On Stage with Gunk

A structure is temporally gunky just in case all of its temporal parts have proper temporal parts. Joshua Stuchlik [2003] objects to the stage theory of persistence from temporal gunk by arguing that the former requires instantaneous entities while the latter precludes them. It is argued here that stage theory can accommodate temporal gunk by invoking short-lived persisting stages. However, a new and more serious problem for stage theory is not far to seek. The short-lived stages that are needed to accommodate gunk accord with stage theory only if they are appropriately qualitatively static. The problem is that, unless stage theory abandons much of its dialectical force, some of the required stages fail this condition. Thus, Stuchlik is right that gunk shows a large class of worlds not to be stages, but wrong about which worlds these are.     

What is Classical Mereology?

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.     

Slot Mereology Revised

The paper suggests two revisions of K. Bennett's system of slot mereology. The revisions do not touch on the philosophical rationale for this system, but are focused on certain logical deficiencies in her formalisation.     

Towards a Rough Mereology-Based Logic for Approximate Solution Synthesis. Part 1

We are concerned with formal models of reasoning under uncertainty. Many approaches to this problem are known in the literature e.g. Dempster-Shafer theory [29], [42], bayesian-based reasoning [21], [29], belief networks [29], many-valued logics and fuzzy logics [6], non-monotonic logics [29], neural network logics [14]. We propose rough mereology developed by the last two authors [22-25] as a foundation for approximate reasoning about complex objects. Our notion of a complex object includes, among others, proofs understood as schemes constructed in order to support within our knowledge assertions/hypotheses about reality described by our knowledge incompletely.     

The Right Stuff

This paper argues for including stuff in one's ontology. The distinction between things and stuff is first clarified, and then three different ontologies of the physical universe are spelled out: a pure thing ontology, a pure stuff ontology, and a mixed ontology of both things and stuff. (The paper defends the latter.) Eleven different reasons for including stuff (in addition to things) in one's ontology are given (seven of which the author endorses and four of which would be sensible reasons for philosophers with certain metaphysical positions that the author does not happen to hold). Then five objections to positing stuff are considered and rejected.