Bolzano’s Tortoise and a loophole for Achilles

This paper discusses a novel response to two closely related regress arguments from Bolzano’s Theory of Science and Carroll’s What the Tortoise Said to Achilles. Bolzano’s argument aims to refute the thesis that full grounds must include propositions involving notions such as entailment, grounding or lawhood which link the respective grounds to their groundee. This thesis is motivated, Bolzano’s argument is reconstructed, and a response based on self-referential linking propositions is developed and defended against objections concerning self-reference and Curry’s paradox. Finally, the idea is applied to a reading of Carroll’s dialogue and a corresponding solution to the so-called infinite regress problem of inference is proposed.