Sunday, October 28, 2018

Definition and Measurement in Physics

Peter Caws, in his essay, “Definition and Measurement in Physics,” (Measurement : Definitions and Theories; Edited by C. West Churchman and Philburn Ratoosh; 1959), looks at the differences between definition and measurement and the way in which they affect one another. He begins the essay with the remark, “Measurement presupposes something to be measured, and, unless we know what that something is, no measurement can have any significance.”

On page 3 and 4 of the essay, he writes:  “Definition and measurement certainly have functional similarities which make it almost inevitable that a discussion of one should sooner or later involve the other. They both have the character of leading to relations which set the entities of science in order with respect to one another. The kinds of order that they establish can be broadly differentiated, but they run together in many cases, so that there are times when the two procedures seem to amount almost to the same thing. Definition, in general, is concerned with the systematic order of the conceptual schemes of science, and with nature of the relations between different entities. Measurement has a more limited function, that of establishing metrical order among different manifestations of particular properties, and of making scientific events amenable to mathematical description. Often the relation between different properties is not clear unless measurements have been carried out on both in some case where they appear together; nowadays much definition is expressed in a mathematical form which presupposes measurement.”

On page 5, he comes close to suggesting that definition and measurement can be the same: “Definition requires the replacement of one symbol in an expression by another symbol or symbols; measurement requires the replacement of a symbol by a number, itself also a symbol. It is not far from this point to an identification of the two processes.” But in rest of the essay he goes on to distinguish definition from measurement.

On page 16, he notes the important role that measurement (of any kind) plays in the formation of the concepts that we hold in our mind: “The mind inevitably organizes units, thing like concepts, on which relations converge. Confronted with unrelated sense data, it creates the category “thing”; confronted with scientific data, it creates the category “construct.” The construct is not a visual image, nor is it external to the mind; it is analogous to a piece in a game which thought plays. Chess requires not only rules but also men, and physics requires not only laws but also constructs. One could change the rules in chess, yet still play with the same men; and similarly it is not always necessary to replace the old intuitive construct with a new, rigidly formalized one, even if a new technique of measurement appears, as long as one understands the new relations into which it enters.” 

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