By Joel Michell

This booklet strains how this kind of probably immutable concept as dimension proved so arguable while it collided with the subject material of psychology. This ebook addresses philosophical and social affects (such as scientism, practicalism, and Pythagoreanism) reshaping the idea that of size and identifies a basic challenge on the center of this reshaping: the problem of no matter if mental attributes particularly are quantitative. the writer argues that the belief of size now recommended inside psychology truly subverts makes an attempt to set up a certainly quantitative technological know-how, and he urges a brand new course. This quantity relates perspectives on size by means of thinkers corresponding to Hölder, Russell, Campbell, and Nagel to prior perspectives, like these of Euclid and Oresme. in the heritage of psychology, it considers contributions via Fechner, Cattell, Thorndike, Stevens and Suppes, between others. It additionally features a nontechnical exposition of conjoint size conception and up to date foundational paintings by way of best dimension theorist R. Duncan Luce. This thought-provoking publication can be really valued through researchers within the fields of mental historical past and philosophy of technological know-how.

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The idea is that there must be some physical  operation for combining objects possessing the relevant attribute, the result of which depends only upon the magnitudes of the relevant attribute possessed by those  gadgets. But, if the relationship between the magnitude of the outcome and the magnitudes of the objects combined is analogous to numerical addition and if the  magnitude of the outcome depends only upon the magnitudes of the objects combined, then the formal similarity between the physical operation and numerical addition  must derive from relations between the magnitudes. This is what 'only' means here. That is, Campbell's view entailed that the additivity of magnitudes is fundamental to  understanding the physical operation of addition between objects. If there were no additive relations between magnitudes, the idea of the outcome of the physical  operation depending only upon the magnitudes combined would have no content. Once this is recognised, it is clear that there is at least the logical possibility of detecting additive relations between magnitudes in ways other than by the obvious, direct  methods applying to fundamental measurement. Campbell was clearly deflected from considering this because he attended only to physical measurement, but his failure  to consider the issue is puzzling, given that he considered derived measurement and that he thought of fundamental and derived magnitudes as quantities in the same  feel. It is a very small step from this insight to the recognition of derived measurement as an indirect identification of underlying quantitative additivity. The reason he  failed to take this step, I believe, was because he emphasised epistemological issues at the expense of ontological ones. While he did have something like the classical  concept of quantity in the background,    Page 127 influencing his understanding of measurement and guiding his attempt to construct a representational theory, this underlying concept of quantity was never explicitly  stated. Instead, his theory of measurement remained a theory about how quantitative attributes are detected and never considered what quantitative attributes  are. Later representationalists (e. g. , Stevens, 1951) criticised Campbell because he confined measurement to just the numerical representation of operations of physical  addition. Campbell had his reasons. First, he thought of measurement as the numerical representation of quantities, but mistakenly thought that the only evidence for  quantity was via the discovery of operations of physical addition. Even if it was wrong on that point, there was some sense to his position. If measurement is the  numerical representation of quantity, then it is going to be the representation of additive systems exclusively. Had he developed his implicit concept of quantity, he  would have reinvented the classical concept. Second, non­additive structures (e. g. , purely classificatory or ordinal attributes) can be adequately represented by numerals.

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