Online research in philosophy

0. Introduction: Mereology, Metaphysics, and Speculative Grammar 0.1 Mereology, Ancient and Contemporary 0.11 Mereology is, strictly speaking, the theory of ...

Mereotopology is that branch of the theory of regions concerned with topological properties such as connectedness. It is usually developed by considering the parthood relation that characterizes the, perhaps non-classical, mereology of Space (or Spacetime, or a substance filling Space or Spacetime) and then considering an extra primitive relation. My preferred choice of mereotopological primitive is interior parthood . This choice will have the advantage that filters may be defined with respect to it, constructing “points”, as Peter Roeper has done (“Region-based topology”, Journal of Philosophical Logic , 26 (1997), 25–309). This paper generalizes Roeper’s result, relying only on mereotopological axioms, not requiring an underlying classical mereology, and not assuming the Axiom of Choice. I call the resulting mathematical system an approximate lattice , because although meets and joins are not assumed they are approximated. Theorems are proven establishing the existence and uniqueness of representations of approximate lattices, in which their members, the regions, are represented by sets of “points” in a topological “space”.

David Lewis insists that restrictivist composition must be motivated by and occur due to some intuitive desiderata for a relation R among parts that compose wholes, and insists that a restrictivist’s relation R must be vague. Peter van Inwagen agrees. In this paper, I argue that restrictivists need not use such examples of relation R as a criterion for composition, and any restrictivist should reject a number of related mereological theses. This paper critiques Lewis and van Inwagen (and others) on their respective mereological metaphysics, and offers a Golden Mean between their two opposite extremes. I argue for a novel account of mereology I call Modal Mereology that is an alternative to Classical Mereology. A modal mereologist can be a universalist about the possible composition of wholes from parts and a restrictivist about the actual composition of wholes from parts. I argue that puzzles facing Modal Mereology (e.g., puzzles concerning Cambridge changes and the Problem of the Many, and how to demarcate the actual from the possible) are also faced in similar forms by classical universalists. On my account, restricted composition is rather motivated by and occurs due to a possible whole’s instantiating an actual type. Universalists commonly believe in such types and defend their existence from objections and puzzles. The Modal Mereological restrictivist can similarly defend the existence of such types (adding that such types are the only wholes) from similar objections and puzzles.

Philosophical questions concerning parts and wholes have received a tremendous amount of the attention of contemporary analytic metaphysicians. In what follows, I discuss some of the central questions. The questions to be discussed are: how general is parthood? Are there different kinds of parthood or ways to be a part? Can two things be composed of the same parts? When does composition occur? Can material objects gain or lose parts? What is the logical form of the parthood relation enjoyed by material objects?

In this set of excerpts from an earlier book, I examine some philosophical issues surrounding the whole-part relationship. I present a series of thought experiments and other arguments designed to undermine the view that wholes are "nothing but" their parts.

Mereology (from the Greek μερος, ‘part’) is the theory of parthood relations: of the relations of part to whole and the relations of part to part within a whole. Its roots can be traced back to the early days of philosophy, beginning with the Presocratic atomists and continuing throughout the writings of Plato (especially the Parmenides and the Thaetetus), Aristotle (especially the Metaphysics, but also the Physics, the Topics, and De partibus animalium ), and Boethius (especially In Ciceronis Topica ). Mereology has also occupied a prominent role in the writings of medieval ontologists and scholastic philosophers such as Garland the Computist, Peter Abelard, Thomas Aquinas, Raymond Lull, and Albert of Saxony, as well as in Jungius's..

The assumption that wholes have properties, specifically causally efficacious properties, which the sum of its parts seem to lack, lends support to the argument that wholes are something more than the sum of their parts. The properties of the whole are taken to be the result of the particular arrangement of the whole’s parts. The rearrangement of parts makes new properties emerge for a particular whole. This creates hierarchical ontological levels of properties in an object. My purpose in this paper will be to undermine the preceding lines of thought as valid support for wholes being “over and above” the sums of their parts. I begin by pointing out that the costs of a theory where arrangement entails new, unique and distinct properties for a whole carry two unattractive commitments: a reliance on a scientifically disproved version of early Emergentism and causal redundancy. I, then, present an alternative theory to explain the relationship between the properties of wholes and arrangement: my contention will be that the properties that we attribute to wholes are actually the manifestation of preexisting, but heretofore unmanifested, properties of parts, which manifest only when a specific part comes in contact with another specific part in a particular arrangement. I argue that the properties of a part are all we need to give a complete account for the properties of a whole.

Standard theories in mereotopology focus on relations of parthood and connection among spatial or spatio-temporal regions. Objects or processes which might be located in such regions are not normally directly treated in such theories. At best, they are simulated via appeal to distributions of attributes across the regions occupied or by functions from times to regions. The present paper offers a richer framework, in which it is possible to represent directly the relations between entities of various types at different levels, including both objects and the regions they occupy. What results is a layered mereotopology, a theory which can handle multiple layers (analogous to the layers of a lasagna) of spatially or spatiotemporally coincident but mereologically non-overlapping entities. Keywords: Ontology, mereology, mereotopology, qualitative spatial reasoning, map layers, dynamic GIS..

The paper is a contribution to formal ontology. It seeks to use topological means in order to derive ontological laws pertaining to the boundaries and interiors of wholes, to relations of contact and connectedness, to the concepts of surface, point, neighbourhood, and so on. The basis of the theory is mereology, the formal theory of part and whole, a theory which is shown to have a number of advantages, for ontological purposes, over standard treatments of topology in set-theoretic terms. One central goal of the paper is to provide a rigorous formulation of Brentano's thesis to the effect that a boundary can exist as a matter of necessity only as part of a whole of higher dimension which it is the boundary of. It concludes with a brief survey of current applications of mereotopology in areas such as natural-language analysis, geographic information systems, machine vision, naive physics, and database and knowledge engineering.