Topological Foundations of Cognitive Science

A collection of papers presented at the First International Summer Institute in Cognitive Science, University at Buffalo, July 1994, including the following papers: ** Topological Foundations of Cognitive Science, Barry Smith ** The Bounds of Axiomatisation, Graham White ** Rethinking Boundaries, Wojciech Zelaniec ** Sheaf Mereology and Space Cognition, Jean Petitot ** A Mereotopological Definition of 'Point', Carola Eschenbach ** Discreteness, Finiteness, and the Structure of Topological Spaces, Christopher Habel ** Mass Reference and the Geometry of Solids, Almerindo E. Ojeda ** Defining a 'Doughnut' Made Difficult, N .M. Gotts ** A Theory of Spatial Regions with Indeterminate Boundaries, A.G. Cohn and N.M. Gotts ** Mereotopological Construction of Time from Events, Fabio Pianesi and Achille C. Varzi ** Computational Mereology: A Study of Part-of Relations for Multi-media Indexing, Wlodek Zadrozny and Michelle Ki

Against the iterative conception of set

According to the iterative conception of set, each set is a collection of sets formed prior to it. The notion of priority here plays an essential role in explanations of why contradiction-inducing sets, such as the Russell set, do not exist. Consequently, these explanations are successful only to the extent that a satisfactory priority relation is made out. I argue that attempts to do this have fallen short: understanding priority in a straightforwardly constructivist sense threatens the coherence of the empty set and raises serious epistemological concerns; but the leading realist interpretations---ontological and modal interpretations of priority---are deeply problematic as well. I conclude that the purported explanatory virtues of the iterative conception are, at present, unfounded

Between Atomism and Superatomism

There are at least three vaguely atomistic principles that have come up in the literature, two explicitly and one implicitly. First, standard atomism is the claim that everything is composed of atoms, and is very often how atomism is characterized in the literature. Second, superatomism is the claim that parthood is well-founded, which implies that every proper parthood chain terminates, and has been discussed as a stronger alternative to standard atomism. Third, there is a principle that lies between these two theses in terms of its relative strength: strong atomism, the claim that every maximal proper parthood chain terminates. Although strong atomism is equivalent to superatomism in classical extensional mereology, it is strictly weaker than it in strictly weaker systems in which parthood is a partial order. And it is strictly stronger than standard atomism in classical extensional mereology and, given the axiom of choice, in such strictly weaker systems as well. Though strong atomism has not, to my knowledge, been explicitly identified, Shiver appears to have it in mind, though it is unclear whether he recognizes that it is not equivalent to standard atomism in each of the mereologies he considers. I prove these logical relationships which hold amongst these three atomistic principles, and argue that, whether one adopts classical extensional mereology or a system strictly weaker than it in which parthood is a partial order, standard atomism is a more defensible addition to one’s mereology than either of the other two principles, and it should be regarded as the best formulation of the atomistic thesis

The Mereology of Emergence

The debate about the ontological innocence of mereology has generally been framed as a debate about the plausibility of Universal Fusion. Ontologically loaded fusions must be more than the sum of their parts, and this seems to violate parsimony if fusion is universal. Less attention has been paid to the question of what sort of emergence mereological fusions must exhibit if they are irreducible to their parts. The philosophy of science literature provides several models of such strong emergence. Examining those models suggests that the difficulty with emergent fusions has at least as much to do with extensionality as it does with Universal Fusion. Some accounts of emergence fail to ensure irreducibility when combined with extensional mereologies. The most promising model for the strong emergence of ontologically loaded fusions fails to validate Anti-Symmetry, which naturally leads to failures of extensionality. These results suggest that the focus on Universal Fusion may have been misplaced

Spinoza on Composition, Monism, and Beings of Reason

In this paper, I argue that Spinoza holds a perspectivalist view of mereological composition, a form of anti-realism. The paper has two parts: In the first half of the paper, I introduce interpretive puzzles for the standard realist reading of Spinoza’s mereology. In the second half of the paper, I discuss Spinoza’s positive view on mereological composition and present a perspectivalist reading that avoids the interpretive puzzles

Towards a Conceptualization of Sociomaterial Entanglement

In knowledge representation, socio-technical systems can be modeled as multiagent systems in which the local knowledge of each individual agent can be seen as a context. In this paper we propose formal ontologies as a means to describe the assumptions driving the construction of contexts as local theories and to enable interoperability among them. In particular, we present two alternative conceptualizations of the notion of sociomateriality (and entanglement), which is central in the recent debates on socio-technical systems in the social sciences, namely critical and agential realism. We thus start by providing a model of entanglement according to the critical realist view, representing it as a property of objects that are essentially dependent on different modules of an already given ontology. We refine then our treatment by proposing a taxonomy of sociomaterial entanglements that distinguishes between ontological and epistemological entanglement. In the final section, we discuss the second perspective, which is more challenging form the point of view of knowledge representation, and we show that the very distinction of information into modules can be at least in principle built out of the assumption of an entangled reality

Fundamentality and Conditionality of Existence

In metaphysics, fundamentality is a central theme involving debates on the nature of existents, as wholes. These debates are largely object-oriented in their standpoint and engage with composites or wholes through the mereological notion of compositionality. The ontological significance of the parts overrides that of wholes since the existence and identity of the latter are dependent on that of the former. Broadly, the candidates for fundamental entities are considered to be elementary particles of modern physics (since they appear to play the role of ultimate parts to all phenomena). The paper intends to show the inadequacy of the object-oriented notion of conditionality by pointing out that the parts and wholes possess varying conditions of existence. By alleging that only the parts are ontologically significant is to conflate such conditions and neglect the spectrum of conditions which exist in our world. A proposal for a revised notion of compositionality in terms of structural relatedness is also put forward

Reasoning about space: The hole story

Much of our naive reasoning about space involves reasoning about holes and holed objects. We put things in holes, through holes, around them; we jump out of a hole or fall into one; we compare holes, measure them, enlarge them, fill them up

The Intrinsic Structure of Quantum Mechanics

The wave function in quantum mechanics presents an interesting challenge to our understanding of the physical world. In this paper, I show that the wave function can be understood as four intrinsic relations on physical space. My account has three desirable features that the standard account lacks: (1) it does not refer to any abstract mathematical objects, (2) it is free from the usual arbitrary conventions, and (3) it explains why the wave function has its gauge degrees of freedom, something that are usually put into the theory by hand. Hence, this account has implications for debates in philosophy of mathematics and philosophy of science. First, by removing references to mathematical objects, it provides a framework for nominalizing quantum mechanics. Second, by excising superfluous structure such as overall phase, it reveals the intrinsic structure postulated by quantum mechanics. Moreover, it also removes a major obstacle to "wave function realism.