Year: 2018
Type: preprint
Abstract: model with only a small structural error can differ drastically from the probability distribution that would have been obtained using the true dynamical equations.This difference is the result of the Hawkmoth Effect.In the second step, Frigg et al. generalize their example.To this end, they refer to a couple of mathematical theorems in order to show that structural stability cannot be taken for granted in most nonlinear models.In a third and final step, they claim that there is currently no method that can mitigate against the Hawkmoth Effect, and that no such method is likely to be developed.As a consequence of this, they argue that the burden of proof should be shifted.The default assumption should be that nonlinear models are structurally unstable and, hence, susceptible to the Hawkmoth Effect.Those who intend to use a nonlinear model for predictive purposes must prove that their model is structurally stable.If they fail to do so, probabilistic predictions derived from the model must be seen as genuinely unreliable.Section three provides a discussion of Frigg et al.'s argument.We highlight the fact that a crucial part of the argument implicitly relies on the assumption that, in face of their limited knowledge of the true structure of a system, modelers rely on what the authors call the closeness-to-goodness link, i.e. the notion that a model whose structure is close enough to the true structure of system, will produce good enough predictions.We believe that this assumption-that modelers rely on closeness-to-goodness-is not generally true.In many domains where models are used for prediction, closeness-to-goodness is rarely seen as a sufficient criterion for deciding that predictions derived from a nonlinear model are likely to be "good enough".We show that even if there is a strong correlation between nonlinearity and structural instability there are effective strategies against the impact of SME that are currently applied in scientific practice.In fact, there are a number of approaches that can guard against the potential
Authors: Karim Bschir, Lydia Braunack-Mayer
Language: English
Subfield: History and Philosophy of Science
Field: Arts and Humanities
Domain: Social Sciences
Open Access status: green
OpenAlex ID: W2900423155