Thomas Müller (Utrecht) gives a talk at the MCMP Colloquium (21 November, 2012) titled "Toward a formal account of substance via case-intensional logic". Abstract: Things - concrete individuals persisting through time, or more traditionally speaking, substances - are a central ontological category of our commonsensical as well as of our scientific worldview. There is, however, no satisfactory formal account of substance, or so I will argue - despite a plethora of systems of modal and temporal logic available in the literature. I will indicate some of the shortcomings of available accounts by contrasting them with what I take to be a more adequate formal approach.

In my talk, which for a large part is based on joint work with Nuel Belnap (Journal of Philosophical Logic, forthcoming), I will introduce a general logical framework for modality and quantification, called "Case-intensional first-order logic" (CIFOL). CIFOL combines first-order quantification and a universal S5 modality in a straightforward way and is meant to provide a neutral formal framework for discussing various metaphysical and scientific arguments. CIFOL's generality is made possible by an innovation due to Aldo Bressan: All terms (including definite descriptions, variables and constants) have an extension in each case (where the interpretation of the cases is left open; they do not need to be thought of as "possible worlds"), and an intension, which is the function from cases to the case-relative extensions. Predication is intensional (i.e, whether a predicate applies, may depend on more than what is so in a single case). This makes it possible to define a class of so-called absolute predicates, which allow the tracing of a thing from case to case without building into the logical framework metaphysical assumptions about "rigid designation" or "trans-world identity" to handle the reidentification of things. Concrete individuals are thereby seen to be represented not by extensions, as in standard quantified modal logic (in which one tends to think in terms of "inhabitants of possible worlds"), but by intensions. This approach leaves the nature of the extensions completely unspecified - their only systematic role is to figure in case-relative identity statements.

In the second part of the talk, I will switch to specific formal structures of cases that are adequate for representing indeterminism: branching history structures. I will argue that CIFOL based on these structures allows for a detailed discussion of formal aspects of things (substances) and their qualities, and thereby provides a useful formal framework within which, e.g., problems of the identity of substances can be formulated and discussed.