The literature on mathematical explanation contains numerous examples of explanatory, and not so explanatory proofs. In this paper we report results of an empirical study aimed at investigating mathematicians’ notion of explanatoriness, and its relationship to accounts of mathematical explanation. Using a Comparative Judgement approach, we asked 38 mathematicians to assess the explanatory value of several proofs of the same proposition. We found an extremely high level of agreement among mathematicians, and some inconsistencies between their assessments and claims in the (...) literature regarding the explanatoriness of certain types of proofs. (shrink)

The measurement of sensory intensity has had a long history, attracting the attention of investigators from many disciplines including physiology, psychology, physics, mathematics, philosophy, and even chemistry. While there has been a continuing doubt by some that sensation has the properties necessary for measurement, experiments designed to obtain estimates of sensory intensity have found that a general rule applies: Equal stimulus ratios produce equal sensory ratios. Theories concerning the basis for this simple psychophysical rule are discussed, with emphasis given to (...) the physical correlate theory, which considers judgments of subjective magnitudes to be based upon estimates of physical dimensions that vary regularly with changes in degree of stimulation. For the most thoroughly investigated sensory scales, brightness and loudness, the physical correlate is considered to be distance. Our “tacit knowledge” of the sensory effects of changing distance plays an essential role in matching motor activities to environmental conditions and in ensuring accurate perceptual evaluations through brightness and loudness constancies. In psychophysical experiments, subjects apparently use this same tacit knowledge when required to estimate relative subjective magnitudes. The evidence related to the physical correlate theory is summarized, and it is concluded that, while under appropriate conditions we demonstrate considerable skill in evaluating environmental relationships, we are quite unable to estimate the neurophysiological nature or quantity of sensory response. A psychophysics devoted to studying conditions required for accuracy and conditions producing errors in the perception of environmental relationships would seem to be more valuable than one devoted to subjective magnitudes. (shrink)

Academia’s mathematical metaphysics are briefly explored en route to an elaboration of the qualitatively rigorous requirements underpinning the calibration and unambiguous interpretation of quantitative instrumentation in any science. Of particular interest are Gadamer’s emphases on number as the paradigm of the noetic, on the role of play in interpretation, and on Hegel’s sense of method as the activity of the thing itself that thought experiences. These point toward and overlap with (1) Latour’s study of the metrological social networks through which (...) technological phenomena are brought into language as modes of being that can be understood, and (2) the way that Rasch’s models for measurement comprise a potential beginning for metaphysically astute, qualitatively and quantitatively integrated, mathematical methods in the social sciences. The paper closes with observations on the general problem that is philosophy, the need to remain open to multiplicities of meaning even as clear understandings are sought and obtained. (shrink)

ABSTRACTThis paper consists of a story about unorthodox assessment procedures in theology, and a discussion of their implications. Among the issues raised are the possibility of testing values, the relationship of test validity to test reliability and ethical questions involved in assessment.

Le psychologue français Alfred Binet est à l'origine du développement de tests mentaux destinés à diagnostiquer le « niveau intellectuel » des enfants. Initialement conçus comme des tests cliniques, leur importation aux États-Unis dans les années 1910 a considérablement modifié leur usage, leur portée pratique et leur interprétation. Devenus les instruments de politiques eugéniques ou héréditaristes, utilisés dans des processus de sélection de grande échelle, les tests ont transformé la conception que les psychologues se faisaient de l'intelligence: initialement conçue comme (...) multiforme et qualitative, elle est devenue une grandeur unique quantifiable. C'est dans ce contexte que le psychologue américain Louis Léon Thurstone, critiquant le manque de rigueur des méthodes statistiques utilisées dans les tests, a développé une nouvelle méthode permettant de disposer d'une unité et d'un zéro absolu pour la mesure (échelonnement) de l'intelligence. Une fois objectivée, sa méthode est devenue une « loi » générale permettant de rendre compte de tous les processus mentaux, de disposer d'un outil d'analyse des opinions et des attitudes. (shrink)

After writing my response to the commentaries, I sat back and reflected on the fascination and frustration of work on this topic. There is the ancient fascination of trying to understand the nature of the sensory bridge linking us to the external world. Also, discussing the measurability of sensation brings to the surface concepts we use and take for granted when we are working in other areas of psychology; and it holds them before us for critical examination. The frustration lies (...) chiefly in the difficulty of formulating concepts clearly, in a way understood by all. At least when constructing the original Tower of Babel, workers hearing strange words knew that communication was not occurring. The psychophysical Tower of Babel sometimes has workers using the same words, but with different meanings. Much of my response is based on attempts to clarify concepts and clear up confusions. (shrink)

Illusions of control and fantasies of power are important themes in human history and culture. The first objective of this paper is to explore Zarathustran fantasies in the information society, and our dreams of God-like control and mastery over ourselves and the Universe. This paper does not try to be faithful to Nietzschean philosophical concepts of Zarathustra, but instead explore cultural themes, which can be related to a mythology of God-like control and omniscient perception. It draws together strands from science (...) fiction, anthropology, philosophy, technology development, systems engineering, socio-technical systems, finance and e-business to set out how we have fallen for the technocultural illusions we have created. The paper then shifts gear, and in an attempt to address these technocultural problems, identifies an intellectual trajectory centred on an anthropological perspective. Using examples from e-business and Schwartz’s universal model of human values, applied into a technocultural context, the paper shows how it is possible to create meaningful systems of organisation that utilise advanced technologies to help provide a deeply value-laden cultural system. Our world is changing fundamentally and dramatically, and we desperately need new approaches to help us understand these transitions. The paper’s primary contribution is to critique both human-centred thinking, and mechanistic, Taylorist views of organisation and technology. It stimulates debate concerning the relationship between technology and culture as it is worked out in the information society. Shifting the perspective from humans as social, functioning creatures, this paper offers a new human-centred approach based upon humans as cultural, valuing beings. (shrink)

Warren's major contention is that judgments of subjective magnitude are not possible, and therefore subjects base such judgments upon physical correlates of the dimension in question. It would appear that Warren's theory will almost surely fail as a comprehensive model, even though it does provide a heuristic account of judgments of loudness and brightness. In order for the theory to succeed, Warren must specify a physical correlate for judgments ofeverysubjective attribute that has yielded orderly data with Stevens's scaling procedures.