Infinity (philosophy)

In philosophy and theology, infinity is explored in articles under headings such as the Ultimate, 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). The Jain metaphysics and mathematics was the first to define and delineate different "types" of infinities. The work of the mathematician Georg Cantor first placed infinity into a coherent mathematical framework. Keenly aware of his departure from traditional wisdom, Cantor also presented a comprehensive historical and philosophical discussion of infinity. In Judeo-Christian theology, for example in the work of Duns Scotus, the infinite nature of God invokes a sense of being without constraint, rather than a sense of being unlimited in quantity. In ethics infinity plays an important role designating that which cannot be defined or reduced to knowledge or power.

An early engagement with the idea of infinity was made by Anaximander who considered infinity to be a foundational and primitive basis of reality. Anaximander was the first in the Greek philosophical tradition to recognise the universe was infinite.

Anaxagoras (500–428 BCE) was of the opinion that matter of the universe had an innate capacity for infinite division.

A group of thinkers of ancient Greece (later identified as the Atomists) all similarly considered matter to be made of an infinite number of structures as considered by imagining an dividing or separating matter from itself an infinite number of times.

Aristotle, alive for the period 384–322 BCE, is credited with being the root of a field of thought, in his influence of succeeding thinking for a period spanning more than one subsequent millennium, by his rejection of the idea of actual infinity.

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