The Concept of Infinity in Ancient Mathematics and Philosophy

Abstract

The present analysis it was finds that Aristotle's admission of the problem of infinity was a position on the problem that arose in ancient mathematics and philosophy at least a century earlier. Infinity in mathematics appeared in connection with the discovery of incommensurability and the introduction of infinity procedures. This was pointed out by Pythagoreans. In another intellectual centre of Great Greece, among the Eleates, the problem of infinity arose in connection with the ontological and physical samples of the negation of the effect of movement. Zeno's well-known aporias showed the paradoxes associated with the concept of infinity and continuity. Aristotle, with the help of Eudoxius, tried to avoid the problems associated with infinity. Therefore, despite not providing the definition of infinity (infinite sets), he introduced a dichotomy of current and potential infinity. He came in favour of the Dasein of potential infinity. That was the expression of the ancient "fear of infinity". Ancient problems associated with the concept of infinity was not solved until the 19th century, when the theory of infinite sets (set theory) arose. But that was connected with the rejection of the ancient axiom which states that "the whole is greater than a part".

The Aristotelian distinction between potential and current infinity has found a permanent place among tools used by philosophers and philosophical mathematicians. To this day, there is no agreement among them whether the existence of the currently infinite numbers should be accepted. One thing is for sure: mathematics has been in need of some form of infinity since ancient times.