Review of Symbolic Logic 9 (4):836-847 (2016)

Haidar Al-Dhalimy
University of Minnesota
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.
Keywords Time  Supertask  Hypertask  Surreal Numbers  Infinitesimals  Temporal continuum  Continuity  Zeno
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DOI 10.1017/s1755020316000289
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References found in this work BETA

Parts of Classes.David K. Lewis - 1991 - Mind 100 (3):394-397.
Parts of Classes.Michael Potter - 1993 - Philosophical Quarterly 43 (172):362-366.
The Classical Continuum Without Points.Geoffrey Hellman & Stewart Shapiro - 2013 - Review of Symbolic Logic 6 (3):488-512.

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Citations of this work BETA

Quick and Easy Recipes for Hypergunk.Patrick Reeder - 2020 - Australasian Journal of Philosophy 98 (1):178-191.

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