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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]
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.
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 ...
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 .
This list compiles some of the most famous quotes by Aristotle and a few lesser-known ones, but equally as profound. Related: 75 Stoic Quotes from Philosophers of Stoicism About Life, Happiness ...
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.
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]