Kallfelz, W: Clifford Algebra

Robert Batterman's ontological insights are apt (nature indeed abhhors singularities), though his epistemic assessments are murky. For he writes that singularities play an essential role in certain classes of physical theories representing critical phenomena. I outline a procedure which makes essential use of Clifford Algebra to counter his claims. I use some of the demonstrated formal unity of Clifford Algebra to argue that Batterman appears to conflate a physical theory's ontology with its purely mathematical content. Carefully distinguishing the two, and employing Clifford Algebraic methods reveals a symmetry between explanation and reduction that Batterman overlooks. I refine this point by showing that the methods adopted in Clifford Algebraic computational fluid dynamics undercut many of Batterman's claims concerning the essentially explanatory role played by singularities. I also argue that the model of inter-theoretic reduction and explanation offered by Fritz Rohrlich and aspects of structuralism provide the best framework for accommodating the burgeoning research tradition of Clifford Algebra in the mathematical sciences.