Cosmos and History: The Journal of Natural and Social Philosophy, Vol 15, No 1 (2019)

Font Size:  Small  Medium  Large

Hegel's Logic and Frege's Star Paradox

Pauli Pylkkö

Abstract


In 1892 Frege published an essay "Über Sinn und Bedeutung" where he presented a paradox, the so-called Star paradox. The paradox and Frege's own solution to it became later very famous and influential. This paradox of how to relate logical and contingent identities is perhaps the major characteristic problem of Analytic philosophy, and Frege's solution has been celebrated as a brilliant opening of a whole new era of philosophy. Because Analytic philosophy, its British branch in particular, has been regarded as an anti-Hegelian movement par excellence it is not only interesting, but fair, to ask how a Hegelian would have reacted to this problem. Any Hegelian approach to the problem must be ready to question the assumption that natural language identity statements are strict logical identity statements. Inspired by their project of logicism, Frege and Russell just decided to formalize natural language identity statement as a = a and a = b, and this gave the misleading impression that also natural expressions satisfy the properties of logical identity (reflexivity, symmetry, transitivity, substitutivity). According to Hegel, what looks like a logical identity statement is, in fact, an asymmetric subject-predicate sentence whose predicate is not decomposable. Therefore, logical and contingent identities of natural discourses are never equivalent. This prevents the Star paradox from arising.

Full Text: PDF