Uwe A. Meixner

This treatise delves into the construction and formalization of a precise theory to encapsulate a pivotal facet of Thomas Aquinas’s ontology. In particular, it focuses on the development of a formal language that is adequate for formulating Aquinas’s understanding of the simultaneous nature of divinity as both an object of subsistence and a universal, individual, and actuating form—a concept evocative of the original Platonic sense of form. The presented axiomatized theory as a medium for expounding the ontological principles enunciated by Thomas Aquinas. A comprehensive set of axioms is systematically justified, exhibiting their congruence with Aquinas’s ontological doctrines. To elucidate this harmony, an extensive series of theorems is deduced, closely aligned with the verbal tenets of Aquinas’s teachings. The inherent consistency of the axiom system is proven by the provision of a geometrico-topological model tailored to support it.

This paper has two parts. The first part is historical, presenting a brief history of the concept of necessity from the time of antiquity to the present. It is shown that the conceptions of necessity in antiquity had four main sources: matter-necessity, form-necessity, efficiencynecessity, and purpose-necessity. Special attention is accorded to the syncretistic concept of the necessity of fate, and its transformations from the beginning of antiquity to its end. Moreover, it is pointed out that already in antiquity we find the conception of proofnecessity, and the distinction between intrinsic and extrinsic necessity. At present, of the original four main sources of conceptions of necessity, three have dried up, leaving only form-necessity still active. The second part of the paper is dedicated to the development of a rigorous theory of form-necessity, at the end of which a skeptical note is struck regarding laws of nature

In this paper, a paradox is shown to arise in the context of classical logic from prima facie highly plausible assumptions for the existence predicate as applied to definite descriptions. There are several possibilities to evade the paradox; all involve modifications in the principles of first-order logic with identity, existence, and definite descriptions; some stay within classical logic, others leave it. The merits of the various "ways out" are compared. The most attractive "way out," it is argued, stays within classical logic, except for the fact that it involves a new logical truth: "There is at least one non-existent object." But this "exit" will certainly not be to everyone's taste and liking. Thus, the paradox defies complete resolution.

In a time which it is not amiss to term “the Dark Ages of logic”, Karl Christian Friedrich Krause stayed not only true to logic but actually did something for its advancement. Besides making systematic use of Venn-diagrams long before Venn, Krause — once more taking his inspiration from Leibniz — propounded what appears to be the first completely symbolic systematic representation of logical forms, strongly suggestive of the powerful symbolic languages that have become the mainstay of logic since the beginning of the 20th century. However, Krause’s limits in logic are also clearly visible: Krause’s method in logic is, in the main, not axiomatic; it is combinatorial. More importantly, Krause remained entirely within the confines of traditional syllogistics, neglecting propositional logic and, of course, first-order relational terms.

How might one tackle the subject of causation with the least amount of preformed conceptions – and arrive by a series of well-motivated conceptual decisions at a concept of causation that captures the “heart of the matter”? This essay is a sustained attempt to answer this question. On the way, causal predicates of various degrees of importance are defined and causal principles of various degrees of plausibility discussed, all of this in the service of approaching, step by step, “the heart of the matter.”