Michael James Bevan

Metaphysical foundationalism is the view that ground is well-founded. Despite its reputation as the default view of the general structure of reality, it is a view with few explicit defenders whose theoretical virtues remain largely unexplored. This paper makes an abductive case for metaphysical foundationalism, which lays emphasis on these virtues as relevant to theory choice. As part of the discussion I outline a new theory of ground and of generative relations, and describe a formalism for regimenting it.

I consider and argue against various versions of the view that logical truth and necessity are identical. I criticise purely modalist accounts of logical consequence, according to which consequence is just necessary truth-preservation, and I also criticise views on which necessity is identified with some prior understanding of logical truth (as semantic validity, or substitutional validity, or as syntactic derivability). In the process I develop various systems of modal semantics in detail and investigate the logic of logical truth under various alternative hypotheses.

In §1 I investigate a system of modal semantics in which ☐φ is true if and only if φ is entailed by a designated set of formulas by a designated logic. I prove some strong completeness results as well as a natural connection to normal modal logics via an application of some lattice-theoretic fixpoint theorems. I additionally draw a connection to recent work by Andrew Bacon and Kit Fine on McKinsey’s substitutional modal semantics. In §2 I apply the semantics to investigate Ted Sider's Humeanism about modality, raising a new objection to the theory as stated. I introduce a new theory, Procedural Conventionalism, which avoids these objections.