Alternative combining operations in extensive measurement

Philosophy of Science 65 (1):136-150 (1998)
Abstract
This paper concerns the ways in which one can/cannot combine extensive quantities. Given a particular theory of extensive measurement, there can be no alternative ways of combining extensive quantities, where 'alternative' means that one combining operation can be used instead of another causing only a change in the number assigned to the quantity. As a consequence, rectangular concatenation cannot be an alternative combining operation for length as was suggested by Ellis and agreed by Krantz, Luce, Suppes, and Tversky. I argue as well that a theory which imposes such restrictions on the combining operation is more desirable than less stringent rival theories
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