Wittgenstein revisited

In his monumental Tractatus Logico-Philosphicus, Austrian philosopher Ludwig Wittgenstein attempted to arrive at a comprehensive definition of knowledge based upon an analysis of language. Wittgenstein's application of logical methodologies to this task proved influential in the development of modern theories of linguistics, computation, and machine intelligence. Given that science, philosophy, and art evolve in parallel, it is surely no coincidence that the rigorous formalism of Wittgenstein's thought found a counterpart in the development of contemporary music theory. As one noted academic succinctly observed, "The ubiquitous preoccupation with polyphony (i.e. with fundamental voices contributing ordered subsets to form larger, more comprehensive sets which may themselves be subject to transformation as intrinsic voices in a musical dimension) should be viewed as an attempt to achieve profound levels of integration in the hierarchy of structures generated by the partition of fundamental lines relative to appropriate criteria of relatedness vis-a-vis the total set of structures."