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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).
Aristotle postulated that an actual infinity was impossible, because if it were possible, then something would have attained infinite magnitude, and would be "bigger than the heavens." However, he said, mathematics relating to infinity was not deprived of its applicability by this impossibility, because mathematicians did not need the infinite ...
Temporal finitism is the doctrine that time is finite in the past. [clarification needed] The philosophy of Aristotle, expressed in such works as his Physics, held that although space was finite, with only void existing beyond the outermost sphere of the heavens, time was infinite.
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]
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]
50 Aristotle Quotes on Philosophy, Virtue and Education. Morgan Bailee Boggess. April 6, 2024 at 5:25 AM. Ancient Greek philosopher Aristotle statue.
Finitism is a philosophy of mathematics that accepts the existence only of finite mathematical objects. It is best understood in comparison to the mainstream philosophy of mathematics where infinite mathematical objects (e.g., infinite sets) are accepted as existing.