As the seventeenth century progressed, there was a growing realization among those who reflected on the kind of knowledge the new sciences could afford (among them Kepler, Bacon, Descartes, Boyle, Huygens) that hypothesis would have to be conceded a much more significant place in natural philosophy than the earlier ideal of demonstration allowed. Then came the mechanics of Newton's Principia, which seemed to manage quite well without appealing to hypothesis (though much would depend on how exactly terms like "force" and (...) "attraction" were construed). If the science of motion could dispense with causal hypothesis and the attendant uncertainty, why should this not serve as the goal of natural philosophy generally? The apparent absence of causal hypothesis from the highly successful new science of motion went far towards shaping, in different ways, the account of scientific knowledge given by many of the philosophers of the century following, notable among them Berkeley, Hume, Reid, and Kant. This "Newtonian" interlude in the history of the philosophy of science would today be accounted on the whole a byway. The Principia, despite its enormous achievement in shaping subsequent work in mechanics, was from the beginning too idiosyncratic from an epistemic standpoint to serve as model for the natural sciences generally. (shrink)

Purpose: One of my goals in the paper is to investigate why realists reject radical constructivism (RC) as well as social constructivism (SC) out of hand. I shall do this by means of commenting on Peter Slezak’s critical paper, Radical Constructivism: Epistemology, Education and Dynamite. My other goal is to explore why realists condemn the use of RC and SC in science and mathematics education for no stated reason, again by means of commenting on Slezak’s paper. Method: I restrict my (...) comments to Slezak’s paper and leave it to the reader to judge which, if any, of the reasons that I advance for these two states of affairs are not specific to Slezak’s paper. Other readers might not agree with my interpretations of Slezak’s paper, including Slezak himself, but I offer them after having worked with von Glasersfeld in interdisciplinary research in mathematics education for over 25 years. Findings: My findings are that Slezak: (1) rejects RC and SC on the basis of unjustified criticisms, (2) does not explore basic tenets of RC nor of SC beyond the unjustified criticisms, (3) rejects how SC and RC have been used in science and mathematics education, based at least in part on the unjustified criticisms, (3) dislikes how SC has been used in science and mathematics education, a dislike that fuels his rejection of any constructivism, and (4) doesn’t explore how RC has been used in scientific investigations in mathematics education. On the basis of these findings, I conclude that how epistemological models of knowing might be used in science or mathematics education would be better left to the educators who use them in interdisciplinary work. (shrink)