Counting to infinity, successive addition, and the length of the past

International Journal for Philosophy of Religion 92 (3):167-176 (2022)
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The Successive Addition Argument (SAA) is one of the arguments proposed by the defenders of the Kalām Cosmological Argument to support the claim that the universe has a beginning. The main premise of SAA states that a collection formed by successive addition cannot be an actual infinite. This premise is challenged by an argument originally proposed by Fred Dretske. According to Dretske’s Argument (DA), the scenario of a counter who starts counting numbers and never stops can provide a counterexample to the main premise of SAA. I argue that neither DA nor its past-oriented counterpart—which discusses the scenario of a counter who has always been counting negative integers from the infinite past—can play a decisive role in our evaluation of the strength of the arguments that are intended to establish the finitude of the past based on the impossibility of an actually infinite number of successive additions.



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Mohammad Saleh Zarepour
University of Manchester

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All the time in the world.Alex Malpass - 2022 - Mind 131 (523):786-804.
The Kalām Cosmological Argument.W. Craig - 1980 - British Journal for the Philosophy of Science 31 (4):408-411.
Endless and Infinite.Alex Malpass & Wes Morriston - 2020 - Philosophical Quarterly 70 (281):830-849.
Counting to Infinity.F. I. Dretske - 1965 - Analysis 25 (Suppl-3):99--101.

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