This is a survey of the concept of continuity. Efforts to explicate continuity have produced a plurality of philosophical conceptions of continuity that have provably distinct expressions within contemporary mathematics. I claim that there is a divide between the conceptions that treat the whole continuum as prior to its parts, and those conceptions that treat the parts of the continuum as prior to the whole. Along this divide, a tension emerges between those conceptions that favor philosophical idealizations of continuity and (...) those that are more readily available for mathematico-scientific use. (shrink)

Suppose that a material object is gunky: all of its parts are located in space, and each of its parts has a proper part. Does it follow from this hypothesis that the space in which that object resides must itself be gunky? I argue that it does not. There is room for gunky objects in a space that decomposes without remainder into mereological simples.

In a recent paper titled ' Simples ', Ned Markosian asks and answers the Simple Question, which is, 'under what circumstances is it true of some object that it has no proper parts?' Markosian 's answer to the simple question is MaxCon, which states that an object is a simple if and only if it is a maximally continuous object. I present several arguments against MaxCon.

Are there any non‐composite objects? Are there any objects every part of which is composite? Are items of either kind even possible? What would they be like? Of what significance would they be? How best can we come to have reasonable beliefs about the answers to these inquiries? Such questions – about the actuality and possibility, the analysis and significance, the methodology and epistemology of simples and pieces of gunk – have been center stage in recent contemporary analytic metaphysics. The (...) following article provides a general overview of some of the current debates on their proper answers as well as a pair of slightly more detailed investigations into two issues of special interest in the recent literature devoted to these topics. (shrink)

Through contact algebras we study theories of mereotopology in a uniform way that clearly separates mereological from topological concepts. We identify and axiomatize an important subclass of closure mereotopologies called unique closure mereotopologies whose models always have orthocomplemented contact algebras , an algebraic counterpart. The notion of MT-representability, a weak form of spatial representability but stronger than topological representability, suffices to prove that spatially representable complete OCAs are pseudocomplemented and satisfy the Stone identity. Within the resulting class of contact algebras (...) the strength of the algebraic complementation delineates two classes of mereotopology according to the key ontological choice between mereological and topological closure operations. All closure operations are defined mereologically if and only if the corresponding contact algebras are uniquely complemented while topological closure operations highly restrict the contact relation but allow not uniquely complemented and nondistributive contact algebras. Each class contains a single ontologically coherent theory that admits discrete models. (shrink)

Both early analytic philosophy and the branch of mathematics now known as topology were gestated and born in the early part of the 20th century. It is not well recognized that there was early interaction between the communities practicing and developing these fields. We trace the history of how topological ideas entered into analytic philosophy through two migrations, an earlier one conceiving of topology geometrically and a later one conceiving of topology algebraically. This allows us to reassess the influence and (...) significance of topological methods for philosophy, including the possible fruitfulness of a third conception of topology as a structure determining similarity. (shrink)

Composition as Identity is the view that an object is identical to its parts taken collectively. I elaborate and defend a theory based on this idea: composition is a kind of identity. Since this claim is best presented within a plural logic, I develop a formal system of plural logic. The principles of this system differ from the standard views on plural logic because one of my central claims is that identity is a relation which comes in a variety of (...) forms and only one of them obeys substitution unrestrictedly. I justify this departure from orthodoxy by showing some problems which result from attempts to avoid inconsistencies within plural logic by means of postulating other non-singular terms besides plural terms. Thereby, some of the main criticisms raised against Composition as Identity can be addressed. Further, I argue that the way objects are arranged is relevant with respect to the question which object they compose, i.e. to which object they are identical to. This helps to meet a second group of arguments against Composition as Identity. These arguments aim to show that identifying composite objects on the basis of the identity of their parts entails, contrary to our common sense view, that rearranging the parts of a composite object does not leave us with a different object. Moreover, it allows us to carve out the intensional aspects of Composition as Identity and to defend mereological universalism, the claim that any objects compose some object. Much of the pressure put on the latter view can be avoided by distinguishing the question whether some objects compose an object from the question what object they compose. Eventually, I conclude that Composition as Identity is a coherent and plausible position, as long as we take identity to be a more complex relation than commonly assumed. (shrink)

An overview of contemporary part-whole theories, with reference to both their axiomatic developments and their philosophical underpinnings.

We think of a boundary whenever we think of an entity demarcated from its surroundings. There is a boundary (a line) separating Maryland and Pennsylvania. There is a boundary (a circle) isolating the interior of a disc from its exterior. There is a boundary (a surface) enclosing the bulk of this apple. Sometimes the exact location of a boundary is unclear or otherwise controversial (as when you try to trace out the margins of Mount Everest, or even the boundary of (...) your own body). Sometimes the boundary lies skew to any physical discontinuity or qualitative differentiation (as with the border of Wyoming, or the boundary between the upper and lower halves of a homogeneous sphere). But whether sharp or blurry, natural or artificial, for every object there appears to be a boundary that marks it off from the rest of the world. Events, too, have boundaries — at least temporal boundaries. Our lives are bounded by our births and by our deaths; the soccer game began at 3pm sharp and ended with the referee's final whistle at 4:45pm. It is sometimes suggested that even abstract entities, such as concepts or sets, have boundaries of their own, and Wittgenstein could emphatically proclaim that the boundaries of our language are the boundaries of our world. Whether all this boundary talk is coherent, however, and whether it reflects the structure of the world or simply the organizing activity of our mind, are matters of deep philosophical controversy. (shrink)

A critical survey of the fundamental philosophical issues in the logic and formal ontology of space, with special emphasis on the interplay between mereology (the theory of parthood relations), topology (broadly understood as a theory of qualitative spatial relations such as continuity and contiguity), and the theory of spatial location proper.