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.