James Marks

In this work, I develop a novel mereotopology: a logic of the connection between objects or regions structured by mereological relations. The mereotopology here developed is explicitly guided by Descartes’ unique theories of surfaces. As I argue, Descartes’ philosophy has the requisite richness and depth to motivate a rigorous topological extension of mereology: an extension which rivals popular extant mereotopologies. The distinctive aspect of Descartes’ theory is that he takes boundaries to be modes of objects (or regions), rather than parts. To do justice to this key Cartesian choice point, I cast the developed mereotopology in a higher-order logic. The axiomatization for this higher-order mereotopology is initially inspired by Descartes’ arguments, and several definitions and theorems are given based on this axiomatization. I conclude by discussing the philosophical merits of a Cartesian mereotopology. An appendix proves the consistency of this mereotopology, relative to ZF.

Much of the interest in higher-order metaphysics stems from the idea that reality is “typed” in a manner captured by the simply typed lambda calculus (STLC). However, relatively little attention has been paid to the typing of plurals and plural terms in a plural logic. I show that two extant broad strategies for the typing of plurals stand in tension with one another, yet I argue each fails to accommodate independent desiderata for the plural metaphysician and logician. Prompted by these issues, I argue that plural logic ought to be formulated in a subtyped logic, and hence that higher-order metaphysicians must extend their expressive resources beyond the STLC. I conclude by considering the formal and philosophical advantages brought on by positing subtyping relations to be built into the type-theoretical hierarchy.

David Armstrong claims that a law of nature is both a universal as well as a state of affairs. Unfortunately, this leaves his account vulnerable to a “logician’s protest”, first privately raised by Tichý, that appeals to the type theory of higher-order logic. In this paper, I flesh out the objection and show how Armstrong’s cursory response is inadequate. I argue that the logician’s protest is a very serious problem for Armstrong, as well as any other account of lawhood that posits such a ‘dual nature’ (according to which a law is both a universal and state of affairs). As a result, the logician’s protest serves as an important dilemma for any theory of laws: laws of nature can be identified with universals or with states of affairs, but not both. I conclude that the seriousness of the logician’s protest is an underappreciated constraint on the metaphysics of one's theory.

Charles Sanders Peirce’s abductive logic is a logic which provides a model of scientific discovery. The logic is meant to provide an account of how scientists discover (or pursue) hypotheses during scientific inquiry. I focus on a version of Peirce’s abduction, one where the hypotheses being generated are in response to anomalies, and argue that this logic of abduction is an instance of ideal theory. I show that scientific abduction is influenced by facts about the scientific community, and that features of systemic oppression systematically influence the processes of each step of the abductive process which abductive logic seeks to model. Peirce’s logic of abduction idealizes over these facts, and so I conclude that abductive logic is systematically inaccurate as a model of scientific inquiry. This work, then, provides an instance of a feminist philosophy of logic. By investigating the subject matter of abductive logic from a distinctively feminist perspective, I argue that the logic, itself, is in need of revision.

A common phrase expressed in ‘record sports’ – sports like track & field, swimming and weightlifting – is something like ‘records get broken, medals are forever’. This phrase is shorthand for the argument that earning medals at championships is preferable for athletes in record sports to breaking records. Thus, athletes should focus their attention on performing at championships, rather than running fast times. The argument depends on the assumption that, although records are mere ‘temporary accomplishments’, championship performances are, instead, ‘permanent accomplishments’. I show that this assumption is false. To do so, I show that the distinction between permanent and temporary accomplishments rests on the metaphysical distinction between tensed and tenseless facts, and then show that this distinction fails to provide the force needed for the aforementioned argument. I conclude that, if one wants to argue that championship performances are preferable to breaking records in record sports, a different argument is needed, and I provide one such argument.