Grounding in Medieval Philosophy, an edited volume whose contributions explore the notion of grounding across medieval epistemology, logic and metaphysics, came out today from Springer. I contributed an essay for the volume on grounding in medieval theories of consequence. The paper can be found online here. A preprint version is available here. Here’s the introduction:

Introduction

Grounding is an irreflexive, assymetric, and transitive relation between different elements within an ontology, according to which one or several elements serve as grounds for another. The notion of grounding is meant to capture that expressed in non-causal uses of phrases like ‘because’ or ‘in virtue of’, and commonly invoked examples of grounding include that of true statements in facts, of true non-atomic propositions in their atomic constituents, of qualities in substances, and of sets in their members. On one currently widespread understanding of metaphysics, the basic problem of metaphysics is to determine what beings are fundamental, and how other beings are grounded in them.

In its broadest sense, a consequence is a relation obtaining between an antecedent and a consequent, signified by a sign of consequence; an antecedent, a premise or set of premises from which a consequent follows; a consequent, a conclusion following from an antecedent; a sign of consequence, a word, symbol, or phrase signifying a consequent’s following from an antecedent, e.g. ‘if’, ‘therefore’, ‘because’ and their analogues in other natural languages, the |= of model theory, or the proof-theoretic |-. Though elements that would enter into the theory may be found in earlier work on Aristotelian syllogistic, fallacies, and topical argument, the theory of consequence proper first arises in the later medieval period.

In what follows, I explain how consequence was grounded in the medieval period. I begin with a basic introduction to how consequence is grounded today, indicating its similarities to the best-known approach to formal consequence in later medieval philosophy, that of John Buridan. I then show how first medieval theories of topical argument, then of supposition served to ground earlier medieval accounts of inference, detailing two important shifts: the first from a non-unified, topics-based grounding of consequence to one based on the theory of supposition; the second, within the supposition-based theory, from an understanding of personal supposition licensing appeal to concepts to one based wholly on a sparse ontology of individuals. Over time, these changes in the foundations of the medieval theory of inference accelerate a shift in its focus, one away from a characteristically medieval concern with sound and demonstrative arguments towards a more modern focus on formal validity.