Surreal Time and Ultratasks

Review of Symbolic Logic 9 (4):836-847 (2016)
Download Edit this record How to cite View on PhilPapers
Abstract
This paper suggests that time could have a much richer mathematical structure than that of the real numbers. Clark & Read (1984) argue that a hypertask (uncountably many tasks done in a finite length of time) cannot be performed. Assuming that time takes values in the real numbers, we give a trivial proof of this. If we instead take the surreal numbers as a model of time, then not only are hypertasks possible but so is an ultratask (a sequence which includes one task done for each ordinal number—thus a proper class of them). We argue that the surreal numbers are in some respects a better model of the temporal continuum than the real numbers as defined in mainstream mathematics, and that surreal time and hypertasks are mathematically possible.
PhilPapers/Archive ID
ALDSTA
Revision history
Archival date: 2018-08-15
View upload history
References found in this work BETA
Parts of Classes.Lewis, David K.
Parts of Classes.Potter, Michael
The Classical Continuum Without Points.Hellman, Geoffrey & Shapiro, Stewart

View all 8 references / Add more references

Citations of this work BETA

Add more citations

Added to PP index
2018-02-09

Total views
473 ( #8,824 of 50,265 )

Recent downloads (6 months)
206 ( #1,926 of 50,265 )

How can I increase my downloads?

Downloads since first upload
This graph includes both downloads from PhilArchive and clicks to external links.