06341 Abstracts Collection -- Computational Structures for Modelling Space, Time and Causality

From 20.08.06 to 25.08.06, the Dagstuhl Seminar 06341 ``Computational Structures for Modelling Space, Time and Causality\u27\u27 was held in the International Conference and Research Center (IBFI), Schloss Dagstuhl. During the seminar, several participants presented their current research, and ongoing work and open problems were discussed. Abstracts of the presentations given during the seminar as well as abstracts of seminar results and ideas are put together in this paper. The first section describes the seminar topics and goals in general. Links to extended abstracts or full papers are provided, if available

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

The Necessary Structure of the All-pervading Aether: Discrete or Continuous? Simple or Symmetric?

In this book I investigate the necessary structure of the aether – the stuff that fills the whole universe. Some of my conclusions are. 1. There is an enormous variety of structures that the aether might, for all we know, have. 2. Probably the aether is point-free. 3. In that case, it should be distinguished from Space-time, which is either a fiction or a construct. 4. Even if the aether has points, we should reject the orthodoxy that all regions are grounded in points by summation. 5. If the aether is point-free but not continuous, its most likely structure has extended atoms that are not simples. 6. Space-time is symmetric if and only if the aether is continuous. 7. If the aether is continuous, we should reject the standard interpretation of General Relativity, in which geometry determines gravity. 8. Contemporary physics undermines an objection to discrete aether based on scale invariance, but does not offer much positive support

The Introduction of Topology into Analytic Philosophy: Two Movements and a Coda

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

Relativistic Spacetime Structure

I survey from a modern perspective what spacetime structure there is according to the general theory of relativity, and what of it determines what else. I describe in some detail both the "standard" and various alternative answers to these questions. Besides bringing many underexplored topics to the attention of philosophers of physics and of science, metaphysicians of science, and foundationally minded physicists, I also aim to cast other, more familiar ones in a new light

Relativistic Spacetime Structure

I survey from a modern perspective what spacetime structure there is according to the general theory of relativity, and what of it determines what else. I describe in some detail both the "standard" and various alternative answers to these questions. Besides bringing many underexplored topics to the attention of philosophers of physics and of science, metaphysicians of science, and foundationally minded physicists, I also aim to cast other, more familiar ones in a new light

The Metaphysics of Mental Representation

The representational theory of mind (RTM) explains the phenomenon of intentionality in terms of the existence and nature of mental representations. Despite the typical characterisation of mental representations in terms of their semantics, RTM is best understood as a metaphysical – more specifically formal ontological – theory whose primary defining feature is stipulating the existence of a class of mental particulars called representations. In this regard it is false, since mental representations do not exist. My argument is primarily methodological. Using an extended analysis of mereology and its variants as paradigmatic examples of a formal ontological theory, I argue for a 'synthetic’ approach to ontology which seeks to form a sound descriptive characterisation of the relevant phenomena from empirical data, to which philosophical analysis is applied to produce a rigorous theory. The value and necessity of this method is proved by example in our discussion of mereology which is shown to be defensible given certain assumptions, in particular perdurantism, but still inadequate as an account of parthood without considerable supplementation. We also see that there are viable alternatives which adopt a more synthetic approach and do not require the same assumptions. Having effectively demonstrated the value of a synthetic approach in ontology I critically examine the methodology employed by RTM and find it severely lacking. In the guise of ‘commonsense psychology’ RTM cavalierly imposes a theoretical framework without regard to empirical data, and this results in a severe distortion of the phenomenon of intentionality it purports to explain. RTM is methodologically unsound, and so its commitment to the existence of mental representations is utterly undermined. Furthermore the most attractive aspect of RTM – its semantics – can be separated from any commitment to mental representations existing. Even RTM’s strongest advocates lack motivation to believe that mental representations exist

The Structure of Gunk: Adventures in the Ontology of Space

Could space consist entirely of extended regions, without any regions shaped like points, lines, or surfaces? Peter Forrest and Frank Arntzenius have independently raised a paradox of size for space like this, drawing on a construction of Cantor’s. I present a new version of this argument and explore possible lines of response