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.

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.”

This chapter offers a version of Cartesian dualism that draws on the resources of a Husserlian account of intentionality. For example, it argues that 'I can locate myself at the point in space from which I am looking at the world (my 'center of perspective')'. It relies on empirical phenomenology to show that this location that does not correspond to my body or any part of it. Phantom sensations provide confirming evidence. Next, the chapter uses the example of blurred (versus sharp) vision to provide evidence of qualitative properties that cannot be instantiated within the physical world. Finally, it argues that the self's endurance through calls for explanation in terms of patterns of psychophysical causation or interaction.

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.

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