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In philosophy and theology, infinity is explored in articles under headings such as the Absolute, God, and Zeno's paradoxes. In Greek philosophy, for example in Anaximander, 'the Boundless' is the origin of all that is. He took the beginning or first principle to be an endless, unlimited primordial mass (ἄπειρον, apeiron).
But since Aristotle holds that such treatments of infinity are impossible and ridiculous, the world cannot have existed for infinite time. [9] Philoponus's works were adopted by many; his first argument against an infinite past being the "argument from the impossibility of the existence of an actual infinite", which states: [10]
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]
In the philosophy of mathematics, the abstraction of actual infinity, also called completed infinity, [1] involves infinite entities as given, actual and completed objects. The concept of actual infinity has been introduced in mathematics near the end of the 19th century by Georg Cantor , with his theory of infinite sets , later formalized into ...
50 Aristotle Quotes on Philosophy, Virtue and Education. Morgan Bailee Boggess. April 6, 2024 at 8:25 AM. Ancient Greek philosopher Aristotle statue.
Giordano Bruno's insistence on an infinity of worlds was not based on the theories of Copernicus, or on observation, but on the principle applied to God. His death may then be attributed to his conviction of its truth, as he refused to recant even while facing capital punishment for his view about this and other matters, which caused him to be ...
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 .
In this usage, infinity is a mathematical concept, and infinite mathematical objects can be studied, manipulated, and used just like any other mathematical object. The mathematical concept of infinity refines and extends the old philosophical concept, in particular by introducing infinitely many different sizes of infinite sets.