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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 ...
In Book 3 of his work entitled Physics, Aristotle deals with the concept of infinity in terms of his notion of actuality and of potentiality. [ 8 ] [ 9 ] [ 10 ] It is always possible to think of a larger number: for the number of times a magnitude can be bisected is infinite.
Aristotle [A] (Attic Greek: Ἀριστοτέλης, romanized: Aristotélēs; [B] 384–322 BC) was an Ancient Greek philosopher and polymath. His writings cover a broad range of subjects spanning the natural sciences, philosophy, linguistics, economics, politics, psychology, and the arts.
Many of Aristotle's works are extremely compressed, and many scholars believe that in their current form, they are likely lecture notes. [2] Subsequent to the arrangement of Aristotle's works by Andronicus of Rhodes in the first century BC, a number of his treatises were referred to as the writings "after ("meta") the Physics" [b], the origin of the current title for the collection Metaphysics.
Aristotle here says the only type of infinity that exists is the potentially infinite. Aristotle characterizes this as that which serves as "the matter for the completion of a magnitude and is potentially (but not actually) the completed whole" (207a22-23).
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.
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.
Actuality is often used to translate both energeia (ἐνέργεια) and entelecheia (ἐντελέχεια) (sometimes rendered in English as entelechy). Actuality comes from Latin actualitas and is a traditional translation, but its normal meaning in Latin is 'anything which is currently happening.'