40 research outputs found

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

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    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

    The prospects for mathematical logic in the twenty-first century

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    The four authors present their speculations about the future developments of mathematical logic in the twenty-first century. The areas of recursion theory, proof theory and logic for computer science, model theory, and set theory are discussed independently.Comment: Association for Symbolic Logi

    Analytical Guide and updates for "Cardinal Arithmetic"

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    Part A: A revised version of the guide in "Cardinal Arithmetic" ([Sh:g]), with corrections and expanded to include later works. Part B: Corrections to [Sh:g]. Part C: Contains some revised proof and improved theorems. Part D: Contains a list of relevant references

    Zeno’s Paradoxes. A Cardinal Problem. I. On Zenonian Plurality

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    It will be shown in this article that an ontological approach for some problems related to the interpretation of Quantum Mechanics (QM) 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. More well known are the derivative paradoxes of Zeno: the paradox of motion and the paradox of the One and the Many. They stem from what was perceived by classical philosophy to be the fundamental enigma for thinking about the world: the seemingly contradictory results that followed from the co-incidence of being and non-being in the world of change and motion as we experience it, and the experience of absolute existence here and now. The most clear expression of both stances can be found, again following classical thought, in the thinking of Heraclitus of Ephesus and Parmenides of Elea. The problem put forward by these paradoxes reduces for both Plato and Aristotle to the possibility of the existence of stable objects as a necessary condition for knowledge. Hence the primarily ontological nature of the solutions they proposed: Plato’s Theory of Forms and Aristotle’s metaphysics and logic. 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. So it becomes possible to forbid contradiction on an epistemological level, and thus to guarantee the certainty of knowledge that seemed to be threatened before. 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

    Studies in the contemporary Spanish-American short story

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    Bibliography: page 123-124Includes indexThis work deals with selected Latin-American writers of short stories and, in the case of each author, with only one or a limited number of texts. No attempt has been made to write a history of the contemporary short story in Latin America or even to deal with a canon of representative authors. Each of the texts studied has been chosen because it is indicative of a facet of the short story that parallels the so-called Latin American new novel.Introduction -- The �criture of literary texts -- Toward a characterization of �criture in the stories of Borges --Rulfo's "Luvina" and structuring figures of diction --Garc�a M�rquez and the �criture of complicity: "La prodigiosa tarde de Baltazar" -- The double inscription of the Narrataire in "Los funerales de la Mam� Grande" -- The �criture of rupture and subversion of language in Cort�zar's Historias de cronopios y famas -- Cort�zar's "Las armas secretas" and structurally anomalous narratives -- The �criture of social protest in Mario Benedetti's "El cambiazo" -- Guillermo Cabrera Infante's Vista del amanecer en el tr�pico and the generic ambiguity of narrativeDigitized at the University of Missouri--Columbia MU Libraries Digitization Lab in 2012. Digitized at 600 dpi with Zeutschel, OS 15000 scanner. Access copy, available in MOspace, is 400 dpi, grayscale
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