To investigate mechanisms of rational representation, I consider construction of an ordered continuum of psychophysical scale of magnitude of sensation; counting mechanism leading to an approximate numerosity scale for integers; and conjoint measurement structure pitting the denominator against the numerator in tradeoff positions. Number sense of resulting rationals is neither intuitive nor expedient in their manipulation.

Of S. S. Stevens's well-known classification of nominal, ordinal, interval and ratio ‘scales of measurement’, perhaps its least-known aspect is its most distinctive, namely the distinction between interval and ratio scales. This article investigates the circumstances of the typology's origins among the experimental psychologists at Harvard in the 1930s and the unique fusion of personal, technical and intellectual forces this setting represented. It shows how it came to be that an influential psychologist reconceptualized measurement from first principles in such a (...) way as to both preserve the distinction between psychology and physics in this regard and yet implicitly classify his own work as the latter. The article concludes with the general suggestion that, if it is necessary to measure something, it might as well be something tangible enough to be measured usefully. (shrink)

This article examines how experimental psychology experienced a revolution as cognitive science replaced behaviorism in the mid-20th century. This transition in the scientific account of human nature involved making normal what had once been normative: borrowing ideas of democratic thinking from political culture and conceptions of good thinking from philosophy of science to describe humans as active, creatively thinking beings, rather than as organisms that simply respond to environmental conditions. Reflexive social and intellectual practices were central to this process as (...) cognitive scientists used anti-positivist philosophy of science simultaneously to justify their own work as valid and also as a model of human thinking. In the process, the normative philosophy of science or ‘good academic thinking’ that cognitive scientists used to reshape the discipline of psychology and characterize themselves became, at the same time, the descriptive model of human nature. (shrink)

In our target article, we argued that the number sense represents natural and rational numbers. Here, we respond to the 26 commentaries we received, highlighting new directions for empirical and theoretical research. We discuss two background assumptions, arguments against the number sense, whether the approximate number system represents numbers or numerosities, and why the ANS represents rational numbers.