Actual versus Potential Infinity (BPhil manuscript.)

Dissertation, University of Oxford (1997)

Authors
Anne Newstead
Swinburne University of Technology
Abstract
Do actual infinities exist or are they impossible? Does mathematical practice require the existence of actual infinities, or are potential infinities enough? Contrasting points of view are examined in depth, concentrating on Aristotle’s ancient arguments against actual infinities. In the long 19th century, we consider Cantor’s successful rehabilitation of the actual infinite within his set theory, his views on the continuum, Zeno's paradoxes, and the domain principle, criticisms by Frege, and the axiomatisation of set theory by Zermelo, as well as Zermelo’s assertion of the primacy of potential infinity in mathematics.
Keywords infinity  Aristotle  Cantor  potential versus actual infinite  Zermelo
Categories (categorize this paper)
Options
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


Upload a copy of this paper     Check publisher's policy     Papers currently archived: 64,159
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

Infinity in Science and Religion. The Creative Role of Thinking About Infinity.Wolfgang Achtner - 2005 - Neue Zeitschrift für Systematicsche Theologie Und Religionsphilosophie 47 (4):392-411.
Varieties of Finitism.Manuel Bremer - 2007 - Metaphysica 8 (2):131-148.
Infinity: New Research Frontiers.Michał Heller & W. H. Woodin (eds.) - 2011 - Cambridge University Press.
Aristotelian Infinity.John Bowin - 2007 - Oxford Studies in Ancient Philosophy 32:233-250.
Cantor on Infinity in Nature, Number, and the Divine Mind.Anne Newstead - 2009 - American Catholic Philosophical Quarterly 83 (4):533-553.
Paradox and Potential Infinity.Charles McCarty - 2013 - Journal of Philosophical Logic 42 (1):195-219.

Analytics

Added to PP index
2012-12-06

Total views
3 ( #1,328,934 of 2,454,830 )

Recent downloads (6 months)
2 ( #303,284 of 2,454,830 )

How can I increase my downloads?

Downloads

My notes