María José Frápolli (U Granada):"The Fate of Fregean Logicism: Lessons Learned and Forgotten"

May 16th, 2025. 3:00 pm.

Venue: Carlos Santamaria Zentroa, room 4.

Abstract:

Russell’s paradox comes into conflict with several key Fregean principles that remained central to Frege’s thinking throughout his life. The first is the object–concept distinction, a fundamentally semantic principle. The second is the context principle, which is explicitly linguistic. A third, pragmatic principle appears early in Frege’s work: the assertion principle, which holds that logic is concerned only with entities that can be meaningfully asserted—that is, those for which truth is at issue. In other words, logic concerns itself solely with judgeable contents.

Had Frege remained fully committed to these insights, his response to Russell’s 1903 letter might have been very different. But does his actual reaction suggest that he abandoned or revised his semantics? That seems unlikely. Frege remained consistent with the semantic commitments characteristic of neo-Kantianism until the end of his life.

Russell’s paradox, then, does not undermine Frege’s semantic or conceptual foundations, but rather the set-theoretic framework he employed in his attempt to ground arithmetic. The true source of the problem lies not in the notion of concepts, but in that of extensions. In this sense, the paradox exposes the failure of a Russellian version of logicism, while leaving the core of Fregean logicism fundamentally intact.

In my talk, I will defend Frege’s project and highlight the resources it offers for addressing Russell’s objection.