"All followers of the axiomatic method and most mathematicians think that there is some such thing as an absolute ‘mathematical rigor’ which has to be satisfied by any deduction if it is to be valid. The history of mathematics shows that this is not the case, that, on the contrary, every generation is surpassed in rigor again and again by its successors." (Richard von Mises, "Positivism: A Study in Human Understanding", 1951)
"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)
"Rigor is to the mathematician what morality is to man. It does not consist in proving everything, but in maintaining a sharp distinction between what is assumed and what is proved, and in endeavoring to assume as little as possible at every stage." (André Weil, Mathematical Teaching in Universities", The American Mathematical Monthly Vol. 61 (1), 1954)
"[…] no branch of mathematics competes with projective geometry in originality of ideas, coordination of intuition in discovery and rigor in proof, purity of thought, logical finish, elegance of proofs and comprehensiveness of concepts. The science born of art proved to be an art." (Morris Kline,"Projective Geometry", Scientific America Vol. 192 (1), 1955)
"The well-known virtue of the experimental method is that it brings situational variables under tight control. It thus permits rigorous tests of hypotheses and confidential statements about causation. The correlational method, for its part, can study what man has not learned to control. Nature has been experimenting since the beginning of time, with a boldness and complexity far beyond the resources of science. The correlator’s mission is to observe and organize the data of nature’s experiments." (Lee J Cronbach, "The Two Disciplines of Scientific Psychology", The American Psychologist Vol. 12, 1957)
"Two qualifications of this observation are in order, First, it is by no means true that every ‘open system’ is able to exhibit equifinality. ‘Equifinality’ as a property of all open systems has never been rigorously defined. If one assumes a rigorous definition in terms of a unique steady state, then, of course, this is realizable only on paper […]" (Joseph M Yoffey, "Homeostatic Mechanisms", 1958)
"With the idol of certainty (including that of degrees of imperfect certainty or probability) there falls one of the defences of obscurantism which bar the way of scientific advance. For the worship of this idol hampers not only the boldness of our questions, but also the rigor and the integrity of our tests. The wrong view of science betrays itself in the craving to be right; for it is not his possession of knowledge, of irrefutable truth, that makes the man of science, but his persistent and recklessly critical quest for truth. (Karl R Popper, "The Logic of Scientific Discovery", 1959)
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