Peirce, Clifford, and Dirac

There is a clear line of progression from the “logic of relations” of Charles Sanders Peirce through the algebras of William Kingdon Clifford. Further, it has been shown how one can obtain the nonrelativistic quantum theory of spin one-half particles from Peirce logic. Continuing the hypothetical history, it is demonstrated here that the relativistic Dirac theory can also be related to Peirce logic. The most natural way to accomplish this is to represent the Dirac wave functions themselves as Clifford numbers rather than as spinors. The wave functions can thus appear as 4× 4 matrices. All quantities in this quantum theory can actually be expressed in terms of the Clifford basis, independent of a specific matrix representation.