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.

Autorentext

William Kallfelz holds Masters Degrees in Physics and in Applied Mathematics from the Georgia Institute of Technology, and a Doctorate in Philosophy from the University of Maryland, with an area of specialization in the philosophy of physics and in the philosophy of science. He is actively researching in the foundations of physics.

Klappentext

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.