Classical mereology is a formal theory of the part-whole relation, essentially involving a notion of mereological fusion, or sum. There are various different definitions of fusion in the literature, and various axiomatizations for classical mereology. Though the equivalence of the definitions of fusion is provable from axiom sets, the definitions are not logically equivalent, and, hence, are not inter-changeable when laying down the axioms. 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. (shrink)
Classical mereology (CM) is usually taken to be formulated in a tenseless language, and is therefore associated with a four-dimensionalist metaphysics. This paper presents three ways one might integrate the core idea of flat plenitude, i.e., that every suitable condition or property has exactly one mereological fusion, with a tensed logical setting. All require a revised notion of mereological fusion. The candidates differ over how they conceive parthood to interact with existence in time, which connects to the distinction between endurance (...) and perdurance. Similar issues arise for the integration of mereology with modality, and much of our discussion applies to this project as well. (shrink)
The concept of weak emergence is a refinement or specification of the intuitive, general notion of emergence. Basically, a fact about a system is said to be weakly emergent if its holding both (i) is derivable from the fundamental laws of the system together with some set of basic (non-emergent) facts about it, and yet (ii) is only derivable in a particular manner, called “simulation.” This essay analyzes the application of this notion Conway’s Game of Life, and concludes that a (...) modification of the notion would provide a better refinement of the general notion of emergence. It is proposed that emergence be taken as a matter of degree, defined in terms of the amount of simulation required to derive a fact. (shrink)
I suggest that the core ideas of Kit Fine’s Semantic Relationism are the notion of semantic requirement and the notion of manifest consequence, the non-classical logical relation associated with semantic requirement. Surrounding this core are novel “relational” systems of coordinated sequences of expressions, relational (as opposed to intrinsic) semantic values, coordinated propositions, and coordinated content. I take Fine to take the periphery to be reducible to the core (but see below). I will make some primarily exegetical remarks about the two (...) core ideas, and then make more critical remarks about the periphery. I should say that I find the book, as a whole, illuminating and, for the most part, convincing. I hesitantly suggest that the core constitutes an important and novel model for thinking about semantics (and representation in general), while the periphery might result from an attempt to force the new model into the old mold. (shrink)
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. (shrink)
Ontological innocence You can undertake two commitments, once to object x and once to object y; or you could commit yourself to them all at once by committing yourself to the mereological fusion of x and y. It’s the same commitment either way. So once you have committed to some things, commitment to objects composed of those things is not a further commitment. (Cf. Lewis, Parts of Classes.).