"In every physical science we have carefully to distinguish between the facts which form its subject-matter and the theories by which we attempt to explain these facts, and group them in our scientific systems." (Josiah P Cooke, "The New Chemistry", 1876)
"There is a maxim which is often quoted, that ‘The same causes will always produce the same effects.’ To make this maxim intelligible we must define what we mean by the same causes and the same effects, since it is manifest that no event ever happens more that once, so that the causes and effects cannot be the same in all respects. [...] There is another maxim which must not be confounded with that quoted at the beginning of this article, which asserts ‘That like causes produce like effects’. This is only true when small variations in the initial circumstances produce only small variations in the final state of the system. In a great many physical phenomena this condition is satisfied; but there are other cases in which a small initial variation may produce a great change in the final state of the system, as when the displacement of the ‘points’ causes a railway train to run into another instead of keeping its proper course." (James C Maxwell, "Matter and Motion", 1876)
"Science is the systematic classification of experience." (George H Lewes, "The Physical Basis of Mind", 1877)
"The very genius of the common geometry as a method of reasoning - a system of investigation - is, that it is but a series of observations. The figure being before the eye in actual representation, or before the mind in conception, is so closely scrutinized, that all its distinctive features are perceived; auxiliary lines are drawn (the imagination leading in this), and a new series of inspections is made; and thus, by means of direct, simple observations, the investigation proceeds." (Edward Olney, "Mathematics", The Cyclopedia of Education, 1877)
"As long as the training of a naturalist enables him to trace the action only of a particular material system, without giving him the power of dealing with the general properties of all such systems, he must proceed by the method so often described in histories of science - he must imagine model after model of hypothetical apparatus, till he finds one which will do the required work. If this apparatus should afterwards be found capable of accounting for many of the known phenomena, and not demonstrably inconsistent with any of them, he is strongly tempted to conclude that his hypothesis is a fact, at least until an equally good rival hypothesis has been invented." (James C Maxwell, "Tait’s Thermodynamics", Nature Vol. XVII (431), 1878)
"It is very different to make a practical system and to introduce it. A few experiments in the laboratory would prove the practicability of system long before it could be brought into general use." (Thomas Edison, 1879)
"Science, while it penetrates deeply the system of things about us, sees everywhere, in the dim limits of vision, the word mystery." (James D Dana, "Corals and Coral Islands", 1879)
"[…] not only a knowledge of the ideas that have been accepted and cultivated by subsequent teachers is necessary for the historical understanding of a science, but also that the rejected and transient thoughts of the inquirers, nay even apparently erroneous notions, may be very important and very instructive. The historical investigation of the development of a science is most needful, lest the principles treasured up in it become a system of half-understood prescripts, or worse, a system of prejudices." (Ernst Mach, "The Science of Mechanics", 1883)
"The easiest and surest way of acquiring facts is to learn them in groups, in systems, and systematized knowledge is science. You can very often carry two facts fastened together more easily than one by itself, as a house-maid can carry two pails of water with a hoop more easily than one without it." (Oliver W Holmes, "Medical Essays", 1883)
"Since a given system can never of its own accord go over into another equally probable state but into a more probable one, it is likewise impossible to construct a system of bodies that after traversing various states returns periodically to its original state, that is a perpetual motion machine." (Ludwig Boltzmann, "The Second Law of Thermodynamics", [Address to a Formal meeting of the Imperial Academy of Science], 1886)
"Science is a match that man has just got alight. He thought he was in a room - in moments of devotion, a temple - and that his light would be reflected from and display walls inscribed with wonderful secrets and pillars carved with philosophical systems wrought into harmony. It is a curious sensation, now that the preliminary splutter is over and the flame burns up clear, to see his hands and just a glimpse of himself and the patch he stands on visible, and around him, in place of all that human comfort and beauty he anticipated - darkness still." (Herbert G Wells, "The Rediscovery of the Unique", The Fortnightly Review, 1891)
"In every symmetrical system every deformation that tends to destroy the symmetry is complemented by an equal and opposite deformation that tends to restore it. […] One condition, therefore, though not an absolutely sufficient one, that a maximum or minimum of work corresponds to the form of equilibrium, is thus applied by symmetry." (Ernst Mach, "The Science of Mechanics: A Critical and Historical Account of Its Development", 1893)
"Society is not a mere sum of individuals. Rather, the system formed by their association represents a specific reality which has its own characteristics. [...] The group thinks, feels, and acts quite differently from the way in which its members would were they isolated. If, then, we begin with the individual, we shall be able to understand nothing of what takes place in the group." (Émile Durkheim, "The Rules of Sociological Method", 1895)
"An act cannot be defined by the end sought by the actor, for an identical system of behaviour may be adjustable to too many different ends without altering its nature." (Émile Durkheim, "Suicide: A Study in Sociology", 1897)
"Certainly, if a system moves under the action of given forces and its initial conditions have given values in the mathematical sense, its future motion and behavior are exactly known. But, in astronomical problems, the situation is quite different: the constants defining the motion are only physically known, that is with some errors; their sizes get reduced along the progresses of our observing devices, but these errors can never completely vanish." (Jacques Hadamard, "Les surfaces à courbures opposées et leurs lignes géodésiques", Journal de mathématiques pures et appliqués 5e (4), 1898)
"The ordinary logic has a great deal to say about genera and species, or in our nineteenth century dialect, about classes. Now a class is a set of objects compromising all that stand to one another in a special relation of similarity. But where ordinary logic talks of classes the logic of relatives talks of systems. A system is a set of objects compromising all that stands to one another in a group of connected relations. Induction according to ordinary logic rises from the contemplation of a sample of a class to that of a whole class; but according to the logic of relatives it rises from the contemplation of a fragment of a system to the envisagement of the complete system." (Charles S Peirce, "Cambridge Lectures on Reasoning and the Logic of Things: Detached Ideas on Vitally Important Topics", 1898)
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