Logic & Philosophy of Science


Jamie Tappenden
Department of Philosophy, University of Michigan

“A Reassessment of the Mathematical Roots of Frege's Logicism:
Some History, Some Philosophy”

Standard interpretations of Frege's logicism take at face value a drastically oversimplified picture of nineteenth century mathematics. Against this background, Frege can easily seem to be outside the mathematical mainstream, and many commentators have recently concluded exactly this. This paper digs into the historical background to show that Frege (and nineteenth century foundations more generally) was more profoundly engaged with ongoing mathematics than has been realized. Among other things that are relevant to assessing the mathematical thrust of Frege's work are a contrast between the Riemann - inspired, Lie and Klein developed "conceptual" style of Göttingen and the arithmetical style of Weierstrass and Berlin, differences between Riemann and Weierstrass on definitional practices, and the early applications of (what is now called in English) the theory of cyclotomic extensions to number theory. This historical background is not just interesting in its own right, but it also prompts a revised assessment of what Frege was trying to do in Grundlagen.

The historical study suggests a broader (meta-) philosophical moral. Because of Frege's perceived position as an early pillar of what has come to be called the analytic tradition, the view of Frege's philosophy as disengaged with mathematical practice both draws plausibility from, and lends support to a widespread "quietistic" picture of the relations between foundational philosophy on one hand and mathematics and the natural sciences on the other. I'll suggest that it is misguided to hold that philosophy should "leave everything as it was."

Friday, December 1, 2000
SST 777, 3 pm

Wine & Cheese reception to follow