A puzzle about rates of change

Philosophical Studies 177 (10):3155-3169 (2020)
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Abstract

Most of our best scientific descriptions of the world employ rates of change of some continuous quantity with respect to some other continuous quantity. For instance, in classical physics we arrive at a particle’s velocity by taking the time-derivative of its position, and we arrive at a particle’s acceleration by taking the time-derivative of its velocity. Because rates of change are defined in terms of other continuous quantities, most think that facts about some rate of change obtain in virtue of facts about those other continuous quantities. For example, on this view facts about a particle’s velocity at a time obtain in virtue of facts about how that particle’s position is changing at that time. In this paper we raise a puzzle for this orthodox reductionist account of rate of change quantities and evaluate some possible replies. We don’t decisively come down in favour of one reply over the others, though we say some things to support taking our puzzle to cast doubt on the standard view that spacetime is continuous.

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Author Profiles

David Builes
Princeton University
Trevor Teitel
University of Toronto, St. George Campus

Citations of this work

The World Just Is the Way It Is.David Builes - 2021 - The Monist 104 (1):1-27.
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Lawful Persistence.David Builes & Trevor Teitel - 2022 - Philosophical Perspectives 36 (1):5-30.
Derivatives and Consciousness.David Builes - 2020 - Journal of Consciousness Studies 27 (9-10):87-103.

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On what grounds what.Jonathan Schaffer - 2009 - In David Manley, David J. Chalmers & Ryan Wasserman (eds.), Metametaphysics: New Essays on the Foundations of Ontology. Oxford University Press. pp. 347-383.
No Work for a Theory of Grounding.Jessica M. Wilson - 2014 - Inquiry: An Interdisciplinary Journal of Philosophy 57 (5-6):535-579.
Science Without Numbers: A Defence of Nominalism.Hartry H. Field - 1980 - Princeton, NJ, USA: Princeton University Press.

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