|Abstract||This article discusses the history of the concepts of potential infinity and actual infinity in the context of Christian theology, mathematical thinking and metaphysical reasoning. It shows that the structure of Ancient Greek rationality could not go beyond the concept of potential infinity, which is highlighted in Aristotle's metaphysics. The limitations of the metaphysical mind of ancient Greece were overcome through Christian theology and its concept of the infinite God, as formulated in Gregory of Nyssa's theology. That is how the concept of actual infinity emerged. However, Gregory of Nyssa's understanding of human rationality went still further. He said that access to the infinity of God was to be found only in an asymptotic ascension, as expressed in apophatic theology, and this view endangered the rationality of theology. Deeply influenced by the apophatic tradition, Nicholas of Cusa avoided this danger by showing that infinity could be accessed by symbolic representation and asymptotic mathematical reasoning. Thus, he made an immense contribution in making infinity rationally accessible. This endeavor was finally realized by Georg Cantor. This rational accessibility revealed discernible structures of infinity, such as the continuum hypothesis, and the cardinal numbers. However, the probable logical inconsistency of Georg Cantor's all-encompassing Absolute Infinity points to an intuitive understanding of infinity that goes beyond its rational structures – as in apophatic theology.|
|Keywords||No keywords specified (fix it)|
|Through your library||Configure|
Similar books and articles
Eric Steinhart (2007). Infinity. In Encyclopedia of American Philosophy. Routledge.
Edward Nelson (2011). Part II. Perspectives on Infinity From Mathematics : 2. The Mathematical Infinity / Enrico Bombieri ; 3. Warning Signs of a Possible Collapse of Contemporary Mathematics. [REVIEW] In Michał Heller & W. H. Woodin (eds.), Infinity: New Research Frontiers. Cambridge University Press.
Brian Clegg (2003). Infinity: The Quest to Think the Unthinkable. Distributed by Publishers Group West.
Michael Heller (2011). Part IV. Perspectives on Infinity From Physics and Cosmology : 7. Some Considerations on Infinity in Physics / Carlo Rovelli ; 8. Cosmological Intimations of Infinity / Anthony Aguirre ; 9. Infinity and the Nostalgia of the Stars/ Marco Bersanelli ; 10. Infinities in Cosmology. [REVIEW] In Michał Heller & W. H. Woodin (eds.), Infinity: New Research Frontiers. Cambridge University Press.
Denys A. Turner (2011). A Partially Skeptical Response to Hart and Russell. [REVIEW] In Michał Heller & W. H. Woodin (eds.), Infinity: New Research Frontiers. Cambridge University Press.
Michał Heller & W. H. Woodin (eds.) (2011). Infinity: New Research Frontiers. Cambridge University Press.
Wolfgang Achtner (2011). Part I. Perspectives on Infinity From History : 1. Infinity as a Transformative Concept in Science and Theology. In Michał Heller & W. H. Woodin (eds.), Infinity: New Research Frontiers. Cambridge University Press.
Added to index2009-01-28
Total downloads63 ( #15,073 of 556,837 )
Recent downloads (6 months)2 ( #39,010 of 556,837 )
How can I increase my downloads?