Events, Topology and Temporal Relations

Abstract

We are used to regarding actions and other events, such as Brutus' stabbing of Caesar or the sinking of the Titanic, as occupying intervals of some underlying linearly ordered temporal dimension. This attitude is so natural and compelling that one is tempted to disregard the obvious difference between time periods and actual happenings in favor of the former: events become mere "intervals cum description".1 On the other hand, in ordinary circumstances the point of talking about time is to talk about what actually happens or might happen at some time or another. We talk about 'now' and 'then' in an effort to put some order in our description of what goes on. And since different events seem to overlap in so many different ways, a full account of their temporal relations seems to run afoul of a reductionist strategy.This raises two philosophical questions. The first is whether we can actually go beyond time, as it were, i.e., whether we can take events as bona fide entities and deal with them directly, just as we can deal with spatial entities such as physical bodies or masses without confining ourselves to their spatial representations. This is a controversial issue (though probably not as controversial as it used to be), and ties in with a number of unsettled problems concerning, e.g., the structure of causality or the definition of adequate identity and individuation criteria for events. 2 The second question is whether we can perhaps do without time, i.e., whether we can dispense with time points or intervals as an independent ontological category and focus only on actual or potential happenings, in opposition to the form of reductionism mentioned above-in short, whether we can account for the temporal dimension in terms of suitable relations among events. This is also a highly controversial issue, and relates to the classical dispute concerning relational vs. absolutist conceptions of (space and) time. It is this second question that we intend to focus on here. Even if the acceptance of events as part of our ontological inventory is in itself a matter of dispute, we shall assume there to be enough good arguments to justify a positive attitude in this regard: events are part of the furniture of the world, whatever their exact ontological make up. We shall actually assume that events are individuals, as opposed to, for instance, states of affairs. 4 The focus of our concern is whether this assumption allows one to answer also the second question in the af-

Parts, wholes, and part-whole relations: The prospects of mereotopology

“…For instance, [65] gives a version of the theory using 'IP' as a primitive; [48,49,50] give an equivalent formulation based on 'c' as a primitive and (60)- (61) as axioms. A version of the same theory based on the primitive 'boundary' is found in [51]. A slightly weaker formulation, based on 'IP', can also be found in [70], though this theory turns out to be defective in various respects.…”

The Context-Dependency of Temporal Reference in Event Semantics

“…In [6] we have shown that such relations can ultimately be construed from some basic ontological properties that a domain of events must arguably satisfy-specifically, mereological and topological properties. The construction is refined in [7], and in [8] it is shown to be especially liable to the sort of refinement that is requiired to account for the context-dependence exhibited by natural language. Here is a brief review of this construction.…”

“…In addition to the these basic mereotopological notions, the following notions are introduced in [7] with an eye to their use in characterizing event domains:…”

Reasoning about space: The hole story

“…This becomes apparent especially in connection with qualitative reasoning about space and time: here mereology proves useful to account for certain basic relationships among things or events; but one needs topology to account, say, for the fact that two objects or events can be continuous with each other, or for the relation of something being inside, abutting, or surrounding something else. (My present concern will be with the mereotopology of spatial structures; I have explored eventive and other temporal structures in joint work with Fabio Pianesi [25,26,27]. )…”

“…This is the strategy favored here. Following in the footsteps of [45], the topological primitive will be a binary relation of topological connection (we could as well use the notion of boundary, or that of interior parthood: see [26,36,38,42] for some such alternatives). This relation will be denoted by 'C(x, y)' and will be read "x is connected with y".…”