The world as a graph: defending metaphysical graphical structuralism

Analysis 71 (1):10-21 (2011)
Abstract
Metaphysical graphical structuralism is the view that at some fundamental level the world is a mathematical graph of nodes and edges. Randall Dipert has advanced a graphical structuralist theory of fundamental particulars and Alexander Bird has advanced a graphical structuralist theory of fundamental properties. David Oderberg has posed a powerful challenge to graphical structuralism: that it entails the absurd inexistence of the world or the absurd cessation of all change. In this paper I defend graphical structuralism. A sharper formulation, some theorems about such structures, and careful attention to the interaction of metaphysical and mathematical features, shows that the absurdities depend on assumptions that are not essential to the view and brings to light a surprising fact about the necessary structure of fundamental properties.
Keywords metaphysical graphical structuralism  graphical structuralism for particulars  graphical structuralism for properties  structural realism  dispositions and powers  nodes and edges  Snowflake Lemma  potency graph  Uniquely Manifesting Potencies Regress Theorem  manifestation regress
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