Historical Notes

The purpose of this section is to satisfy the historical interests of the reader and, as far as I am able, to discharge the obligations of academic honesty.

Before entering into the details, I would like to point out that more of my ideas than I am able to trace are due to the influence of my teachers of logic: Rudolf Carnap, Evert W. Beth, Arend Heyting, and Stephen C. Kleene, to whom I must add, primarily through their writings, Alonzo Church and Alfred Tarski. The influence of these teachers on my thinking is so pervasive that the tracing of any idea of mine to one or more of them would never surprise me.

With regard to more specific indebtedness:

Chapters 1-2: The modern concept of logical calculus on which these definitions rest is primarily due to Gottlob Frege and to a lesser degree to David Hilbert, Bert rand Russell, and Charles Saunders Peirce. The formulation of structure and derivation concepts is, I believe, original in its detail, but to a considerable degree, is based on formulations by Church, Rosser, and to a lesser degree, Carnap and Gentzen.

Chapter 3: The greater portion of this chapter is based on the work of E.L Post and J.B. Rosser.

Chapter 4: With few exceptions, the systems in chapters 4 - 9 were determined by a natural architectonic. Most of them had however been independently developed earlier and the following notes indicate the earliest source I have been able to discover.