Applying the rules and systems of mathematics and logic to instance ontology, this work argues for the validity and problem-solving capacities of instance ontology, and associates it with a version of the realist position which is named by the author as moderate realism.

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. (shrink)

It is a common occurence to find Galileo claimed as the father of modern science, particularly as to his method being appropriate for its pursuit. Yet, it is apparent from the literature that little agreement has been reached concerning the specifics of the structure and nature of his method(s). Galileo himself is explicit in little more than describing it as „geometrical“, and as such contrasting its greater demonstrative power with that of the traditional Peripatetic logic. One is then left with (...) examples and glosses in the text as to hints that might place his method in a known context of ancient or medieval science, or metaphysics and logic, or both. (shrink)

It is generally agreed that Galileo’s distinctive place in the history of science is due to the power of his method, and that, in general terms, this consists in an effective combination of mathematics and physical experiment. In attempting to be more specific, some authors have assigned a particular method to Galileo as either new or a unique adaptation of a traditional method, e.g. hypothetico-deduction, the method of analysis, or ex suppositione. William Wallace, for example, has argued that by the (...) time of the «Two New Sciences» (1638) Galileo had fashioned his own version of ex suppositione, combining elements of the Archimedean and Aristotelian traditions into a distinct two-stage mode of reasoning of his own creation. We shall have reason to comment upon this below. (shrink)