Actual versus Potential Infinity (BPhil manuscript.)

Dissertation, University of Oxford (1997)

Anne Newstead
Swinburne University of Technology
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
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