By Donald W. Katzner
In plying their exchange, social scientists usually are faced with major phenomena that seem incapable of size. previous perform may recommend that how to take care of those circumstances is to paintings tougher at discovering applicable measures in order that commonplace quantitative research can nonetheless be utilized. Professor Katzner's strategy, notwithstanding is kind of varied. instead of targeting the development of measures, he increases the query of ways such phenomena will be investigated and understood within the absence of numerical gauges to symbolize them.
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Many concepts taken for granted here are described later in Part I. The reader who is interested in proofs and further development is referred to Pfanzagl  and Krantz et al. . Let A be a collection of objects and suppose some property such as longness orders the elements of A. 1). " It is p defined on A that is the underlying phenomenon to be, when possible, recorded by measurement. ) Note that p induces an equivalence relation on A that partitions A into a collection, A, of equivalence classes.
But the converse assertions do not hold. An operation is additive if it is associative, commutative, cancelable, and continuous in each variable separately. Because associativity and commutativity imply bisymmetry, additive operations are metrical. It, therefore, follows that if an additive operation is defined on A, it is permissible to add units on the representing scale/. Thus it is meaningful in terms of the underlying phenomenon to add a 3-inch length and a 6-inch length to obtain a 9-inch length.
Review of A Method and Its Application to Investment Activity, by J. Tinbergen, Economic Journal, 49 (1939):558-68. 29. Keynes, J. , Comment on "On a Method of Statistical Business-Cycle Research. A Reply," by J. Tinbergen, Economic Journal, 50 (1940): 154-6. 30. , Anti-Equilibrium (Amsterdam: North Holland, 1971). 31. Kuenne, R. , "Quality Space, Interproduct Competition, and General Equilibrium Theory," in R. E. , Monopolistic Competition Theory: Studies in Impact (New York: Wiley, 1967), pp.