Linnemann, Niels and Michels, Robert
(2024)
Laws of nature as results of a trade-off -- Rethinking the Humean trade-off conception.
[Preprint]
Abstract
According to the standard Humean theory of the laws of nature, Lewis' Best System Analysis (BSA), laws of nature have their status at least partly as the result of an optimal trade-off between scientific values such as simplicity and descriptive strength.
This idea has recently come under pressure. Authors like Roberts and Woodward have pointed out that there might, pace what proponents of the BSAs like to suggest, be no such trade-off in the way laws of nature are identified in the natural sciences. Roberts has it that considerations of strength in theory choice are never compromised by simplicity considerations; and Woodward argues that choices between scientific theories and the associated laws often rather involve a threshold of descriptive strength which has to be met before simplicity can even begin to matter.
In this paper, we make three points: first, we employ recent results from automated scientific discovery (or rather a subfield of it known as `symbolic regression') to provide concrete support for Roberts and Woodward's point that scientific theories are chosen based on strength-thresholds. Second, drawing on the same example, we argue that discussions of the BSA involve an overly simplistic view of what a trade-off between theoretical virtues amounts to; taking into account how trade-offs are treated in scientific practice, the idea of there being a single optimal theory has to make way for the view that a properly operationalized trade-off allows for a whole Pareto front of equally optimal theories. Third, we argue that a threshold behaviour with respect to a virtue like strength is not only compatible with this more systematic yet more complex view of trade-offs but also helps to bring it in line with the BSA's original preference for a single, or given the possibility of multiple optimal theories, a small number of best systems.
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