On Hypotheses (1950-1959)

"As a set of cognitive beliefs, religion is a speculative hypothesis of an extremely low order of probability." (Sidney Hook, The Partisan Review, 1950) 

"Hypothesis is a tool which can cause trouble if not used properly. We must be ready to abandon out hypothesis as soon as it is shown to be inconsistent with the facts." (William I B Beveridge, "The Art of Scientific Investigation", 1950) 

"[…] no one believes an hypothesis except its originator but everyone believes an experiment except the experimenter." (William I B Beveridge, "The Art of Scientific Investigation", 1950)

"The hypothesis is the principal intellectual instrument in research. Its function is to indicate new experiments and observations and it therefore sometimes leads to discoveries even when not correct itself. We must resist the temptation to become too attached to our hypothesis, and strive to judge it objectively and modify it or discard it as soon as contrary evidence is brought to light. Vigilance is needed to prevent our observations and interpretations being biased in favor of the hypothesis. Suppositions can be used without being believed." (William I B Beveridge, "The Art of Scientific Investigation", 1950)

"The usefulness of observation and measurement in testing economic theories arises because the theorems of economics are supposed to relate to the actual world. [...] Any economic theorem rigorously deduced from given postulates may be regarded as a hypothesis about the actual world which experience may show to be false." (Richard Stone, "The Role of Measurement in Economics", 1951)

"A collection of observable concepts in a purely formal hypothesis suggesting no analogy with anything would consequently not suggest either any directions for its own development." (Mary B Hesse, "Operational Definition and Analogy in Physical Theories", British Journal for the Philosophy of Science 2 (8), 1952)

"Being built on concepts, hypotheses, and experiments, laws are no more accurate or trustworthy than the wording of the definitions and the accuracy and extent of the supporting experiments." (Gerald Holton, "Introduction to Concepts and Theories in Physical Science", 1952)

"Statistics is the fundamental and most important part of inductive logic. It is both an art and a science, and it deals with the collection, the tabulation, the analysis and interpretation of quantitative and qualitative measurements. It is concerned with the classifying and determining of actual attributes as well as the making of estimates and the testing of various hypotheses by which probable, or expected, values are obtained. It is one of the means of carrying on scientific research in order to ascertain the laws of behavior of things - be they animate or inanimate. Statistics is the technique of the Scientific Method." (Bruce D Greenschields & Frank M Weida, "Statistics with Applications to Highway Traffic Analyses", 1952)

"Whenever we attempt to test a hypothesis we naturally try to avoid errors in judging it. This seems to indicate the right way of proceeding: when choosing a test we should try to minimize the frequency of errors that may be committed in applying it." (Jerzy Neyman, "Lectures and Conferences on Mathematical Statistics", 1952) 

"The construction of hypotheses is a creative act of inspiration, intuition, invention; its essence is the vision of something new in familiar material. The process must be discussed in psychological, not logical, categories; studied in autobiographies and biographies, not treatises on scientific method; and promoted by maxim and example, not syllogism or theorem." (Milton Friedman, "Essays in Positive Economics", 1953)

"The only relevant test of the validity of a hypothesis is comparison of prediction with experience." (Milton Friedman, "Essays in Positive Economics", 1953)

"We are driven to conclude that science, like mathematics, is a system of axioms, assumptions, and deductions; it may start from being, but later leaves it to itself, and ends in the formation of a hypothetical reality that has nothing to do with existence; or it is the discovery of an ideal being which is, of course, present in what we call actuality, and renders it an existence for us only by being present in it." (Poolla T Raju, "Idealistic Thought of India", 1953)

"[…] the grand aim of all science […] is to cover the greatest possible number of empirical facts by logical deductions from the smallest possible number of hypotheses or axioms." (Albert Einstein, 1954)

"The theory of relativity is a fine example of the fundamental character of the modern development of theoretical science. The initial hypotheses become steadily more abstract and remote from experience. On the other hand, it gets nearer to the grand aim of all science, which is to cover the greatest possible number of empirical facts by logical deduction from the smallest possible number of hypotheses or axioms." (Albert Einstein, 1954)

"It is very easy to devise different tests which, on the average, have similar properties, [...] hey behave satisfactorily when the null hypothesis is true and have approximately the same power of detecting departures from that hypothesis. Two such tests may, however, give very different results when applied to a given set of data. The situation leads to a good deal of contention amongst statisticians and much discredit of the science of statistics. The appalling position can easily arise in which one can get any answer one wants if only one goes around to a large enough number of statisticians." (Frances Yates, "Discussion on the Paper by Dr. Box and Dr. Andersen", Journal of the Royal Statistical Society B Vol. 17, 1955)

"If two objects or human beings show similar behaviour in all their relevant aspects open to observation, the assumption of some unobservable hidden difference between them must be regarded as a completely gratuitous hypothesis and one contrary to sound scientific method." (John C Harsanyi, "Cardinal Welfare, Individualistic Ethics, and Interpersonal Comparisons of Utility", Journal of Political Economy vol. 63 (4), 1955)

"Is evolution a theory, a system or a hypothesis? It is much more: it is a general condition to which all theories, all hypotheses, all systems must bow and which they must satisfy henceforward if they are to be thinkable and true. Evolution is a light illuminating all facts, a curve that all lines must follow." (Pierre Teilhard de Chardin, "The Phenomenon of Man", 1955)

"Out of our image we predict the messages which will return to us as a result of our acts.  If this prediction is fulfilled the image is confirmed, if it is not fulfilled the image must be changed.  This is the essence of the logical-positivist view that definitions must be operational and hypotheses must be testable as an open system of a very different and much more complex character than that of the biological organism." (Kenneth E Boulding, "The Image: Knowledge in life and society", 1956)

"It was not simply a new theory of the nature of the celestial movements that was feared, but a new theory of the nature of theory; namely, that, if a hypothesis saves all the appearances, it is identical with truth." (Owen Barfield, "Saving the Appearances: A Study in Idolatry", 1957)

"Null hypotheses of no difference are usually known to be false before the data are collected [...] when they are, their rejection or acceptance simply reflects the size of the sample and the power of the test, and is not a contribution to science." (I Richard Savage, "Nonparametric statistics", Journal of the American Statistical Association 52, 1957)

"It is perhaps possible to distinguish two different aspects of numeracy […]. On the one hand is an understanding of the scientific approach to the study of phenomena - observation, hypothesis, experiment, verification. On the other hand, there is the need in the modern world to think quantitatively, to realise how far our problems are problems of degree even when they appear as problems of kind." (Sir Geoffrey Crowther, "A Report of the Central Advisory Committee for Education", 1959)

"Mathematics is neither a description of nature nor an explanation of its operation; it is not concerned with physical motion or with the metaphysical generation of quantities. It is merely the symbolic logic of possible relations, and as such is concerned with neither approximate nor absolute truth, but only with hypothetical truth. That is, mathematics determines what conclusions will follow logically from given premises. The conjunction of mathematics and philosophy, or of mathematics and science is frequently of great service in suggesting new problems and points of view." (Carl B Boyer, "The History of the Calculus and Its Conceptual Development", 1959)