Prolegomena to an Ontology of Shape
Antony Galton
In Proceedings of the Second Interdisciplinary Workshop "The Shape of Things", Rio de Janeiro, Brazil, April 3-4, 2013. Published online at http://ceur-ws.org/Vol-1007/.
Abstract
Influenced by the four-category ontology of Aristotle, many modern
ontologies treat shapes as accidental particulars which (a) are
specifically dependent on the substantial particulars which act as
their bearers, and (b) instantiate accidental universals which are
exemplified by those bearers. It is also common to distinguish
between, on the one hand, these physical shapes which form part of the
empirical world and, on the other, ideal geometrical shapes which
belong to the abstract realm of mathematics. Shapes of the former kind
are often said to approximate, but never to exactly instantiate,
shapes of the latter kind. Following a suggestion of Frege, ideal
mathematical shapes can be given precise definitions as equivalence
classes under the relation of geometrical similarity. One might,
analogously, attempt to define physical shape universals as
equivalence classes under a relation of physical similarity, but this
fails because physical similarity is not an equivalence relation. In
this talk I will examine the implications of this for the ontology of
shape and in particular for the relationship between mathematical
shapes and the shapes we attribute to physical objects.
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Slides from the presentation
Antony Galton
Last modified: Mon Jul 8 12:49:09 BST 2013