Edward G. Belaga
Strasbourg University
What is so special and mysterious about the Continuum, this ancient, always topical, and alongside the concept of integers, most intuitively transparent and omnipresent conceptual and formal medium for mathematical constructions and the battle field of mathematical inquiries ? And why it resists the century long siege by best mathematical minds of all times committed to penetrate once and for all its set-theoretical enigma ? The double-edged purpose of the present study is to save from the transfinite deadlock of higher set theory the jewel of mathematical Continuum -- this genuine, even if mostly forgotten today raison d'etre of all set-theoretical enterprises to Infinity and beyond, from Georg Cantor to W. Hugh Woodin to Buzz Lightyear, by simultaneously exhibiting the limits and pitfalls of all old and new reductionist foundational approaches to mathematical truth: be it Cantor's or post-Cantorian Idealism, Brouwer's or post-Brouwerian Constructivism, Hilbert's or post-Hilbertian Formalism, Goedel's or post-Goedelian Platonism. In the spirit of Zeno's paradoxes, but with the enormous historical advantage of hindsight, we claim that Cantor's set-theoretical methodology, powerful and reach in proof-theoretic and similar applications as it might be, is inherently limited by its epistemological framework of transfinite local causality, and neither can be held accountable for the properties of the Continuum already acquired through geometrical, analytical, and arithmetical studies, nor can it be used for an adequate, conceptually sensible, operationally workable, and axiomatically sustainable re-creation of the Continuum. From a strictly mathematical point of view, this intrinsic limitation of the constative and explicative power of higher set theory finds its explanation in the identified in this study ultimate phenomenological obstacle to Cantor's transfinite construction, similar to topological obstacles in homotopy theory and theoretical physics: the entanglement capacity of the mathematical Continuum.
Keywords the mathematical Continuum  higher set theory  post-Goedelian incompleteness scheme  post-Turingean halting principle
Categories (categorize this paper)
Edit this record
Mark as duplicate
Export citation
Find it on Scholar
Request removal from index
Translate to english
Revision history

Download options

PhilArchive copy

 PhilArchive page | Other versions
External links

Setup an account with your affiliations in order to access resources via your University's proxy server
Configure custom proxy (use this if your affiliation does not provide a proxy)
Through your library

References found in this work BETA

No references found.

Add more references

Citations of this work BETA

No citations found.

Add more citations

Similar books and articles

Is Cantor's Continuum Problem Inherently Vague?Kai Hauser - 2002 - Philosophia Mathematica 10 (3):257-285.
The Genesis of the Peircean Continuum.Matthew E. Moore - 2007 - Transactions of the Charles S. Peirce Society 43 (3):425 - 469.
Continuum, Name and Paradox.Vojtěch Kolman - 2010 - Synthese 175 (3):351 - 367.
Kurt Godel and Phenomenology.Richard Tieszen - 1992 - Philosophy of Science 59 (2):176-194.
Mathematics as a Quasi-Empirical Science.Gianluigi Oliveri - 2004 - Foundations of Science 11 (1-2):41-79.


Added to PP index

Total views
677 ( #11,183 of 2,499,013 )

Recent downloads (6 months)
17 ( #48,579 of 2,499,013 )

How can I increase my downloads?


My notes