On Concepts VII

"All human knowledge begins with intuitions, proceeds from thence to concepts, and ends with ideas." (Immanuel Kant, "Critique of Pure Reason", 1781)

"Common sense […] may be thought of as a series of concepts and conceptual schemes which have proved highly satisfactory for the practical uses of mankind. Some of those concepts and conceptual schemes were carried over into science with only a little pruning and whittling and for a long time proved useful. As the recent revolutions in physics indicate, however, many errors can be made by failure to examine carefully just how common sense ideas should be defined in terms of what the experimenter plans to do." (James B Conant, "Science and Common Sense", 1951)

"A collection of observable concepts in a purely formal hypothesis suggesting no analogy with anything would consequently not suggest either any directions for its own development." (Mary B Hesse, "Operational Definition and Analogy in Physical Theories", British Journal for the Philosophy of Science 2 (8), 1952)

"In general, we mean by any concept nothing more than a set of operations; the concept is synonymous with the corresponding set of operations." (Percy W. Bridgman, "The Logic of Modern Physics", 1960)

"For a physicist mathematics is not just a tool by means of which phenomena can be calculated, it is the main source of concepts and principles by means of which new theories can be created." (Freeman J Dyson, "Mathematics in the Physical Sciences", Scientific American, 1964)

"Every rule has its limits, and every concept its ambiguities. Most of all is this true in the science of life, where nothing quite corresponds to our ideas; similar ends are reached by varied means, and no causes are simple." (Lancelot L Whyte, "Internal Factors in Evolution", 1965)

"The concepts of science, in all their richness and ambiguity, can be presented without any compromise, without any simplification counting as distortion, in language accessible to all intelligent people." (Stephen J Gould, "Wonderful Life: The Burgess Shale and the Nature of History", 1990)

"For strictly scientific or technological purposes all this is irrelevant. On a pragmatic view, as on a religious view, theory and concepts are held in faith. On the pragmatic view the only thing that matters is that the theory is efficacious, that it ‘works’ and that the necessary preliminaries and side issues do not cost too much in time and effort. Beyond that, theory and concepts go to constitute a language in which the scientistic matters at issue can be formulated and discussed." (Bertram N Brockhouse, [lecture] 1994)

"At every major step physics has required, and frequently stimulated, the introduction of new mathematical tools and concepts. Our present understanding of the laws of physics, with their extreme precision and universality, is only possible in mathematical terms." (Michael F Atiyah, 2005)

"In the world of human thought generally, and in physical science particularly, the most important and fruitful concepts are those to which it is impossible to attach a well-defined meaning." (Hendrik A Kramers)