Objects as Limits of Experience and the Notion of Horizon in Mathematical Theories

  • Stathis Livadas University of Patras

Abstract

The present work is an attempt to bring attention to the application of several key ideas of Husserl's Krisis in the construction of certain mathematical theories that claim to be altenative nonstandard versions of the standard Zermelo-Fraenkel set theory. In general, these theories refute, at least semantically, the platonistic context of the Cantorian system and to one or the other degree are motivated by the notions of the lifeworld as the pregiven holistic field of experience and that of horizon as the boundary of human perceptions and the de facto constraint in reaching limit-idealizations. Moreover, I try to give convincing reasons for the existence of an ultimate constitutional "vacuum" of a subjective origin that is formally reflected in the application of a notion of actual infinity in dealing generally with the mathematical infinite.
Keywords: Actual infinity; alternative theory; field of expenence; horizon; life-world; limit-idealization; nonstandard

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Published
2012-10-01
How to Cite
LIVADAS, Stathis. Objects as Limits of Experience and the Notion of Horizon in Mathematical Theories. Phainomenon, [S.l.], n. 25, p. 131-153, oct. 2012. ISSN 2183-0142. Available at: <http://phainomenon-journal.pt/index.php/phainomenon/article/view/326>. Date accessed: 22 june 2018.
Section
Monographic Section: Mathematizing Nature