The Interval of Motion in Leibniz's <i>Pacidius Philalethi</i>

Levey, Samuel

doi:10.1111/1468-0068.00444

Cited by 10 publications

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References 25 publications

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“…Or rather, he has denied that change is always densely ordered. For a somewhat different reading than this, see Levey (2003), which ascribes a fractal theory of change to Leibniz, one in which at least some changes are not densely ordered. 40 The exposition of this third alternative -topologically discrete matter forming a material plenum -tracks Levey (1999): "Contiguity really is supposed to preserve the integrity of the plenum because immediately neighboring bodies will touch in the strong sense that there is no empty space between them… all the parts of matter in the universe are so packed together that the boundaries of contiguous parts are 'indistant' from one another, leaving no empty spaces anywhere" (84 and 86; cf.…”

Section: Space and Time As Continuous Magnitudesmentioning

confidence: 99%

Leibniz's Metaphysics of Time and Space

Futch¹

2008

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Section: Space and Time As Continuous Magnitudesmentioning

confidence: 99%

Leibniz's Metaphysics of Time and Space

Futch¹

2008

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Leibniz on the Continuity of Space

Risi

2019

Boston Studies in the Philosophy and History of Science

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The present essay describes Leibniz's foundational studies on continuity in geometry. In particular, the paper addresses the long-debated problem of grounding a theory of intersections in elementary geometry. In the early modern age, in fact, several mathematicians had claimed that Euclid's Elements needed to be complemented with additional axioms in order to ground the existence of the intersection points between straight lines and circles. Leibniz was sensible to similar foundational issues in the Euclidean tradition, and dedicated several studies to investigate a good definition of the continuity of space, in order to ground a general theory of intersections of curves and surfaces. While Leibniz's researches on continuity in relation with the Calculus have been extensively studied in the past, the present essay deals with the less-known Leibnizian notion of a continuous space, as it is to be found in several unpublished writings preserved in Hannover. The subject widens as to encompass the relation between mereology and analysis situs, Leibniz's studies on a geometrical characteristics, and Leibniz's theory of space at large. Acknowledgements. I thank the Max Planck Institute for Mathematics in the Sciences and his director Jürgen Jost for providing me with the possibility of writing a good part of this paper while I was based in Leipzig, and more in general for having fostered important occasions of discussion with other Leibniz scholars. I also thank Richard Arthur, Eberhard Knobloch, Julien Narboux and Erich Reck, who have discussed with me this paper in several occasions; and Andrea Costa, Siegmund Probst and Javier Echeverría for sharing with me some unpublished papers by Leibniz.

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Baroquian Folds: Leibniz on Folded Fabrics and the Disruption of Geometry

Friedman¹

2021

Handbook of the Mathematics of the Arts and Sciences

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The Interval of Motion in Leibniz's Pacidius Philalethi

Cited by 10 publications

References 25 publications

Leibniz's Metaphysics of Time and Space

Leibniz's Metaphysics of Time and Space

Leibniz on the Continuity of Space

Baroquian Folds: Leibniz on Folded Fabrics and the Disruption of Geometry

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