Universal Principle of Consistency

Around 300 BCE, a debate emerged concerning the truth conditions of conditional propositions–a debate that, to this day, has not culminated in a formulation genuinely satisfying to philosophers. Nevertheless, the material implication proposed by Philo the Dialectician achieved considerable prominence, despite its evident divergence from the patterns of ordinary human reasoning. Its success may be attributed, at least in part, to its formal simplicity. It is now widely acknowledged, however, that Philo’s implication is not the long-sought representation of implication that would faithfully capture intuitive reasoning. This recognition is underscored by the vigorous development of formal logic, much of which has been driven by the search for a notion of implication that aligns more closely with our cognitive intuitions. As Susan Haack once remarked, a true solution to a philosophical problem is recognizable by the deep internal conviction it evokes regarding its adequacy. Arguably, none of the proposed definitions of implication to date have elicited such conviction, not even among their originators–hence, the search continues. The present study introduces a principle that appears to underlie human reasoning regardless of its subject matter–whether one is engaged in mathematical theorizing or reflecting on matters of everyday life, the same logical structure, the same inferential tool, seems to be consistently employed. We propose that this tool is the Universal Principle of Consistency (UPC), or, in its strengthened form, the Strong Universal Principle of Consistency (SUPC). This universal principle is derived from the definitions of two content-based implications: the hyperintensional content inclusion implication and the intensional content relationship implication. Both appear to align closely with the structure of ordinary reasoning, both resonate with the logical intuitions of the Ancients–particularly Chrysippus and Diodorus–and both prove effective in domains such as legal and mathematical reasoning. Moreover, they offer a precise account of key pragmatic phenomena, including presupposition and implicatures. If the proposal put forward here is accurate, it may be argued that it brings to a close the debate that began in antiquity.