"Scientific facts are of little value in themselves. Their significance is their bearing upon other facts, enabling us to generalize and so to discover principles, just as the accurate measurement of the position of a star may be without value in itself, but in relation to other similar measurement of other stars may become the means of discovering their proper motions. We refine our instruments; we render more trustworthy our means of observation we extend our range of experimental inquiry, and thus lay the foundation for the future work, with the full knowledge that, although our researches can not extend beyond certain limits, the field itself is, even within those limits, inexhaustible." (Elihu Thompson, "The Field of Experimental Research", 1901)
"Treatises on mechanics do not clearly distinguish between what is experiment, what is mathematical reasoning, what is convention, and what is hypothesis." (Henri Poincaré, "Science and Hypothesis", 1901)
"We see that experience plays an indispensable role in the genesis of geometry; but it would be an error thence to conclude that geometry is, even in part, an experimental science. If it were experimental it would be only approximative and provisional. And what rough approximation!" (Henri Poincaré, "Science and Hypothesis", 1901)
"Experiment is the sole source of truth. It alone can teach us something new; it alone can give us certainty." (Henri Poincaré,"Science and Hypothesis", 1902)
"It has been said that no science is established on a firm basis unless its generalisations can be expressed in terms of number, and it is the special province of mathematics to assist the investigator in finding numerical relations between phenomena. After experiment, then mathematics. While a science is in the experimental or observational stage, there is little scope for discerning numerical relations. It is only after the different workers have 'collected data' that the mathematician is able to deduce the required generalisation." (Joseph W Mellor, "Higher Mathematics for Students of Chemistry and Physics', 1902)
"The laws of thermodynamics, as empirically determined, express the approximate and probable behavior of systems of a great number of particles, or, more precisely, they express the laws of mechanics for such systems as they appear to beings who have not the fineness of perception to enable them to appreciate quantities of the order of magnitude of those which relate to single particles, and who cannot repeat their experiments often enough to obtain any but the most probable results." (Josiah W Gibbs, "Elementary Principles in Statistical Mechanics", 1902)
"Chemistry and physics are experimental sciences; and those who are engaged in attempting to enlarge the boundaries of science by experiment are generally unwilling to publish speculations; for they have learned, by long experience, that it is unsafe to anticipate events. It is true, they must make certain theories and hypotheses. They must form some kind of mental picture of the relations between the phenomena which they are trying to investigate, else their experiments would be made at random, and without connection." (William Ramsay, "Radium and Its Products", Harper’s Magazine, 1904)
"The mathematical formula is the point through which all the light gained by science passes in order to be of use to practice; it is also the point in which all knowledge gained by practice, experiment, and observation must be concentrated before it can be scientifically grasped. The more distant and marked the point, the more concentrated will be the light coming from it, the more unmistakable the insight conveyed. All scientific thought, from the simple gravitation formula of Newton, through the more complicated formulae of physics and chemistry, the vaguer so called laws of organic and animated nature, down to the uncertain statements of psychology and the data of our social and historical knowledge, alike partakes of this characteristic, that it is an attempt to gather up the scattered rays of light, the different parts of knowledge, in a focus, from whence it can be again spread out and analyzed, according to the abstract processes of the thinking mind. But only when this can be done with a mathematical precision and accuracy is the image sharp and well-defined, and the deductions clear and unmistakable. As we descend from the mechanical, through the physical, chemical, and biological, to the mental, moral, and social sciences, the process of focalization becomes less and less perfect, - the sharp point, the focus, is replaced by a larger or smaller circle, the contours of the image become less and less distinct, and with the possible light which we gain there is mingled much darkness, the sources of many mistakes and errors. But the tendency of all scientific thought is toward clearer and clearer definition; it lies in the direction of a more and more extended use of mathematical measurements, of mathematical formulae. (John T Merz, "History of European Thought in the 19th Century" Vol. 1, 1904)
"A physical theory is not an explanation. It is a system of mathematical propositions, deduced from a small number of principles, which aim to represent as simply, as completely, and as exactly as possible a set of experimental laws. […] Thus a true theory is not a theory which gives an explanation of physical appearances in conformity with reality; it is a theory which represents in a satisfactory manner a group of experimental laws. A false theory is not an attempt at an explanation based on assumptions contrary to reality; it is a ·group of propositions which do not agree with the experimental laws. Agreement with experiment is the sole criterion of truth for a physical theory." (Pierre-Maurice-Marie Duhem, "La théorie physique. Son objet, sa structure", 1906)
"It is best to prove things by actual experiment; then you know; whereas if you depend on guessing and supposing and conjecturing, you will never get educated." (Samuel L Clemens [Mark Twain], "Eve’s Diary", 1906)
"[...] the aim of physical theory is to become a natural classification, to establish among diverse experimental laws a logical coordination serving as a sort of image and reflection of the true order according to which the realities escaping us are organized." (Pierre-Maurice-Marie Duhem, "La théorie physique. Son objet, sa structure", 1906)
"The physicist can never subject an isolated hypothesis to experimental test, but only a whole group of hypotheses." (Pierre Duhem, "The Aim and Structure of Physical Theory", 1906)
