Historians of psychology, notably Boring, fostered Fechner's idea that Weber's law is the indispensable basis for the derivation of the logarithmic psychophysical law. However, it is shown here that Bernoulli in 1738 and Thurstone in 1931 derived the logarithmic law using principles other than Weber's law and that Fechner and Thurstone based their derivations on the principles originally employed by Bernoulli. It is concluded that awareness of researchers about Bernoulli's and Thurstone's derivations could expand the directions of research on the form of the psychophysical law. (c) 2009 Wiley Periodicals, Inc.

Historians acknowledge Euclid and Fechner, respectively, as the founders of classical geometry and classical psychophysics. At all times, their ideas have been reference points and have shared the same destiny of being criticized, corrected, and even radically rejected, in their theoretical and methodological aspects and in their epistemological value. According to a model of measurement of magnitudes which goes back to Euclid, Fechner (1860) developed a theory for psychical magnitudes that opened a lively debate among numerous scholars. Fechner's attempt to apply the model proposed by Euclid to subjective sensation magnitudes--and the debate that followed--generated ideas and concepts that were destined to have rich developments in the psychological and (more generally) scientific field of the twentieth century and that still animate current psychophysics.

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A study of the interactions between mathematics and cognitive science, carried out within a historical perspective, is important for a better understanding of mathematics education in the present. This is evident when analysing the contribution made by the epistemological theories of Ernst Mach. On the basis of such theories, a didactic method was developed, which was used in the teaching of mathematics in Austria at the beginning of the twentieth century and applied to different subjects ranging from simple operations in arithmetic to calculus. Besides the relevance of this method—also named the ‘‘Jacob method’’ after Josef Jacob who proposed it—to teaching practice, it could also be considered interesting in a wider context with reference to the mind-body problem. In particular, the importance that Jacob gives to ‘‘muscular activity’’ in the process of forming and elaborating mathematical concepts, derived from Mach, resounds in the current debate on embodied cognition, where cognitive processes are understood not as expressions of an abstract and merely computational mind but as based on our physicality as human beings,\ud equipped not just with a brain but also a (whole) body. This model has been applied to mathematics in the ‘‘theory of embodied mathematics’’, the objective of which is to study, with the methods and apparatus of embodied cognitive science, the cognitive mechanisms used in the human creation and conceptualisation of mathematics. The present article shows that the ‘‘Jacob method’’ may be considered a historical example of didactical application of analogous ideas

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