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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.
Our beliefs must not be justified after all (as is posited by philosophical skeptics). Infinitism, the view, for example, of Peter D. Klein , challenges this consensus, referring back to work of Paul Moser (1984) and John Post (1987). [ 2 ]
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.
Philosophical Perspectives on Infinity. Philosophia Mathematica 15 (3). Elliott Mendelson (1956) "Some Proofs of Independence in Axiomatic Set Theory", Journal of Symbolic Logic 21(3): 291–303. Elliott Mendelson (1990) "Second Thoughts About Church's Thesis and Mathematical Proofs", Journal of Philosophy 87(5): 225–233.
Contemporary Perspectives on Religious Epistemology. Oxford University Press. pp. 257– 269. Rescher, Nicholas (1985). Pascal's Wager: A Study of Practical Reasoning in Philosophical Theology. University of Notre Dame Press. ISBN 9780268015565. (The first book-length treatment of the Wager in English.) Whyte, Jamie (2004).
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.
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 ...
The relevant section of Two New Sciences is excerpted below: [2]. Simplicio: Here a difficulty presents itself which appears to me insoluble.Since it is clear that we may have one line greater than another, each containing an infinite number of points, we are forced to admit that, within one and the same class, we may have something greater than infinity, because the infinity of points in the ...