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.     

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.     

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.     

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.     

A Necessary Relation Algebra for Mereotopology

The standard model for mereotopological structures are Boolean subalgebras of the complete Boolean algebra of regular closed subsets of a nonempty connected regular T ₀ topological space with an additional "contact relation" C defined by xCy x ØA (possibly) more general class of models is provided by the Region Connection Calculus (RCC) of Randell et al. We show that the basic operations of the relational calculus on a "contact relation" generate at least 25 relations in any model of the RCC, and hence, in any standard model of mereotopology. It follows that the expressiveness of the RCC in relational logic is much greater than the original 8 RCC base relations might suggest. We also interpret these 25 relations in the the standard model of the collection of regular open sets in the two-dimensional Euclidean plane.     

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.     

Leibniz on Infinite Numbers,Infinite Wholes,and Composite Substances

Leibniz claims that nature is actually infinite but rejects infinite number. Are his mathematical commitments out of step with his metaphysical ones? It is widely accepted that Leibniz has a viable response to this problem: there can be infinitely many created substances, but no infinite number of them. But there is a second problem that has not been satisfactorily resolved. It has been suggested that Leibniz's argument against the world soul relies on his rejection of infinite number, and, as such, Leibniz cannot assert that any body has a soul without also accepting infinite number, since any body has infinitely many parts. Previous attempts to address this concern have misunderstood the character of Leibniz's rejection of infinite number. I argue that Leibniz draws an important distinction between ‘wholes’ – collections of parts that can be thought of as a single thing – and ‘fictional wholes’ – collections of parts that cannot be thought of as a single thing, which allows us to make sense of his rejection of infinite number in a way that does not conflict either with his view that the world is actually infinite or that the bodies of substances have infinitely many parts.     

Emergentism and supervenience physicalism

I argue that it is intuitive and useful to think about composition in the light of the familiar functionalist distinction between role and occupant. This involves factoring the standard notion of parthood into two related notions: being a parthood slot and occupying a parthood slot. One thing is part of another just in case it fills one of that thing's parthood slots. This move opens room to rethink mereology in various ways, and, in particular, to see the mereological structure of a composite as potentially outreaching the individual entities that are its parts. I sketch one formal system that allows things to have individual entities as parts multiple times over. This is particularly useful to David Armstrong, given Lewis's charge that his structural universals must do exactly that. I close by reflecting upon the nature and point of formal mereology.     

The architecture of Fazang’s six characteristics

This paper examines the Huayan teaching of the six characteristics as presented in the Rafter Dialogue from Fazang’s Treatise on the Five Teachings. The goal is to make the teaching accessible to those with minimal training in Buddhist philosophy, and especially for those who aim to engage with the extensive question-and-answer section of the Rafter Dialogue. The method for achieving this goal is threefold: first, contextualizing Fazang’s account of the characteristics with earlier Buddhist attempts to theorize the relationships between wholes and their parts; second, explicating the meaning Fazang likely attributes to each of the six characteristics; third, situating the characteristics as explicated within Fazang’s broader metaphysical framework.     

Critical Notice: Thomas Sattig’s The Double Lives of Objects: An Essay in the Metaphysics of the ordinary world,Oxford: Oxford University Press, 2015

This critical notice describes some of Thomas Sattig’s book The Double Lives of Objects: An Essay in the Metaphysics of the Ordinary World and raises several critical issues about it.