Uwe A. Meixner

The paradigmatic mereological relation is the relation of spatial part. Already much less paradigmatic is the relation of temporal part. The realm of abstract entities seems to be the ontological region where the notion of part and whole has no application at all. In what follows, I will contend that this is not true. There are part-whole relationships between abstract entities, and indeed relationships that are systematic to the point of constituting mereologically structured universes of abstract entities, “intelligible worlds”, as I will call them (in translation of the Latin “mundi intelligibiles”). The part-whole relations between abstract entities differ significantly from those between spatial, or temporal, or spatio-temporal entities. However, there are also significant analogies between abstract and concrete part-whole relations.

The paper analyzes the concept of a first cause, both for event causation and for agent causation. It turns out that one is rather ready to believe in the existence of first causes that are events, but not in the existence of first causes that are agents. The paper, however, develops and defends a complex argument to the conclusion that there is a first agent-cause. one version of that argument proves -- not necessarily the existence of God -- but still the existence of a godlike agent. Finally, the notion of a first agent-cause is employed for an analysis of freely willed human action.

The paper presents a new version of the "Cosmological Argument" – considered to be an ontological argument, since it exclusively uses ontological concepts and principles. It employs famous results of modern physics, and distinguishes between event-causation and agent-causation. Due to these features, the argument manages to avoid the objection of infinite regress. It remains true, however, that the conclusion of the argument is too unspecific to be unambiguously considered an argument for the existence of God.

This paper has two parts. The first part (sections 1 to 5) 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 (sections 6 to 9) is dedicated to the development of a rigorous theory of form-necessity (or nomological necessity, broadly conceived), 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.”

In Plato's Parmenides we find on the one hand that the One is denied every property , and on the other hand that the One is attributed every property . In the course of the history of Platonism , these assertions - probably meant by Plato as ontological statements of an entirely formal nature - were repeatedly made the starting points of metaphysical speculations. In the Mystical Theology of the Pseudo-Dionysius they became principles of Christian mysticism and negative theology. I shall show that the two assertions can each be interpreted within the ontological framework of ancient and medieval logic in such a manner that it becomes true, and I shall make plausible that they were understood, with regard to their logical core, by pagan and Christian Platonic metaphysicians just as is indicated by that interpretation. The mentioned ontological framework is basically the Boolean algebra of first-order properties. The main points of the interpretation are on the one hand the identification of the One with the maximal element of the algebra of properties, and on the other hand two alternative intuitively prominent mereological definitions of ontic predication

Existenz und Nichtexistenz werden in mehreren, mehr oder minder stark syntaktisch und/oder semantisch voneinander abweichenden Weisen ausgesagt. Dies gilt insbesondere von der deutschen Sprache; das meiste der nachfolgenden Beschreibungen des Sprachgebrauchs lässt sich jedoch auf jede andere indoeuropäische Sprache übertragen. Beschreibung aber gibt es nicht ohne Analyse; Beschreibung ist immer schon Analyse. Auch von der logischen Phänomenologie gilt: Die Beschreibung der Phänomene – die dafür notwendige Analyse – enthüllt die philosophische Tiefe, die unter, hinter, bei den Phänomenen ist.

One of the perennial questions of philosophy concerns the simple statements which say that an object is so and so or that such and such objects are so and so related: simple predicative statements. Do such statements have an ontological basis, and if so, what is that basis? The answer to this question determines—or in any case, is expressive of—a specific fundamental outlook on the world. In the course of the history of Western philosophy, various philosophers have given various answers to the question of predication. This essay presents the main, crucial answers: the paradigms and theories of predication of the Sophists (and of all later radical relativists), of Plato, of Aristotle, of the Aristotelian-minded non-nominalists, of Leibniz, and of Frege. In addition, the essay follows (to some extent) the most influential—the Aristotelian or mereological—paradigm of predication in its continuity and modification through the many centuries of its reign. However, the essay is not content to adopt the merely historical point of view; it also poses the question of adequacy. Prior to Frege, there was no philosophically adequate theory of predication, and the essay points out the shortcomings (besides aspects that can be viewed as advantages) of each pre-Fregean predication theory considered in it. Frege, in the nineteenth century, brought the philosophy of predication on the right track, but his own theory of predication has its own deficits. The essay ends with the presentation of a theory of predication that the author himself considers adequate.