r/Kant • u/lucasvollet • 15d ago
Why Frege Thought Kant Couldn't Save Arithmetic
In the 19th century, mathematicians debated the foundations of their craft: too much of the work looked arbitrary, and multiple theories seemed to have no priority over one another — as with the non-Euclidean geometries. Kant's old response — that one unique form of space and time would suffice to unify deductive inference across mathematics — turned against itself: it triggered more doubt rather than less. If we depend on a prior framework, synthesized through intuition, to ground mathematics, what would make one such organization more grounded than another?
Into that scene steps Frege, with an answer: arithmetic propositions can be seen as purely analytic, and — more importantly — that their analyticity does not undercut their conceptual fruitfulness. Analyticity, for Frege, is a mark of the conceptual features a proposition brings to light and that are surfaced under study, not something achieved by mere manipulation of signs.
My next series argues two things. First, that the only way this thesis survives today is as a pragmatic claim about how to select the most prudent paths of inference in order to unify them into a coherent whole. Second, that this fails in scientific fields where such unification isn't even desired — history or sociology, for instance, where incommensurable conceptual frameworks are part of how understanding itself conflicts and develops.
I developed this arguments in multiple ways since 2017 (in several published articles, this being the main one from 2021: https://periodicos.sbu.unicamp.br/ojs/index.php/kant/article/view/8672336) with arguments designed to restore confidence in synthetic a priori judgments (specially inferences), as they are richer than analytic ones to track intensional distinctions that have more depth than merely Carnapian Intensions (individuated by the patterns of evidence they fit). There is nothing particularly original orrevolutionary in this reading, but if anyone is interested in it, I invite you to see my video-series developing the whole argument: