When I can find the time to put it here, you will find my following, already completed, research into the foundations of mathematics:

**The Axiomatic Structure of Boolean Algebras
** Using the notation presented by G Spencer-Brown in

It is demonstrated that this can be achieved using any one of exactly 5 distinct nontrivial single initial-equations.

The five single initial-equations and their consequences are stated.

Using the same notation a complete boolean algebra can factored into a maximum of 6 independent operations.

The 6 operations, and equations representing them, are presented with an analysis of the 64 algebras obtained by asserting an incomplete set.

Transliterations of these results into traditional notations are provided.

**The Axiomatic Structure of the Propositional Calculus
**Using the same notation, a complete propositional calculus is demonstrated
from a single initial-proposition.

It is demonstrated that this can be achieved using either of exactly 2 distinct nontrivial single initial-propositions.

The two single initial-propositions and their consequences are stated.

Using the same notation a complete propositional calculus can factored into a maximum of 12 independent operations.

The 12 operations, and propositions representing them, are presented.

Quantum logic is shown to be a calculus with one of the 12 operations omitted.

Transliterations of these results into traditional notations are provided.

A brief commentary on how this work relates to Wittgenstein's

**Re-entrant Boolean Structures, Information Waves and the
Causal Interpretation of Quantum Mechanics**

A discussion of how recursive boolean structures relate to the causal, ontological,
pilot-wave interpretation of quantum mechanics originally proposed by Louis
de Broglie and more recently developed by David Bohm, Basil Hiley and Jean-Pierre
Vigier.

You can email me at graham@ellsbury.com

Copyright © Graham Ellsbury 2001