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Eternity, in common parlance, is an infinite amount of time that never ends or the quality, condition or fact of being everlasting or eternal. [1] Classical philosophy , however, defines eternity as what is timeless or exists outside time, whereas sempiternity corresponds to infinite duration.
The mathematical concept of infinity refines and extends the old philosophical concept, in particular by introducing infinitely many different sizes of infinite sets. Among the axioms of Zermelo–Fraenkel set theory, on which most of modern mathematics can be developed, is the axiom of infinity, which guarantees the existence of infinite sets. [1]
Modern discussion of the infinite is now regarded as part of set theory and mathematics. Contemporary philosophers of mathematics engage with the topic of infinity and generally acknowledge its role in mathematical practice. Although set theory is now widely accepted, this was not always so.
Eternal return (or eternal recurrence) is a philosophical concept which states that time repeats itself in an infinite loop, and that exactly the same events will continue to occur in exactly the same way, over and over again, for eternity.
Cantor said: The actual infinite was distinguished by three relations: first, as it is realized in the supreme perfection, in the completely independent, extra worldly existence, in Deo, where I call it absolute infinite or simply absolute; second to the extent that it is represented in the dependent, creatural world; third as it can be conceived in abstracto in thought as a mathematical ...
However, according to the best currently accepted theory in physics, the Standard Model, there is a distance (called the Planck length, 1.616229(38)×10 −35 metres, named after one of the fathers of Quantum Theory, Max Planck) and therefore a time interval (the amount of time which light takes to traverse that distance in a vacuum, 5.39116(13 ...
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 ...
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]