RESEARCH IN PHENOMENOLOGY 44 (2014) 362-383 K BRILL brill.com/rp Prolegomenon to a Critique of Symbolic Reason Burt C. Hopkins Seattle University Abstract Jacob Klein’s own account of the change from the ancient to the m odem m ode of think- ing presented in his seminal Greek Mathematical Thought and the Origin of Algebra included the observation that it did not consider the larger perspective of this change. The discussion to follow proposes to view the larger perspective of this transition through the lens provided by the Kantian concept of a “critique” of pure reason. By ask- ing and attem pting to answer the question of w hether Klein’s account of what he calls the “symbolic abstraction” responsible for the genesis of the modem concept of num- ber can be seen as what Kant characterizes as an “assessment” of pure reason, it is my intent to venture a prolegom enon to a critique of what, following Klein, I w ant to argue is m ost properly called “symbolic reason.” Keywords Jacob Klein - Kant - Vieta - Greek mathematics - m odem mathematics - symbolic reason aXvjSv) 8£ r &Xsyopeva [piiGijpcrnicoq] ical cralvsi tvjv Introduction Jacob Klein's Greek Mathematical Thought and the Origin of Algebra 12 is as remarkable for what it purports to demonstrate as for what it does not. 1 “The things they [the mathematicians] say are true and fawningly seduce the soul," Aristotle (Metaph. ^.108(^36-7). 2 Jacob Klein, “Die griechische Logistik und die Entstehung der Algebra,” in Quellen und Studien zur Geschichte der Mathematik, Astronomie und Physik, Abteilung B: Studien 3, no. 1 © KONINKLIJKE BRILL NV, LEIDEN, 2014 | DOI 10.1163/15691640-12341293