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Publication - Dr Stuart Presnell

    The Hole Argument and Homotopy Type Theory


    Ladyman, J & Presnell, S, 2019, ‘The Hole Argument and Homotopy Type Theory’. Foundations of Physics.


    The Hole Argument is primarily about the meaning of general covariance in General Relativity (GR). As such it raises many deep issues about identity in mathematics and physics, the ontology of space-time, and how scientic representation works. This paper is about the application of a new foundational programme in mathematics, namely Homotopy Type Theory (HoTT), to the Hole Argument. It is argued that the framework of HoTT is not conducive to the formulation of the Hole Argument, but that the Hole Argument might be contrived in HoTT. The role of the Univalence Axiom in the treatment of the Hole Argument in HoTT is claried.

    Full details in the University publications repository