Zeno's Paradoxes. A Cardinal Problem 1. On Zenonian Plurality

In this paper the claim that Zeno's paradoxes have been solved is contested. Although no one has ever touched Zeno without refuting him (Whitehead), it will be our aim to show that, whatever it was that was refuted, it was certainly not Zeno. The paper is organised in two parts. In the first part we will demonstrate that upon direct analysis of the Greek sources, an underlying structure common to both the Paradoxes of Plurality and the Paradoxes of Motion can be exposed. This structure bears on a correct - Zenonian - interpretation of the concept of division through and through. The key feature, generally overlooked but essential to a correct understanding of all his arguments, is that they do not presuppose time. Division takes place simultaneously. This holds true for both PP and PM. In the second part a mathematical representation will be set up that catches this common structure, hence the essence of all Zeno's arguments, however without refuting them. Its central tenet is an aequivalence proof for Zeno's procedure and Cantor's Continuum Hypothesis. Some number theoretic and geometric implications will be shortly discussed. Furthermore, it will be shown how the Received View on the motion-arguments can easely be derived by the introduction of time as a (non-Zenonian) premiss, thus causing their collapse into arguments which can be approached and refuted by Aristotle's limit-like concept of the potentially infinite, which remained - though in different disguises - at the core of the refutational strategies that have been in use up to the present. Finally, an interesting link to Newtonian mechanics via Cremona geometry can be established.Comment: 41 pages, 7 figure

Newton vs. Leibniz: Intransparency vs. Inconsistency

We investigate the structure common to causal theories that attempt to explain a (part of) the world. Causality implies conservation of identity, itself a far from simple notion. It imposes strong demands on the universalizing power of the theories concerned. These demands are often met by the introduction of a metalevel which encompasses the notions of 'system' and 'lawful behaviour'. In classical mechanics, the division between universal and particular leaves its traces in the separate treatment of cinematics and dynamics. This analysis is applied to the mechanical theories of Newton and Leibniz, with some surprising results

Infinity and the Sublime

In this paper we intend to connect two different strands of research concerning the origin of what I shall loosely call "formal" ideas: firstly, the relation between logic and rhetoric - the theme of the 2006 Cambridge conference to which this paper was a contribution -, and secondly, the impact of religious convictions on the formation of certain twentieth century mathematical concepts, as brought to the attention recently by the work of L. Graham and J.-M. Kantor. In fact, we shall show that the latter question is a special case of the former, and that investigation of the larger question adds to our understanding of the smaller one. Our approach will be primarily historical.Comment: 29 pages and 3 figure

Managing inequality: the political ecology of a small-scale fishery, Mweru-Luapula, Zambia

This paper starts from the perspective on resource management approaches as based upon a body of environmental knowledge. By analysing fisheries management in Mweru-Luapula, Zambia, we argue that this body of environmental knowledge has (i) remained largely unchanged throughout the recent shift to co-management and (ii) is to a great extent based upon general paradigmatic conventions with regard to common property regimes. We therefore simultaneously studied the historical trajectories of both resource management as the political ecology of Mweru-Luapula’s fishing economy. Using a relational perspective – by looking at interaction of the local fishing economy with external developments, but also by examining socioeconomic relations between individual actors – this study exposes constraints and incentives within the local fishing economy that are not absorbed in the current co-management regime. These findings challenge both policy goals as community-based resource management itself. We therefore argue that governance of small-scale fisheries – in order to close the gap between locally based understandings, policy and legislation – should always be built upon all dimensions (social, economic, ecological, political) that define a fisheries system

Early Greek Thought and Perspectives for the Interpretation of Quantum Mechanics: Preliminaries to an Ontological Approach

It will be shown in this article that an ontological approach for some problems related to the interpretation of Quantum Mechanics could emerge from a re-evaluation of the main paradox of early Greek thought: the paradox of Being and non-Being, and the solutions presented to it by Plato and Aristotle. Plato's and Aristotle's systems are argued here to do on the ontological level essentially the same: to introduce stability in the world by introducing the notion of a separable, stable object, for which a principle of contradiction is valid: an object cannot be and not-be at the same place at the same time. After leaving Aristotelian metaphysics, early modern science had to cope with these problems: it did so by introducing ``space'' as the seat of stability, and ``time'' as the theater of motion. But the ontological structure present in this solution remained the same. Therefore the fundamental notion `separable system', related to the notions observation and measurement, themselves related to the modern concepts of space and time, appears to be intrinsically problematic, because it is inextricably connected to classical logic on the ontological level. We see therefore the problems dealt with by quantum logic not as merely formal, and the problem of `non-locality' as related to it, indicating the need to re-think the notions `system', `entity', as well as the implications of the operation `measurement', which is seen here as an application of classical logic (including its ontological consequences) on the material world.Comment: 18 page

Crystallization of microscopic Y2O3 powders by different techniques of fluidization at high temperature

Ahigh temperature fluidized bed reactor (HTFBR)working at 900 to 1200 ◦Chas been developed to crystallize microscopic yttria (Y2O3) powders synthesized by spray pyrolysis. Such crystallization is classically performed in crucible or in moving belt furnaces. In order to demonstrate the advantages of the fluidized bed process over the conventional static mode treatments, a comparative study of the main characteristics of particles after heat treatment in a crucible and in the HTFBR has been performed. The high interparticle forces existing in such Geldart group C powders made it necessary to activate their fluidization. Following previous results, two activated fluidization processes were studied: addition of coarse powders to fine particles and vibrated fluidization. The hydrodynamic behavior of these fluidized beds was analyzed through pressure drop measurements. Convenient fluidization conditions were obtained for the two activated fluidization processes, leading to isothermal beds. The size distribution, the crystallinity and the outer morphology of particles before and after thermal treatments were analyzed and compared for the three processes tested. Some pre-sintering phenomena occurred at 1200 ◦C, which were clearly more intense in crucible than in activated fluidization. The crystallinity of the samples treated was equivalent for the three methods of thermal treatment. The interest of fluidization processes to post-treat microscopic particles is thus fully demonstrated

On what Ontology Is and not-Is

In this paper I study the connection between logic and metaphysics in Plato's participation theory, from the structural properties of the latter. Although Plato was the first ever to formulate the contradiction principle explicitly (in the Phaedo), the logic underlying his system appears to be paraconsistent. This confirms an earlier suggestion by G. Priest. Its technical characteristics and the textual evidence supporting this interpretation are both studied in detail.Comment: 27 pages, 6 figure