Towards foundations for the logic of distinctions

Abstract

This thesis is a contribution to the philosophy of logic and the foundations of metaphysics, and not to logic proper. We suggest how the fundamental concepts of predicate logic and set theory may be reduced entirely, or almost entirely, to relational concepts. We also urge and begin to introduce the use of a new type of interpretation of logic (and we call this type of interpretation a "Chinese-mystical" one). Against this background, we look briefly at a variety of aspects of possible beginnings for the logic of (intensions of) relations (equivalently, for the logic of distinctions). In Chapter 1 we introduce nearly all of the primitive notions and the symbolic vocabulary in terms of which, in Chapter 1 and also later, we attempt to explain all the fundamental concepts of predicate logic and set theory and to explore the logic of contexts and tokenicity. We also remark on some of the differences between our conception of the foundations of logic and the conception presupposed in, or commonly associated with, PM, with special emphasis on the deficiencies of the latter. In Chapter 2 we display various senses in which the properties of the true/false distinction can be said to be generalized to those of certain other distinctions. That is, we suggest that there are certain distinctions any one of which, for the purposes of logic, will effectively achieve all the work the true/false dichotomy can do, and other work besides. And we emphatically suggest that the scope of modern logic should be broadened. In Chapter 3 we attempt to introduce some inchoate aspects of the logic of relations proper (that is, of the intensions of relations). There we also introduce "Chinese-mystical" metaphysics; a "Chinese-mystical" metaphysics can be described as a relational metaphysics which denies any reality to "thing" concepts. In Chapter 4 we explore some of the rudiments of how to attempt to replace the propositional calculus by an analogue which would formalize the logical characteristics of in general unasserted relations instead of those of propositions. In Chapter 5 we briefly explain some of the philosophical inadequacies of contemporary set theory. In Chapter 6 we suggest how set theory can be altered to make it less unacceptable as a formalization of the concept of "manyness" and foundation for mathematics. In Chapter 7 we digress to briefly survey something of the diversity of theories of what are the bearers of truth and falsity. In Chapter 8 we attempt to indulge in a little pioneering work on foundations for the logic of tokenicity. In Chapter 9 we suggest a clearcut way in which the paradoxes of mysticism may be explained logically.