M-Combinatorialism and the Semantics of SQML

The Simplest Quantified Modal Logic (SQML) is controversial because it seems to conflict with some of our most basic intuitions about what is possible and what is necessary. Two controversial principles, the Barcan Schema (BS) and Necessary Existence NE, are valid in SQML models. Informally expressed, BS requires that, if it is possible that something is F, then there is something that is possibly F. This result seems to conflict with the intuition that there is some property F such that F could have been exemplified, though is not possibly exemplified by any existing thing. NE conflicts with the intuition that there could have been more/different existents than there actually are and the intuition that those things that actually exist could have failed to exist. The primary goal of this thesis is to provide a semantics for SQML that justifies the validity of BS and NE with these intuitions in mind. This is the focus of the fifth section of the thesis. In the first four sections of the thesis, I discuss prior attempts to meet my primary goal, all of which I consider unsuccessful.

According to my view, which I call M-combinatorialism, the world is comprised of simples, mereological sums of those simples and universals that the former objects exemplify. I argue that we can justify the validity of BS by appealing to these facts about simples and sums: (1) simples are arranged such that the sums of these simples exemplify certain properties, (2) the actual arrangement of any given number of simples is a contingent matter and (3) had the simples that are actually arranged to form the complex objects in the actual world been arranged differently, the sums of these simples could have exemplified radically different properties.

Insofar as Combinatorialists construct all possible individuals only out of actual individuals, they are committed to the necessary existence of those actual individuals, which allows the M-Combinatorialist to justify the validity of NE. So, the M-Combinatorialist is able to provide an adequate semantics for SQML. In the final section, I defend my view against objections.