A General Symbolic Method with Physical Applications

While certainly taking full responsibility for the contents of this thesis, it would yet be absurd of me to take full credit, for many people have contributed, however indirectly, to its completion. I'd like to at least take the trouble to thank a few of them. I'd first like to note my obvious debt to those scientists of various disciplines whose ideas have influenced mine. In this connection the bibliography is intended to be fairly thorough, though not exhaustive, in indicating the works that, with respect to this paper, I've come into valuable contact with. I'm satisfied to leave it to the reader to arrive at his own conclusions as to the degree of originality of, or influences on, the thoughts expressed herein. My exploration of the above works has been facilitated by the suggestions and criticisms of my committee: Professors Bringsjord, Drew, McLaughlin, and Zenzen. These criticisms have decidedly increased the cogency of the presentation which follows and, not only the content, but also the form of this work has thus benefited. I'm especially indebted to my advisor, Professor Drew, for his patience and encouragement during the many revisions this work has undergone. Finally, I'd like to thank my parents for the innumerable efforts they've made on my behalf over the years. I hope they too find some measure of satisfaction in the completion of this thesis. 3 0.2 ABSTRACT This thesis derives general physical results by an entirely formal process. Beginning with a brief examination of the notion of language itself, it next explores Physics in a schematic fashion in order to arrive at conclusions on the relationship between experience and language. This investigation leads to the hypothesis that there is no separate reality to which language refers, and there-for to the test of constructing physical theory without reference to experiment: If experience is not to direct the interpretation of language then language must yield its own interpretation. To make such an idea acceptable it is next shown how references to such a presumably fictional entity such as an exterior reality may arise within language itself, and how such references may, and must, be retained. From this starting-point an entirely formal language is developed, along with an associated algebra and a Calculus, neither of which are restricted to finite quantities. With the completion of the general symbolic system the derivation of both Relativity Theory and Quantum Theory, as …