Endless and Infinite

Philosophical Quarterly 70 (281):830-849 (2020)
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Abstract

It is often said that time must have a beginning because otherwise the series of past events would have the paradoxical features of an actual infinite. In the present paper, we show that, even given a dynamic theory of time, the cardinality of an endless series of events, each of which will occur, is the same as that of a beginningless series of events, each of which has occurred. Both are denumerably infinite. So if an endless series of events is possible, then the possibility of a beginningless series of past events should not be rejected merely on the ground that it would be an actual infinite. What would be required to rebut our argument is a symmetry breaker – something that motivates treating the past relevantly differently to the future. We consider several attempts to provide a symmetry breaker and show that none of them is successful.

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Alex Malpass
University of Bristol

Citations of this work

Branching actualism and cosmological arguments.Joseph C. Schmid & Alex Malpass - 2023 - Philosophical Studies 180 (7):1951-1973.
Infinity, Time, and Successive Addition.Wes Morriston - 2022 - Australasian Journal of Philosophy 100 (1):70-85.
Andrew Loke’s indirect defence of the successive addition argument.Alex Malpass - 2023 - International Journal for Philosophy of Religion 94 (1):43-61.
Counting to infinity, successive addition, and the length of the past.Mohammad Saleh Zarepour - 2022 - International Journal for Philosophy of Religion 92 (3):167-176.

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References found in this work

Arguing About Gods.Graham Robert Oppy - 2006 - New York: Cambridge University Press.
Craig on the actual infinite.Wes Morriston - 2002 - Religious Studies 38 (2):147-166.
Review of W. L. Craig, The Kalām Cosmological Argument. [REVIEW]G. J. Whitrow - 1980 - British Journal for the Philosophy of Science 31 (4):408-411.

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