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Aristotle's emphasis on the connectedness of the continuum may have inspired—in different ways—modern philosophers and mathematicians such as Charles Sanders Peirce, Cantor, and LEJ Brouwer. [11] [12] Among the scholastics, Aquinas also argued against the idea that infinity could be in any sense complete or a totality.
This means there is only a (developing, improper, "syncategorematic") potential infinity but not a (fixed, proper, "categorematic") actual infinity. There were exceptions, however, for example in England. It is well known that in the Middle Ages all scholastic philosophers advocate Aristotle's "infinitum actu non datur" as an irrefutable principle.
But since Aristotle holds that such treatments of infinity are impossible and ridiculous, the world cannot have existed for infinite time. The most sophisticated medieval arguments against an infinite past were later developed by the early Muslim philosopher , Al-Kindi (Alkindus); the Jewish philosopher , Saadia Gaon (Saadia ben Joseph); and ...
In his philosophy, Aristotle distinguished two meanings of the word dunamis. According to his understanding of nature there was both a weak sense of potential, meaning simply that something "might chance to happen or not to happen", and a stronger sense, to indicate how something could be done well .
Initially, Aristotle's interpretation, suggesting a potential rather than actual infinity, was widely accepted. [1] However, modern solutions leveraging the mathematical framework of calculus have provided a different perspective, highlighting Zeno's significant early insight into the complexities of infinity and continuous motion. [1]
Infinite divisibility arises in different ways in philosophy, physics, economics, order theory (a branch of mathematics), and probability theory (also a branch of mathematics). One may speak of infinite divisibility, or the lack thereof, of matter , space , time , money , or abstract mathematical objects such as the continuum .
50 Aristotle Quotes on Philosophy, Virtue and Education. Morgan Bailee Boggess. April 6, 2024 at 5:25 AM. Ancient Greek philosopher Aristotle statue.
Finally, it has been maintained that a reflection on infinity, far from eliciting a "horror of the infinite", underlay all of early Greek philosophy and that Aristotle's "potential infinity" is an aberration from the general trend of this period. [14]