Carroll's regress, Bradley's regress, and the incoherence of logical consequence - Crawford, Q (2023)
§1 frames Carroll's regress as a problem of metaphysical grounding, i.e. as an instance of Bradley's regress, and attempts to provide it the strongest possible defence. §2 applies this regress to accounts of logical consequence, and argues that all such accounts ultimately fail to explain why modus ponens is valid. §3 argues that rejecting logical consequence as incoherent amounts to rejecting the analytic/synthetic distinction as incoherent, and discusses the devastating consequences of doing so. §4 shows that the self-undermining nature of such a view has its roots in the Principle of Sufficient Reason, and works towards a way of resolving the paradox that is exemplified in §5.