Frege on the Statement of Number

Abstract

Recent interest in history of analytic philosophy has focused attention quite naturally on founding fathers of analysis: Moore, Russell, Wittgenstein, and Carnap. This, in turn, has led to a re-examination of nineteenth century and to intense speculation about work of German mathematician Gottlob Frege (i848-i9z5). Yet Frege's proper position within historical canon of discipline has been difficult to determine. If Frege is a philosopher, why are philosophical doctrines, particularly traditional ones, so hard to find in Frege's writings even Grundlagen? Criticism too has surrounded very prospect of a historical account of Frege's work. Some have questioned whether a credible investigation can be made into Frege's intellectual background or whether such an investigation, once made, can be adequately evaluated. These sceptics fear that only connections historical research will be able to bring to light are parallels, that is, merely analogical features. What such an investigation will be unable to determine are definitive for any of key ideas in Frege's thought. Instead, it will be limited to making comparisons, possibly superficial, between ideas of Frege and those of his predecessors (or successors). The search for distinct sources quickly fixes upon few direct references to works and figures that Frege actually proffers. This brief paper will do likewise in its examination of a possible source for Frege's central doctrine that the content of a statement of number is an assertion about a concept.' This doctrine provides a key element in Frege's logicist project: it is, as Frege himself later described it, most of his results on concept of number and that upon which his account in Grundgesetze rests.' But could this fundamental idea conceivably have appeared before Frege?