the relative." (Rolf Sattler, "Biophilosophy", 1986)
"Competent scientists do not believe their own models or theories, but rather treat them as convenient fictions. […] The issue to a scientist is not whether a model is true, but rather whether there is another whose predictive power is enough better to justify movement from today's fiction to a new one." (Steve Vardeman, " Comment", Journal of the American Statistical Association 82, 1987)
"Cybernetics is simultaneously the most important science of the age and the least recognized and understood. It is neither robotics nor freezing dead people. It is not limited to computer applications and it has as much to say about human interactions as it does about machine intelligence. Today’s cybernetics is at the root of major revolutions in biology, artificial intelligence, neural modeling, psychology, education, and mathematics. At last there is a unifying framework that suspends long-held differences between science and art, and between external reality and internal belief." (Paul Pangaro, "New Order From Old: The Rise of Second-Order Cybernetics and Its Implications for Machine Intelligence", 1988)
"The use of Occam’s razor, along with the related critical, skeptical view toward any speculations about the unknown, is perhaps the most misunderstood aspect of the scientific method. People confuse doubt with denial. Science doesn’t deny anything, but it doubts everything not required by the data. Note, however, that doubt does not necessarily mean rejection, just an attitude of disbelief that can be changed when the facts require it." (Victor J Stenger, "Physics and Psychics: The Search for a World Beyond the Senses", 1990)
"On this view, we recognize science to be the search for algorithmic compressions. We list sequences of observed data. We try to formulate algorithms that compactly represent the information content of those sequences. Then we test the correctness of our hypothetical abbreviations by using them to predict the next terms in the string. These predictions can then be compared with the future direction of the data sequence. Without the development of algorithmic compressions of data all science would be replaced by mindless stamp collecting - the indiscriminate accumulation of every available fact. Science is predicated upon the belief that the Universe is algorithmically compressible and the modern search for a Theory of Everything is the ultimate expression of that belief, a belief that there is an abbreviated representation of the logic behind the Universe's properties that can be written down in finite form by human beings." (John D Barrow, New Theories of Everything", 1991)
"The worst, i.e., most dangerous, feature of 'accepting the null hypothesis' is the giving up of explicit uncertainty. [...] Mathematics can sometimes be put in such black-and-white terms, but our knowledge or belief about the external world never can." (John Tukey, "The Philosophy of Multiple Comparisons", Statistical Science Vol. 6 (1), 1991)
"The belief that the underlying order of the world can be expressed in mathematical form lies at the very heart of science. So deep does this belief run that a branch of science is considered not to be properly understood until it can be cast in mathematics." (Paul C W Davies, "The Mind of God: The Scientific Basis for a Rational World", 1992)
"The most natural way to give an independence proof is to establish a model with the required properties. This is not the only way to proceed since one can attempt to deal directly and analyze the structure of proofs. However, such an approach to set theoretic questions is unnatural since all our intuition come from our belief in the natural, almost physical model of the mathematical universe." (Paul J Cohen, Set Theory and the Continuum Hypothesis", 1966) instead of with words, sounds or watercolors." (John Casti, "Reality Rules", 1992)
"A fundamental difference between religious and scientific thought is that the received beliefs in religion are ultimately based on revelations or pronouncements, usually by some long dead prophet or priest.[...] Dogma is interpreted by a caste of priests and is accepted by the multitude on faith or under duress. In contrast, the statements of science are derived from the data of observations and experiment, and from the manipulation of these data according to logical and often mathematical procedures." (John A Moore, "Science as a Way of Knowing: The Foundations of Modern Biology", 1993)
"Our beliefs about ourselves in relation to the world around us are the roots of our values, and our values determine not only our immediate actions, but also, over the course of time, the form of our society. Our beliefs are increasingly determined by science." (Henry P Stapp, "Mind, Matter and Quantum Mechanics", 1993)
"Science demands a tolerance for ambiguity. Where we are ignorant, we withhold belief. Whatever annoyance the uncertainty engenders serves a higher purpose: It drives us to accumulate better data. This attitude is the difference between science and so much else. Science offers little in the way of cheap thrills. The standards of evidence are strict. But when followed they allow us to see far, illuminating even a great darkness." (Carl Sagan, "Pale Blue Dot: A Vision of the Human Future in Space", 1994)
"Having a scientific outlook means being willing to divest yourself of a pet hypothesis, whether it relates to easy self-help improvements, homeopathy, graphology, spontaneous generation, or any other concept, when the data produced by a carefully designed experiment contradict that hypothesis. Retaining a belief in a hypothesis that cannot be supported by data is the hallmark of both the pseudoscientist and the fanatic. Often the more deeply held the hypothesis, the more reactionary is the response to nonsupportive data." (Michael Zimmerman, "Science, Nonscience, and Nonsense: Approaching Environmental Literacy", 1995)
"In science, for a theory to be believed, it must make a prediction - different from those made by previous theories - for an experiment not yet done. For the experiment to be meaningful, we must be able to get an answer that disagrees with that prediction. When this is the case, we say that a theory is falsifiable - vulnerable to being shown false. The theory also has to be confirmable, it must be possible to verify a new prediction that only this theory makes. Only when a theory has been tested and the results agree with the theory do we advance the statement to the rank of a true scientific theory." (Lee Smolin, "The Trouble with Physics", 2006)
"Under normal conditions the research scientist is not an innovator but a solver of puzzles, and the puzzles upon which he concentrates are just those which he believes can be both stated and solved within the existing scientific tradition." (Thomas S Kuhn, "The Essential Tension: Selected Studies in Scientific Tradition and Change", 2011)
"In the classical deterministic scenario, a model consists of a few variables and physical constants. The relational structure of the model is conceptualized by the scientist via intuition gained from thinking about the physical world. Intuition means that the scientist has some mental construct regarding the interactions beyond positing a skeletal mathematical system he believes is sufficiently rich to capture the interactions and then depending upon data to infer the relational structure and estimate a large number of parameters." (Edward R Dougherty, "The Evolution of Scientific Knowledge: From certainty to uncertainty", 2016)
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