"Theory is not solely an economical representation of experimental laws; it is also a classification of these laws. […] theory, by developing the numerous ramifications of the deductive reasoning which connects principles to experimental laws, establishes an order and a classification among these laws. It brings some laws together, closely arranged in the same group; it separates some of the others by placing them in two groups very far apart. Theory gives, so to speak, the table of contents and the chapter headings under which the science to be studied will be methodically divided, and it indicates the laws which are to be arranged under each of these chapters." (Pierre-Maurice-Marie Duhem, "La théorie physique. Son objet, sa structure", 1906)
"Thus, physical theory never gives us the explanation of experimental laws; it never reveals realities hiding under the sensible appearances; but the more complete it becomes, the more we apprehend that the logical order in which theory orders experimental laws is the reflection of an ontological order, the more we suspect that the relations it establishes among the data of observation correspond to real relations among things, and the more we feel that theory tends to be a natural classification." (Pierre-Maurice-Marie Duhem, "La théorie physique. Son objet, sa structure", 1906)
"From the point of view of the physicist, a theory of matter is a policy rather than a creed; its object is to connect or co-ordinate apparently diverse phenomena, and above all to suggest, stimulate and direct experiment. It ought to furnish a compass which, if followed, will lead to observer further and further into previously unexplored regions." (Sir Joseph J Thomson, "The Corpuscular Theory of Matter", 1907)
"The sole purpose of physical theory is to provide a representation and classification of experimental laws; the only test permitting us to judge a physical theory and pronounce it good or bad is the comparison between the consequences of this theory and the experimental laws it has to represent and classify." (Pierre-Maurice-Marie Duhem,"The Aim and Structure of Physical Theory", 1908)
"If the number of experiments be very large, we may have precise information as to the value of the mean, but if our sample be small, we have two sources of uncertainty: (I) owing to the 'error of random sampling' the mean of our series of experiments deviates more or less widely from the mean of the population, and (2) the sample is not sufficiently large to determine what is the law of distribution of individuals." (William S Gosset, "The Probable Error of a Mean", Biometrika, 1908)
"[...] physics makes progress because experiment constantly causes new disagreements to break out between laws and facts, and because physicists constantly touch up and modify laws in order that they may more faithfully represent the facts." (Pierre-Maurice-Marie Duhem, "The Aim and Structure of Physical Theory", 1908)
"A mind exclusively bent upon the idea of utility necessarily narrows the range of the imagination. For it is the imagination which pictures to the inner eye of the investigator the indefinitely extending sphere of the possible, - that region of hypothesis and explanation, of underlying cause and controlling law. The area of suggestion and experiment is thus pushed beyond the actual field of vision." (John G Hibben, "The Paradox of Research", The North American Review 188 (634), 1908)
"A physical theory is not an explanation. It is a system of mathematical propositions, deduced from a small number of principles, which aim [...] to represent as simply, as completely, and as exactly as possible a group of experimental laws." (Pierre-Maurice-Marie Duhem,"The Aim and Structure of Physical Theory", 1908)
"But, once again, what the physical states as the result of an experiment is not the recital of observed facts, but the interpretation and the transposing of these facts into the ideal, abstract, symbolic world created by the theories he regards as established." (Pierre-Maurice-Marie Duhem, "The Aim and Structure of Physical Theory", 1908)
"If the aim of physical theories is to explain experimental laws, theoretical physics is not an autonomous science; it is subordinate to metaphysics." (Pierre-Maurice-Marie Duhem, "The Aim and Structure of Physical Theory", 1908)
"It is impossible to follow the march of one of the greatest theories of physics, to see it unroll majestically its regular deductions starting from initial hypotheses, to see its consequences represent a multitude of experimental laws down to the smallest detail, without being charmed by the beauty of such a construction, without feeling keenly that such a creation of the human mind is truly a work of art." (Pierre-Maurice-Marie DuhemDuhem, "The Aim and Structure of Physical Theory", 1908)
"Physics makes progress because experiment constantly causes new disagreements to break out between laws and facts, and because physicists constantly touch up and modify laws in order that they may more faithfully represent the facts." (Pierre-Maurice-Marie Duhem,"The Aim and Structure of Physical Theory", 1908)
"The sole purpose of physical theory is to provide a representation and classification of experimental laws; the only test permitting us to judge a physical theory and pronounce it good or bad is the comparison between the consequences of this theory and the experimental laws it has to represent and classify." (Pierre-Maurice-Marie Duhem,"The Aim and Structure of Physical Theory", 1908)
"The views of space and time which I wish to lay before you have sprung from the soil of experimental physics, and therein lies their strength. They are radical. Henceforth, space by itself, and time by itself, are doomed to fade away into mere shadows, and only a kind of union of the two will preserve an independent reality." (Hermann Minkowski, "Space and Time", [Address to the 80th Assembly of German Natural Scientists and Physicians] 1908)
"An experiment is an observation that can be repeated, isolated and varied. The more frequently you can repeat an observation, the more likely are you to see clearly what is there and to describe accurately what you have seen. The more strictly you can isolate an observation, the easier does your task of observation become, and the less danger is there of your being led astray by irrelevant circumstances, or of placing emphasis on the wrong point. The more widely you can vary an observation, the more clearly will be the uniformity of experience stand out, and the better is your chance of discovering laws." (Edward B Titchener, "A Text-Book of Psychology", 1909)
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