ABSTRACT
Everyone is aware that measurement is a cornerstone of science, one that in some cases is highly controversial. Much complex technology underlies the refined measurement of certain physical quantities, some of which can be estimated to surprisingly large numbers of significant figures; one of the more elaborate businesses spawned by the social sciences, a business that affects all of our lives, attempts to measure intellectual ability and/or achievement; and elaborate computer programs are widely used to provide numerical representations (and simplifications), e.g., by factor analysis and multidimensional scaling, of complexes of data. Behind all of this activity is a belief, often sustained by a mixture of intuition and successful–if ill understood–procedures, that certain bodies of data can be represented in some fashion by numbers and their relations to each other. The goal of the semiphilosophical, semimathematical field of our title is to lay bare the types of empirical structures that admit such numerical representations.
