  In this paper we discuss the relevance of the algebraic approach to quantum
phenomena first introduced by von Neumann before he confessed to Birkoff that
he no longer believed in Hilbert space. This approach is more general and
allows us to see the structure of quantum processes in terms of non-commutative
probability theory, a non-Boolean structure of the implicate order which
contains Boolean sub-structures which accommodates the explicate classical
world. We move away from mechanical `waves' and `particles' and take as basic
what Bohm called a {\em structure process}. This enables us to learn new
lessons that can have a wider application in the way we think of structures in
language and thought itself.
