As is known, scientific physics dates its existence from the discovery of the differential calculus. Only when it was learned how to follow continuously the course of natural events, attempts, to construct by means of abstract conceptions the connection between phenomena, met with success. To do this two things are necessary: First, simple fundamental concepts with which to construct; second, some method by which to deduce, from the simple fundamental laws of the construction which relate to instants of time and points in space, laws for finite intervals and distances, which alone are accessible to observation.
Bernhard RiemannRelated topics
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The success of mathematical physics led the social scientist to be jealous of its power without quite understanding the intellectual attitudes that had contributed to this power. The use of mathematical formulae had accompanied the development of the natural sciences and become the mode in the social sciences. Just as primitive peoples adopt the Western modes of denationalized clothing and of parliamentatism out of a vague feeling that these magic rites and vestments will at once put them abreast of modern culture and technique, so the economists have developed the habit of dressing up their rather imprecise ideas in the language of the infinitesimal calculus.
Norbert Wiener
The will is the living principle of the rational soul, is indeed itself reason, when purely and simply apprehended. That reason is itself active, means, that the pure will, as such, rules and is effectual. The infinite reason alone lies immediately and entirely in the purely spiritual order. The finite being lives necessarily at the same time in a sensuous order; that is to say, in one which presents to him other objects than those of pure reason; a material object, to be advanced by instruments and powers, standing indeed under the immediate command of the will, but whose efficacy is conditional also on its own natural laws.
Johann Gottlieb Fichte
Heisenberg finds that facts of observation lead uniquely and inevitably to the theoretical structure known as matrix mechanics. This shows that the total radiation in any region of empty space can change only by a single complete quantum at a time. Thus not only in the photo-electric phenomenon, but in all other transfers of energy through space, energy is always transferred by complete quanta; fractions of a quantum can never occur. This brings atomicity into our picture of radiation just as definitely as the discovery of the electron and its standard charge brought atomicity into our picture of matter and of electricity.
James Jeans
The attempt to construct a fundamental taxonomy of the sciences encounters great difficulties. For instance, logicians and mathematicians disagree among themselves about the objects of their respective research; there is no agreement on the relation of theoretical physics to empirical knowledge and to mathematics. The so-called social sciences are particularly difficult to classify. They have not been demarcated by systematic considerations. In Duhem and Poincarè, general considerations are not only exemplified, but the origins of the concepts and of the problems are traced right from the initial observation of facts if at all possible.
Otto Neurath
You are no doubt aware that the Almighty, desiring to lead us to perfection and to improve our state of society, has revealed to us laws which are to regulate our actions. These laws, however, presuppose an advanced state of intellectual culture. We must first form a conception of the Existence of the Creator according to our capabilities; that is, we must have a knowledge of Metaphysics. But this discipline can only be approached after the study of Physics: for the science of Physics borders on Metaphysics, and must even precede it in the course of our studies, as is clear to all who are familiar with these questions.
Maimonides
