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.