Structure or system is a ubiquitous and indispensable feature of all our experience and theory, and requires an ontological analysis. The essays collected in this volume provide an account of structure founded upon the proper analysis of polyadic relations as the irreducible and defining elements of structure. Following from an analysis of ontic predication there is given a number of principles delineating realist instance ontology, together with a critique of both nominalistic trope theory and modern revivals of Aristotle's instance ontology of the Categories.
It is shown how the resulting theory of facts can, via "horizontal" and "vertical" composition, account for all the hierarchical structuring of our experience and theory, and, importantly, how this can rest upon an atomic ontic level composed of only dependent ontic predicates. The latter is a desideratum for the proposed "Structural Realism" ontology for micro-physics where at its lowest level the physical is said to be totally relational/structural. Nullified is the classic and insidious assumption that dependent entities presuppose a class of independent substrata or "substances," and with this any pressure to admit "bare particulars" and intensionless relations or "ties."
The logic inherent in realist instance ontology--termed "PPL"--is formalized in detail and given a consistency proof. Demonstrated is the logic's power to distinguish legitimate from illegitimate impredicative definitions, and in this how it provides a general solution to the classic self-referential paradoxes. PPL corresponds to Gdel's programmatic "Theory of Concepts." The last essay, not previously published, provides a detailed differentiation of identity from indiscernibility, preliminary to which is given an explanation of in what sense a predicate logic presupposes an ontology of predication. The principles needed for the differentiation have the significant implication (e.g., for the foundations of mathematics) of implying an infinity of logical entities, viz., instances of the identity relation.
Donald Mertz is currently the director of the Center for Academic Development at the University of Missouri - St. Louis. He has taught both university philosophy and mathematics, and has published a number of articles in analytic philosophy. He is the author of Moderate Realism and Its Logic, and is an associate editor of The Modern Schoolman.