On Theories (1900-1914)

"A mathematical theory is not to be considered complete until you have made it so clear that you can explain it to the first man whom you meet on the street." (David Hilbert [paraphrasing Joseph D Gergonne], "Mathematical Problems", 1900)

“One does not ask whether a scientific theory is true, but only whether it is convenient.” (Henri Poincaré, “La Science et l'Hypothèse”, 1902) 

“With the extension of mathematical knowledge will it not finally become impossible for the single investigator to embrace all departments of this knowledge? In answer let me point out how thoroughly it is ingrained in mathematical science that every real advance goes hand in hand with the invention of sharper tools and simpler methods which at the same time assist in understanding earlier theories and to cast aside some more complicated developments. It is therefore possible for the individual investigator, when he makes these sharper tools and simpler methods his own, to find his way more easily in the various branches of mathematics than is possible in any other science.” (David Hilbert. “Mathematical Problems”, Bulletin of the American Mathematical Society Vol. 8, 1902)

"But surely it is self-evident that every theory is merely a framework or scheme of concepts together with their necessary relations to one another, and that the basic elements can be constructed as one pleases." (Gottlob Frege, "On the Foundations of Geometry and Formal Theories of Arithmetic" , cca. 1903-1909)

"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)

"Order, wherever it reigns, brings beauty with it. Theory not only renders the group of physical laws it represents easier to handle, more convenient, and more useful, but also more beautiful." (Pierre-Maurice-Marie Duhem, "La théorie physique. Son objet, sa structure", 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)

"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)

"It [a theory] ought to furnish a compass which, if followed, will lead the observer further and further into previously unexplored regions. Whether these regions will be barren or fertile experience alone will decide; but, at any rate, one who is guided in this way will travel onward in a definite direction, and will not wander aimlessly to and fro." (Sir Joseph J Thomson, "The Corpuscular Theory of Matter", 1907)

"Generally speaking, mathematical theorems are no analytic judgements yet, but we can reduce them to analytic ones through the hypothetical addition of synthetic premises. The logically reduced mathematical theorems emerging in this way are analytically hypothetical judgements which constitute the logical skeleton of a mathematical theory." (Ernst Zermelo, "Mathematische Logik. Vorlesungen gehalten von Prof. Dr. E. Zermelo zu Göttingen im S.S.", 1908)

"Things and events explain themselves, and the business of thought is to brush aside the verbal and conceptual impediments which prevent them from doing so. Start with the notion that it is you who explain the Object, and not the Object that explains itself, and you are bound to end in explaining it away. It ceases to exist, its place being taken by a parcel of concepts, a string of symbols, a form of words, and you find yourself contemplating, not the thing, but your theory of the thing." (Lawrence P Jacks, "The Usurpation Of Language", 1910)

“The existence of analogies between central features of various theories implies the existence of a general theory which underlies the particular theories and unifies them with respect to those central features." (Eliakim H Moore, “Introduction to a Form of General Analysis”, 1910)

“The discovery which has been pointed to by theory is always one of profound interest and importance, but it is usually the close and crown of a long and fruitful period, whereas the discovery which comes as a puzzle and surprise usually marks a fresh epoch and opens a new chapter in science.” (Sir Oliver J Lodge, [Becquerel Memorial Lecture] Journal of the Chemical Society, Transactions 101 (2), 1912) 

"There is no great harm in the theorist who makes up a new theory to fit a new event. But the theorist who starts with a false theory and then sees everything as making it come true is the most dangerous enemy of human reason." (Gilbert K Chesterton, "The Flying Inn", 1914)