Paul Hovda

Please ask permission before quoting works in progress. Comments welcome! What is Classical Mereology? ABSTRACT: Classical mereology is a formal theory of the part-whole relation, essentially involving a notion of mereological fusion, or sum. The theorems are very close to those for complete Boolean algebras. There are various different definitions of fusion in the literature, and various axiomatizations for classical mereology. In the context of a correct axiomatization, the definitions of fusion are provably equivalent, but they are not inter-changeable in the axioms themselves. We examine the relations between the main definitions of fusion and correct some technical errors in prominent discussions of the axiomatization of mereology. We show the equivalence of four different ways to axiomatize classical mereology, using three different notions of fusion. We also clarify the connection between classical mereology and complete Boolean algebra by giving two "neutral" axiom sets which can be supplemented by one or the other of two simple axioms to yield the full theories; one of these uses a notion of "strong complement" that helps explicate the connections between the theories. This paper is in Journal of Philosophical Logic; the original publication is available at http://dx.doi.org/10.1007/s10992-008-9092-4 How to be an Atomist A manuscript detailing one branch of thought about identity and plurals: the thesis that talk of things that are not (mereological) atoms can be systemetically and adequately interpreted without talking about anything but mereological atoms and their properties. Two defenses of composition as identity Approximate ms of a talk I gave at the 2005 Western Canadian Philosophical Association. (A longer version was given at Reed.) Two defenses as postscript file (recommended) Handout from talk as postscript file (recommended) Two defenses as PDF file (figures may not render properly) Handout from talk as PDF file (figures may not render properly) Metaphysical indeterminacy (with Mahrad Almotahari) A report of work done together with my student Mahrad Almotahari, funded by a Ruby Grant, administered by Reed College, from the summer of 2004. Argues that the vagueness connected with identity and existence is, at least in some cases, metaphysical indeterminacy. Presents a novel response to Gareth Evans' argument against indeterminacy of identity, on which the determinacy of 'a=a' is denied. ABSTRACT: We motivate and consider the ramifications of the thesis that there is worldly (or metaphysical) indeterminacy, not mere semantic indeterminacy (or vagueness) about the boundaries and identities of objects. We give general considerations about what objects are that we think help to show that it is plausible that their lack of sharp boundaries is a feature of them, not just of the language used to describe them. Then we consider the difficulties raised by the fact that it is then natural to suppose further that there can be indeterminacy about the identities of objects. In particular, we focus on the argument of Gareth Evans that purports to show (as we interpret it) that indeterminacy of identity statements could not be due to worldly indeterminacy, on pain of logical incoherence. We criticize the response to this argument of Terence Parsons, a leading advocate of worldly indeterminacy of identity. We offer our own approach, on which the threat of Evans’ argument can be effectively defused. Vagueness and the world A talk I gave at various institutions in 2002. Argues that for certain kinds of cases, vagueness should be seen as a metaphysical phenomenon, and that in these cases, supervaluational treatments of vagueness (like David Lewis') are not correct. The Nature and Logic of Vagueness My dissertation, UCLA, 2001, chaired by David Kaplan. ABSTRACT: The dissertation considers both metaphysical and logical issues related to the vagueness of natural language. The principle metaphysical claim is that the vagueness of language is, at least in some cases, a direct result of indeterminacy in the subject matter of the language, rather than any sort of flaw of the language. A limited defense of this claim is given, as well as criticism of alternative views. A number of logical issues are addressed. First, the relationship between the notion of determinacy and the idea of an unsharp line is considered, and it is suggested that the relationship is not as simple as it may at first seem, and that the idea of the unsharp line may be irreducible. Next, it is urged that there is a methodological fork in the road for the systematic treatment of vague language, including formal semantics. On one path, we accept certain intuitively puzzling propositions, exemplified by “This is red or it is not the case that this is red, though it is indeterminate which.” On the other path, we reject classical principles of reasoning in our own reasoning both in and about vague language. Some limited arguments are given for taking the former path, and a formal system relevant to this path is motivated and discussed. Finally, both the metaphysical and logical work of the prior parts of the dissertation are brought to bear on the subject of the indeterminacy of identity.