Commentary on Perspective II: Psychology
In responding to this sample of work on probabilistic thinking, my aim is to highlight some overarching issues and ask questions intended to be provocative, in the best sense.
- PDF / 214,785 Bytes
- 11 Pages / 441 x 666 pts Page_size
- 85 Downloads / 212 Views
1 Introduction In responding to this sample of work on probabilistic thinking, my aim is to highlight some overarching issues and ask questions intended to be provocative, in the best sense. Within mathematics, probability is fascinating from many perspectives. Particularly intriguing is that probability had to wait until the seventeenth century to receive formal mathematical treatment despite its widespread manifestations across centuries and cultures in practices such as divination, gambling, and insurance. As expressed by Davis and Hersh (1986, p. 21), “the delay in the arrival of the theory of probability is one of the enigmas of modern science”. Hacking (1975) discussed this enigma at some length and evaluated several of the proffered explanations. Finding none of these convincing, he suggested that the shift in Europe towards empirical investigation as the source of authority for knowledge might have been the triggering factor. Probability remains a domain of mathematics full of unsettled questions, and thus an important counterexample to the conception of mathematics as timeless and universal. Further developments in the mathematics of uncertainty, such as fuzzy logic and possibility theory, continue to emerge. Hacking (1990, p. 1) declared that “the most decisive conceptual event of twentieth century physics has been the discovery that the world is not deterministic”. Yet, in his account of chaos theory, Stewart (1989, p. 22) commented that “mathematicians are beginning to view order and chaos as two distinct manifestations of an underlying determinism”. Moreover, as documented by Hacking (1975, 1990) the development of probability from its origins in the second half of the seventeenth century has been inextricably linked with issues of statecraft and sociological conceptions of human nature and behavior. B. Greer (B) Portland State University, Portland, OR, USA e-mail: [email protected] E.J. Chernoff, B. Sriraman (eds.), Probabilistic Thinking, Advances in Mathematics Education, DOI 10.1007/978-94-007-7155-0_16, © Springer Science+Business Media Dordrecht 2014
299
300
B. Greer
In short, what is clear is that there are complex mathematical, philosophical, humanistic, and scientific issues regarding probability. Naturally, the same goes for our understanding of probabilistic cognition. Rather than a simplistic “yes or no” question, Meder and Gigerenzer (2014) speak of identifying and characterizing the circumstances under with people are capable of sound probabilistic thinking— particularly when supported by helpful representational tools. In the remainder of the chapter, I first make some comments on research of the type represented here, then on the teaching of probability. Following that, I consider several perspectives: the interplay between biological and cultural evolution; the limited relevance of neuroscientific inputs; the non-probabilistic mathematical underpinnings of probabilistic thinking; the epistemology of probabilistic thinking; the role of intuition; and the utility of dual-process
Data Loading...
