Appreciating global validity

This paper clarifies and defends the global approach to defining logical validity for meta- and higher-level inferences. This is contrary to an emerging consensus in favour of local validity. Prevalent recent arguments claim that global validity is either superfluous in virtue of collapsing into local, or else untenable because it overgenerates validities, compromises the formality of logic, or breaks symmetry with regular validity. Accordingly, the literature on higher inferential logic has come to focus almost exclusively on local validity. Many key philosophical takeaways that have since been drawn from the field are effectively based on local monism: the view that local is the One True Validity Criterion. The present paper argues that this is a mistake, resulting largely from an imprecise understanding of global validity. I untangle some common confusions about how global generalizes beyond the metalevel, and submit that its proper formulation is schematic. These clarifications help dispel each of the aforementioned arguments against global, leaving local monism without any justification. Finally, I outline how much of the philosophical literature around higher-level inferences has been built on local monism, and sketch out the sweeping consequences of rejecting it.