This very brief paperli provides plausible answers to the two residual questions that Jamie Tappenden states, but leaves unanswered, in his 2024 paper ‘Following Bobzien: Some notes on Frege’s development and engagement with his environment’, namely, why Frege read Sigwart’s Logik and what caused Frege to read Prantl. (This paperli is merely historical and offers no special philosophical insights of any sort.) ---------- OPEN ACCESS. Choose 'without proxy' below.

I investigate the role of geometric intuition in Frege’s early mathematical works and the significance of his view of the role of intuition in geometry to properly understanding the aims of his logicist project. I critically evaluate the interpretations of Mark Wilson, Jamie Tappenden, and Michael Dummett. The final analysis that I provide clarifies the relationship of Frege’s restricted logicist project to dominant trends in German mathematical research, in particular to Weierstrassian arithmetization and to the Riemannian conceptual/geometrical tradition at (...) Göttingen. Concurring with Tappenden, I hold that Frege’s logicism should not be understood as a continuing a project of reductionist arithmetization. However, Frege does not quite take up the Riemannian banner either. His logicism supports a hierarchical understanding of the structure of mathematical knowledge, according to which arithmetic is applicable to geometry but not vice versa because the former is more general, as revealed by the strictly logical nature of its objects in comparison to the intuitional nature of geometric objects. I suggest, in particular, that Frege intended that foundational work would show the use of geometric intuition in complex analysis, a source of error for Riemann that Weierstrass was proud to have uncovered, to be inessential. (shrink)

In his article, Vsevolod Ladov poses an important question – might paradoxes admit of a uniform solution? As an answer, I propose looking at an approach in which it is argued that we must recognize the truth predicate as merely analogous to a vague predicate. The proponents of this approach (V. McGee, J. Tappenden, H. Field, G. Priest and D. Hyde) insist that there is a structural relation between sorites paradoxes and self-reference paradoxes and that they should have a (...) unified solution. (shrink)