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In philosophy and theology, infinity is explored in articles under headings such as 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).
Objective availability could be best understood, at least as a working definition, as an existing, truth-apt reason not dependent on the subject. A subjectively available reason is stated as follows: "S must be able to call on r." (Subjectively available is comparatively straightforward compared to objectively available.)
In the philosophy of mathematics, the abstraction of actual infinity, also called completed infinity, [1] involves infinite entities as given, actual and completed objects. Since Greek antiquity , the concept of actual infinity has been a subject of debate among philosophers.
The apeiron is central to the cosmological theory created by Anaximander, a 6th-century BC pre-Socratic Greek philosopher whose work is mostly lost. From the few existing fragments, we learn that he believed the beginning or ultimate reality is eternal and infinite, or boundless (apeiron), subject to neither old age nor decay, which perpetually yields fresh materials from which everything we ...
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.
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 ...
Totality and Infinity: An Essay on Exteriority (French: Totalité et Infini: essai sur l'extériorité) is a 1961 book about ethics by the philosopher Emmanuel Levinas. Highly influenced by phenomenology , it is considered one of Levinas's most important works.
For an infinite regress argument to be successful, it has to show that the involved regress is vicious. [3] A non-vicious regress is called virtuous or benign. [5] Traditionally, it was often assumed without much argument that each infinite regress is vicious but this assumption has been put into question in contemporary philosophy.