In defence of mathematical content

Tommi Buder-Gröndahl

Frances Egan has drawn a distinction between two types of content that can be ascribed to cognitive systems. In contrast to standard representationalist formulations, she takes mathematical content (M-content) to specify the function computed in abstract terms that make no reference to either concrete implementation or the system’s environment. This view has recently come under attack from two perspectives, charging it of explanatory vacuity and succumbing to familiar problems of computational indeterminacy. While these critiques point to important limitations of M-content, we maintain that they do not constitute reasons to discard it. First, M-content is not explanatorily superfluous since it is required to ground abductive inference via hypothesis-testing on a function-theoretic level of analysis that abstracts away from implementational details. Second, we take indeterminacy worries to be less drastic for M-content than for the general theory of physical computation, and discuss various ways to mitigate them. We also highlight that the explanatory value of M-content does not depend on Egan’s pragmatist treatment of cognitive content understood in the more traditional sense. M-content stands on its own, irrespective of the fate of deflationism about mental representation.

In defence of mathematical content.
Philosophical Psychology, 1–33, 2025.