Reasoning about Space: The Hole Story

Varzi, Achille C.

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. What exactly holes are, or even whether such dubious entities do indeed exist, these are of course questions one eventually needs to address in order to make good sense of such forms of reasoning. Holes are enigmatic, and it may be utterly difficult to specify adequate identity and individuation criteria for them. The purpose of this paper is to elaborate on that formalism and to illustrate how it can be exploited to provide a framework for more general patterns of qualitative spatial reasoning. In particular, after a general outline, I shall focus on some issues pertaining to the modelling, the representation, and the taxonomy of spatial inclusion. This is a topic that has received much attention in recent work in spatial reasoning, also in connection to a variety of applications, from naive physics to natural language semantics. My hope is to show that explicit commitment to holes as bona fide individuals introduces a novel and revealing (albeit certainly far from complete) perspective also with respect to such issues.


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Logic and Logical Philosophy

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October 27, 2014