Philosophical hypergraphics: some applications to philosophy of the theory of hypergraphs

TL;DRAbstract

This thesis demonstrates the applicability of hypergraphs to philosophical problems. I employ and enrich the theory of transverse hypergraphs, the colouring theory of hypergraphs, and the novel harmonic theory of hypergraphs. I also demonstrate that the relationship between the latter two theories is one of logical duality. Because this thesis consists of a number of distinct articles, each representing a thematically diverse application of hypergraph theory to philosophy, it is difficult to speak of a unifying thread, except insofar as I may explain the general modus operandi in highly schematic terms. To that end, common to all of the articles is the exemplification of the following: A problem is given whereby there is a collection of objects and a question has arisen as to whether these objects stand in a particular relationship to one another. I use hypergraphs to represent the objects. A key feature of the objects is then modelled using either chromatic or harmonic number, or the

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