Frege’s logicism is a reaction against Kantian philosophy of mathemtics, with two intertwined aspects: a semantic one and an epistemological one. The semantic aspect concerns the inferential nature of judgeable contents, “logic’s only concern”; the epistemological aspect concerns the extent to which arithmetical truths can be justified “independently of the particular characteristic of objects”, only based on “pure thought”. This is what he declares in Begriffsschrift.

There are several key Fregean semantic 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.

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’s semantics remained consistent until the end of his life.

I will defend that Russell’s paradox does not undermine Frege’s semantic or conceptual foundations, but rather the set-theoretic framework Russell employed in his attempt to ground arithmetic. The true source of the problem lies not in concepts, but in 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.
 

REFERENCES

 Brandom, R. (2000), Articulating Reasons. An Introduction to Inferentialism. Cambridge, Mass., Harvard University Press

Burge, T (1984). Frege on Extensions of Concepts, from 1884 to 1903. The Philosophical review 93 (1), 3 -34

Frápolli, M. J. (2023), The Priority of Propositions. A Pragmatist Philosophy of Logic. Synthese Library, Springer

Frege, G. (1879). Begriffsschrift, a formula language, modeled upon that of arithmetic, for pure thought”. In Jean van Heijenoort (1967), From Frege to Gödel. A Source Book in Mathematical Logic, 1879-1931. Harvard University Press, 1- 82.

Frege, G. (1980). Philosophical and Mathematical Correspondence. Oxford, Basil Blackwell

Macbeth, D. (2005). Frege’s Logic.  Cambridge, Mass. and London, England, Harvard University Press (kindle edition).