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https://oxford.universitypressscholarship.com/view/10.1093/oso/9780198809647.001.0001/oso-9780198809647
Aristotle insisted that continuous substances are not composed of points, and that they can only be divided into parts potentially; a continuum is a unified whole. The most dominant account today, traced to Cantor and Dedekind, is in stark contrast with this, taking a continuum …
https://www.jstor.org/stable/2707510
"Nothing that is continuous," Aristotle held, "can be composed of indivisibles."1 Aristotle was clear that time is not composed of instants, nor a line of points.2 For both time and a line are instances of continua, and a continuum is "that which is divisible into divisibles that are in-finitely divisible."
https://www.britannica.com/biography/Aristotle/Physics-and-metaphysics
The continuum Spacial extension, motion, and time are often thought of as continua—as wholes made up of a series of smaller parts. Aristotle develops a subtle analysis of the nature of such continuous quantities. Two entities are continuous, he says, when there is only a …
https://courses.lumenlearning.com/atd-epcc-introethics-1/chapter/aristotles-doctrine-of-the-mean/
Aristotle’s Doctrine of the Mean (Originally appeared in History of Philosophy Quarterly 4/3, July 1987.) Aristotle’s doctrine of the mean is sometimes dismissed as an unhelpful and unfortunate mistake in what would otherwise be — or perhaps, in spite of this lapse, still is — a worthwhile enterprise.
https://www.academia.edu/188285/Aristotle_and_modern_mathematical_theories_of_the_continuum
The isomorphism thesis will still be valid insofar as both space and time are continua for Aristotle, but it will no longer be true that stretches of space and time have the same topological structure. Well-Ordering and the ContinuumIn an eminently sensible passage, Aristotle argues that a continuum cannot be constituted out of points, since a ...
https://www.tandfonline.com/doi/abs/10.1080/01445348808837121
An argument of Aristotle to the effect that what is continuous cannot be constituted of ‘indivisibles’ (e.g., points) is examined from a topological perspective. From that perspective, the argument fails because Aristotle does not recognize a collectiveas well as a distributiveconcept of a multiplicity of points.
https://www.revistas.usp.br/filosofiaantiga/article/download/169952/160789/408382
solution according to which Aristotle’s understanding of continuity can only be saved if he holds a certain kind of mathematical ontology. My topic in this paper is Aristotle’s understanding of mathematical continuity. While the idea that continua are composed of infinitely many points is the present day
https://www.academia.edu/37811202/Mathematical_Continuity_as_Unity_and_Infinity_in_Aristotle_A_reflection_on_the_nature_of_the_physical_universe
The reason why Aristotle affirms that no continuous line is made of indivisible points is the antinomy existing between the continuous divisible line and its discontinuous indivisible points.If it is an analytic contradiction to have a continuous, divisible line made of discontinuous, indivisible points, then a continuous infinitely divisible line is necessarily made of continuous infinitely divisible lines.
https://www.susinpom.com/file/the-history-of-continua
Synopsis : The History of Continua written by Stewart Shapiro, published by Oxford University Press, USA which was released on 01 February 2021. Download The History of Continua Books now!Available in PDF, EPUB, Mobi Format. Mathematical and philosophical thought about continuity has changed considerably over the ages, from Aristotle's insistence that a continuum is a unified whole, to the ...
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