Philosophy of Education in a Poor Historical Moment: A Personal Account

Under the post-metaphysical sky “old” humanistic-oriented education is possible solely at the cost of its transformation into its negative, into a power that is determined to diminish human potentials for self-exaltation. Nothing less than total metamorphosis is needed to rescue the core of humanistic genesis: the quest for edifying Life and resistance to the call for “home-returning” into the total harmony that is promised to us within nothingness.     

Proving quadratic reciprocity: explanation,disagreement, transparency and depth

Gauss’s quadratic reciprocity theorem is among the most important results in the history of number theory. It’s also among the most mysterious: since its discovery in the late eighteenth century, mathematicians have regarded reciprocity as a deeply surprising fact in need of explanation. Intriguingly, though, there’s little agreement on how the theorem is best explained. Two quite different kinds of proof are most often praised as explanatory: an elementary argument that gives the theorem an intuitive geometric interpretation, due to Gauss and Eisenstein, and a sophisticated proof using algebraic number theory, due to Hilbert. Philosophers have yet to look carefully at such explanatory disagreements in mathematics. I do so here. According to the view I defend, there are two important explanatory virtues—depth and transparency—which different proofs (and other potential explanations) possess to different degrees. Although not mutually exclusive in principle, the packages of features associated with the two stand in some tension with one another, so that very deep explanations are rarely transparent, and vice versa. After developing the theory of depth and transparency and applying it to the case of quadratic reciprocity, I draw some morals about the nature of mathematical explanation.

     

Opposite strain-dependent differences for intermale aggressive behavior elicited by individual housing and housing with a female in the mouse

Male mice of the C57BL/6 strain show a significant increase in aggression toward a nonaggressive male conspecific following 72 hr of individual housing. However, this increase was no longer evident following 2 weeks of individual housing. When housed with a female, C57BL/6 mice show significantly more aggression than singly housed mice of the same strain after 72 hr as well as 2, 4, 8 weeks of differential housing. Male C57BL/6 mice housed with a female also show significantly higher levels of aggression than DBA/2 mice living in the same housing condition after 4 or 8 weeks of differential housing. Finally, male DBA/2 mice individually housed for 8 weeks are significantly more aggressive than mice of the same strain housed with a female for the same time. These results indicate that the increase in aggressive behavior observed following isolation and cohabitation with a female in the mouse is not the same phenomenon. © 1994 Wiley-Liss, Inc.