Infinity (philosophy)

In philosophy and theology, infinity is explored in articles under headings such as the Absolute, God, and Zeno's paradoxes.

Keenly aware of his departure from traditional wisdom, Cantor also presented a comprehensive historical and philosophical discussion of infinity.

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

[5] 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 dividing or separating matter from itself an infinite number of times.

[7] 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.

The second view is found in a clearer form by medieval writers such as William of Ockham: Sed omne continuum est actualiter existens.

Igitur quaelibet pars sua est vere existens in rerum natura.

Aristotle's emphasis on the connectedness of the continuum may have inspired—in different ways—modern philosophers and mathematicians such as Charles Sanders Peirce, Cantor, and LEJ Brouwer.

Aristotle deals with infinity in the context of the prime mover, in Book 7 of the same work, the reasoning of which was later studied and commented on by Simplicius.

[14] The Jain upanga āgama Surya Prajnapti (c. 400 BC) classifies all numbers into three sets: enumerable, innumerable, and infinite.

According to Singh (1987), Joseph (2000) and Agrawal (2000), the highest enumerable number N of the Jains corresponds to the modern concept of aleph-null

Galileo Galilei (February 15, 1564 – January 8, 1642[16]) discussed the example of comparing the square numbers {1, 4, 9, 16, ...} with the natural numbers {1, 2, 3, 4, ...} as follows: It appeared by this reasoning as though a "set" (Galileo did not use the terminology) which is naturally smaller than the "set" of which it is a part (since it does not contain all the members) is in some sense the same "size".

Famously, the ultra-empiricist Hobbes (April 5, 1588 – December 4, 1679[17]) tried to defend the idea of a potential infinity in light of the discovery, by Evangelista Torricelli, of a figure (Gabriel's Horn) whose surface area is infinite, but whose volume is finite.

Not reported, this motivation of Hobbes came too late as curves having infinite length yet bounding finite areas were known much before.

Locke (August 29, 1632 – October 28, 1704[18]) in common with most of the empiricist philosophers, also believed that we can have no proper idea of the infinite.

correlates a class with its subclass, we merely have yet another case of ambiguous grammar.Unlike the traditional empiricists, he thought that the infinite was in some way given to sense experience.