In arithmetic, if only because many of its methods and concepts originated in India, it has been the tradition to reason less strictly than in geometry, ...

I ON THE PRIMITIVE TERM OF LOGISTICf IN this article I propose to establish a theorem belonging to logistic concerning some connexions, not widely known, ...

This volume consists of the first of the John Dewey Lectures delivered under the auspices of Columbia University's Philosophy Department as well as other essays by the author. Intended to clarify the meaning of the philosophical doctrines propounded by Professor Quine in 'Word and Objects', the essays included herein both support and expand those doctrines.

If, as it is usually understood, incommensurable theories must be compatible then one need never choose between two such theories. But if theories were incompatible and incommensurable one would have to choose between them. What if they are incompatible only outside the domain of observation? The fact that Darwin's biology can clash with Kelvin's physics (each with their respective auxiliary assumptions) regarding the age of the earth shows how commensurable theories may yet be incompatible. But it also shows that they (...) need not be alternatives--i.e. that one may not be able to simply and satisfactorily replace the other in our world view. But standard examples of scientific revolutions consist of the replacement of one theory by another in one's world view. These alternative theories must therefore be more than merely incompatible--what do they share if not content? (I.e. they must be commensurable.). (shrink)

[Translation of Frege's 'Über das Trägheitsgesetz].