On Hypotheses (1890-1899)

"All true science deals with speculation and hypothesis, and acknowledges as its most valued servant - its indispensable ally and helpmeet - that which our German friends l call 'Phantasie' and we 'the Imagination'." (E Ray Lankester, "The Advancement of Science", 1890)

"Nature, it has been said, gives no reply to a general inquiry - she must be interrogated by questions which already contain the answer she is to give; in other words, the observer can only observe that which he is led by hypothesis to look for: the experimenter can only obtain the result which his experiment is designed to obtain." (Ray Lankester, "The Advancement of Science", 1890)

"The history of thought should warn us against concluding that because the scientific theory of the world is the best that has yet been formulated, it is necessarily complete and final. We must remember that at bottom the generalizations of science or, in common parlance, the laws of nature are merely hypotheses devised to explain that ever-shifting phantasmagoria of thought which we dignify with the high-sounding names of the world and the universe." (Sir James G Frazer, "The Golden Bough: A Study in Magic and Religion", 1890)

"Every hypothesis must derive indubitable results from mechanically well-defined assumptions by mathematically correct methods." (Ludwig Boltzmann, "Certain Questions of the Theory of Gasses", Nature Vol. 51 (1322), 1895) 

"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)

"If men of science owe anything to us, we may learn much from them that is essential. For they can show how to test proof, how to secure fulness and soundness in induction, how to restrain and to employ with safety hypothesis and analogy." (Lord John Acton, [Lecture] "The Study of History", 1895)

"If the working hypothesis fails in any essential particular he [the scientist] is ready to modify or discard it. For the truly inspired investigator, one undoubted fact weighs more in the balance than a thousand theories." (James M Baldwin, "The Processes of Life Revealed by the Microscope: A Plea for Physiological Histology", Science N.S. Vol. 2 (34), 1895)

"The first step, whenever a practical problem is set before a mathematician, is to form the mathematical hypothesis. It is neither needful nor practical that we should take account of the details of the structure as it will exist. We have to reason about a skeleton diagram in which bearings are reduced to points, pieces to lines, etc. and [in] which it is supposed that certain relations between motions are absolutely constrained, irrespective of forces. Some writers call such a hypothesis a fiction, and say that the mathematician does not solve the real problem, but only a fictitious one. That is one way of looking at the matter, to which I have no objection to make: only, I notice, that in precisely the same sense in which the mathematical hypothesis is 'false', so also is this statement 'false', that it is false. Namely, both representations are false in the sense that they omit subsidiary elements of the fact, provided that element of the case can be said to be subsidiary which those writers overlook, namely, that the skeleton diagram is true in the only sense in which from the nature of things any mental representation, or understanding, of the brute existent can be true. For every possible conception, by the very nature of thought, involves generalization; now generalization omits, means to omit, and professes to omit, the differences between the facts generalized." (Charles S Peirce, "Report on Live Loads", cca. 1895)

"In scientific investigations, it is permitted to invent any hypothesis and, if it explains various large and independent classes of facts, it rises to the ranks of a well-grounded theory." (Charles Darwin, "The Variations of Animals and Plants Under Domestication" Vol. 1, 1896)

"It is a great mistake to suppose that the mind of the active scientist is filled with pro-positions which, if not proved beyond all reasonable cavil, are at least extremely probable. On the contrary, he entertains hypotheses which are almost wildly incredible, and treats them with respect for the time being. Why does he do this? Simply because any scientific proposition whatever is always liable to be refuted and dropped at short notice. A hypothesis is something which looks as if it might be true and were true, and which is capable of verification or refutation by comparison with facts. The best hypothesis, in the sense of the one most recommending itself to the inquirer, is the one which can be the most readily refuted if it is false." (Charles S Peirce, 1896)

"Mathematics is the most abstract of all the sciences. For it makes no external observations, nor asserts anything as a real fact. When the mathematician deals with facts, they become for him mere ‘hypotheses’; for with their truth he refuses to concern himself. The whole science of mathematics is a science of hypotheses; so that nothing could be more completely abstracted from concrete reality." (Charles S Peirce, "The Regenerated Logic", The Monist Vol. 7 (1), 1896)

"Everything in physical science, from the law of gravitation to the building of bridges, from the spectroscope to the art of navigation, would be profoundly modified by any considerable inaccuracy in the hypothesis that our actual space is Euclidean. The observed truth of physical science, therefore, constitutes overwhelming empirical evidence that this hypothesis is very approximately correct, even if not rigidly true." (Bertrand Russell, "Foundations of Geometry", 1897)

"To use an old analogy - and here we can hardly go except upon analogy - while the building of Nature is growing spontaneously from within, the model of it, which we seek to construct in our descriptive science, can only be constructed by means of scaffolding from without, a scaffolding of hypotheses. While in the real building all is continuous, in our model there are detached parts which must be connected with the rest by temporary ladders and passages, or which must be supported till we can see how to fill in the understructure. To give the hypotheses equal validity with facts is to confuse the temporary scaffolding with the building itself." (John H Poynting, 1899)