Mereotopology without Mereology

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”.     

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.     

Plurals and Mereology

Journal of Philosophical Logic - In linguistics, the dominant approach to the semantics of plurals appeals to mereology. However, this approach has received strong criticisms from philosophical...     

Tensed Mereology

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.     

Vague Objects within Classical Logic and Standard Mereology,and without Indeterminate Identity

Weatherson (The Philosophical Quarterly, 53, 481–501 2003) argues that whoever accepts classical logic, standard mereology and the difference between vague objects and any others, should conclude that there are no vague objects. Barnes and Williams (Pacific Philosophical Quarterly, 90, 176–187 2009) claim that a supporter of vague objects who accepts classical logic and standard mereology should recognize that the existence of vague objects implies indeterminate identity. Even though it is not clearly stated, they all seem to be committed to the assumption that reality is ultimately constituted by mereological atoms. This assumption is not granted by standard mereology which instead remains silent on whether reality is atomic or gunky; therefore, I contend that whoever maintains classical logic, standard mereology and the difference between vague objects and any others, is not forced to conclude with Weatherson that there are no vague objects; nor is she compelled to revise her point of view according to Barnes and Williams’s proposal and to accept that the existence of vague objects implies indeterminate identity.     

Mereology and time travel

Philosophical Studies - Core principles of mereology have been questioned by appealing to time travel scenarios. This paper questions the methodology of employing time travel scenarios to argue...     

Decidability of General Extensional Mereology

The signature of the formal language of mereology contains only one binary predicate P which stands for the relation “being a part of”. Traditionally, P must be a partial ordering, that is, ${\forall{x}Pxx, \forall{x}\forall{y}((Pxy\land Pyx)\to x=y)}$ and ${\forall{x}\forall{y}\forall{z}((Pxy\land Pyz)\to Pxz))}$ are three basic mereological axioms. The best-known mereological theory is “general extensional mereology”, which is axiomatized by the three basic axioms plus the following axiom and axiom schema: (Strong Supplementation) ${\forall{x}\forall{y}(\neg Pyx\to \exists z(Pzy\land \neg Ozx))}$ , where Oxy means ${\exists z(Pzx\land Pzy)}$ , and (Fusion) ${\exists x\alpha \to \exists z\forall y(Oyz\leftrightarrow \exists x(\alpha \land Oyx))}$ , for any formula α where z and y do not occur free. In this paper, I will show that general extensional mereology is decidable, and will also point out that the decidability of the first-order approximation of the theory of complete Boolean algebras can be shown in the same way.     

Analytic Rules for Mereology

We present a sequent calculus for extensional mereology. It extends the classical first-order sequent calculus with identity by rules of inference corresponding to well-known mereological axioms. Structural rules, including cut, are admissible.     

Modal Mereology and Modal Supervenience

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.     

Neither Mereology nor Magic,but Teleology

Contemporary theories of universals have two things in common: first, they are unable to account for necessary connections between universals that form a structure. Second, they leave teleology out of their accounts of instantiation. These facts are not unrelated; the reason why contemporary theories have such trouble is they neglect the ancient idea that universals are ends at which nature aims. If we want a working theory of universals, however, we must return to this idea. Despite its unpopularity among realists, teleology is not a disposable eccentricity, and its dismissal is not an improvement on ancient views.     

Heyting Mereology as a Framework for Spatial Reasoning

In this paper it is shown that Heyting and Co-Heyting mereological systems provide a convenient conceptual framework for spatial reasoning, in which spatial concepts such as connectedness, interior parts, (exterior) contact, and boundary can be defined in a natural and intuitively appealing way. This fact refutes the wide-spread contention that mereology cannot deal with the more advanced aspects of spatial reasoning and therefore has to be enhanced by further non-mereological concepts to overcome its congenital limitations. The allegedly unmereological concept of boundary is treated in detail and shown to be essentially affected by mereological considerations. More precisely, the concept of boundary turns out to be realizable in a variety of different mereologically grounded versions. In particular, every part K of a Heyting algebra H gives rise to a well-behaved K-relative boundary operator.     

Fazang's Total Power Mereology: An Interpretive Analytic Reconstruction

In his Treatise on the Golden Lion, Fazang says that wholes are in each of their parts and that each part of a whole is every other part of the whole. In this paper, I offer an interpretation of these remarks according to which they are not obviously false, and I use this interpretation in order to rigorously reconstruct Fazang's arguments for his claims. On the interpretation I favor, Fazang means that the presence of a whole's part suffices for the presence of the whole and that the presence of any such part is both necessary and sufficient for the presence of any other part. I also argue that this interpretation is more plausible than its extant competitors.     

An Applied Mereology of the City: Unifying Science and Philosophy for Urban Planning

Based on their research showing that growing cities follow basic principles, two theoretical physicists, Luis Bettencourt and Geoffrey West, call for researchers and professionals to contribute to a grand theory of urban sustainability. In their research, they develop a ‘science of the city’ to help urban planners address problems that arise from population increases. Although they provide valuable insights for understanding urban sustainability issues, they do not give planners a manageable way to approach such problems. I argue that developing an applied mereology to understand the concept of ‘city identity’ gives planners a theoretical device for addressing urban affairs, including ethical concerns. In turn, I devise a model of city identity to show how a ‘philosophy of the city’ contributes to a grand theory of urban sustainability.     

Weak speech reports

Philosophical Studies - Indirect speech reports can be true even if they attribute to the speaker the saying of something weaker than what she in fact expressed, yet not all weakenings of what the...