Whitehead's Principle

According to Whitehead’s rectified principle, two individuals are connected just in case there is something self-connected which overlaps both of them, and every part of which overlaps one of them. Roberto Casati and Achille Varzi have offered a counterexample to the principle, consisting of an individual which has no self-connected parts. But since atoms are self-connected, Casati and Varzi’s counterexample presupposes the possibility of gunk or, in other words, things which have no atoms as parts. So one may still wonder whether Whitehead’s rectified principle follows from the assumption of atomism. This paper presents an atomic countermodel to show the answer is no

Formal Theories of Parthood

A compact overview of the main formal theories of parthood and of their mutual relationships, up to Classical Extensional Mereology. Written as an Appendix to the other essays included in the volume

Universalism Entails Extensionalism

Universalism (also known as Conjunctivism, or Collectivism) is the thesis that mereological composition is unrestricted. More precisely: Any non-empty collection of things has a fusion, i.e., something that has all those things as parts and has no part that is disjoint from each of them. Extensionalism is the thesis that sameness of composition is sufficient for identity. More precisely: No two things have exactly the same proper parts (unless they are atomic, i.e., have no proper parts at all). Clearly these two theses are not equivalent. They are, however, more closely related than one might think. More precisely, the entailment holds as long as it is agreed that the following postulates are constitutive of the meaning of ‘part’: Transitivity: Any part of any part of a thing is itself part of that thing. Supplementation: Whenever a thing has a proper part, it has at least another part that is disjoint from the first

Actuating (Auto)Poiesis

This paper claims that the use of the computer as generative methodological tool for designing urban and building scenarios (when perceived systematically) is a misnomer, because the typical approach does not account for the incompleteness of computational processes. We will argue that the computerisation of architectural and urban scenarios with autopoietic and/or artificial life simulations does not account for what Edsger W. Dijkstra called “radical novelty”; and Gilles Deleuze termed “line of flight”. Typical computational methods do not open up genuine alternatives that produce radical morphologies. Our argument is predicated on the dominant notion of computation as opposed to a critique of computation per se. A critical analysis of the perception of novelty is made to support our view, and its connection with the incompleteness of axiomatic systems is explored in relation to three phases of cybernetic enquiry. Our argument draws on the ontologies of Alfred North Whitehead and Gilles Deleuze, which we utilise to reorient computational design to emphasise the potential of generating radical novelty and identify the inherent locus therein a matter of nonhuman decision-making

Universalism entails Extensionalism

Universalism (also known as Conjunctivism, or Collectivism) is the thesis that mereological composition is unrestricted. More precisely: Any non-empty collection of things has a fusion, i.e., something that has all those things as parts and has no part that is disjoint from each of them. Extensionalism is the thesis that sameness of composition is sufficient for identity. More precisely: No two things have exactly the same proper parts (unless they are atomic, i.e., have no proper parts at all). Clearly these two theses are not equivalent. They are, however, more closely related than one might think. More precisely, the entailment holds as long as it is agreed that the following postulates are constitutive of the meaning of ‘part’: Transitivity: Any part of any part of a thing is itself part of that thing. Supplementation: Whenever a thing has a proper part, it has at least another part that is disjoint from the first

Extension and Self-Connection

If two self-connected individuals are connected, it follows in classical extensional mereotopology that the sum of those individuals is self-connected too. Since mainland Europe and mainland Asia, for example, are both self-connected and connected to each other, mainland Eurasia is also self-connected. In contrast, in non-extensional mereotopologies, two individuals may have more than one sum, in which case it does not follow from their being self-connected and connected that the sum of those individuals is self-connected too. Nevertheless, one would still expect it to follow that a sum of connected self-connected individuals is self-connected too. In this paper, we present some surprising countermodels which show that this conjecture is incorrect

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