# The Compatibility of Differential Equations and Causal Models Reconsidered

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## Abstract

Weber argues that causal modelers face a dilemma when they attempt to model systems in which the underlying mechanism operates according to some set of differential equations. The first horn is that causal models of these systems leave out certain causal effects. The second horn is that causal models of these systems leave out time-dependent derivatives, and doing so distorts reality. Either way causal models of these systems leave something important out. I argue that Weber’s reasons for thinking causal modeling is limited in this domain are lacking.

## Notes

### Acknowledgements

I wish to thank James DiFrisco, Bruce Glymour, Valerie Racine, Marcel Weber, and two anonymous referees for various helpful suggestions on previous drafts of this paper.

## References

- Aalen, O., Røysland, K., Gran, J., & Ledergerber, B. (2012). Causality, mediation, and time: A dynamic viewpoint.
*Journal of the Royal Statistical Society: Series A (Statistics in Society)*,*175*, 831–861.CrossRefGoogle Scholar - Dash, D. (2003). Caveats for causal reasoning with equilibrium models. University of Pittsburgh Ph.D. Dissertation.Google Scholar
- Glymour, B. (2011). Modeling environments: Interactive causation and adaptations to environmental conditions.
*Philosophy of Science*,*78*, 448–471.CrossRefGoogle Scholar - Glymour, C. (2008). When is a brain like the planet?
*Philosophy of Science*,*74*, 330–347.CrossRefGoogle Scholar - Goldbeter, A. (1995). A model for circadian oscillations in the
*Drosophila*period protein (PER). In*Proceedings of the Royal Society of London. Part B: Biological Sciences*(Vol. 261, pp. 319–324).Google Scholar - Hyttinen, A., Plis, S., Järvisalo, M., Eberhardt, F., & Danks, D. (2016). Causal discovery from subsampled time series data by constraint optimization.
*Journal of Machine Learning Research Workshop and Conference Proceedings*,*52*, 216–227.Google Scholar - Iwasaki, Y., & Simon, H. A. (1994). Causality and model abstraction.
*Artificial Intelligence*,*67*, 143–194.CrossRefGoogle Scholar - Jantzen, B. (2015). Projection, symmetry, and natural kinds.
*Synthese*,*192*, 3617–3646.CrossRefGoogle Scholar - Kuorikoski, J. (2012). Mechanisms, modularity, and constitutive explanation.
*Erkenntnis*,*78*, 1–20.Google Scholar - Maier, M. (2014). Causal discovery for relational domains: Representation, reasoning, and learning. Ph.D. Dissertation. University of Massachusetts Amherst.Google Scholar
- Mooij, J. M., Janzing, D., & Schölkopf, B. (2013). From ordinary differential equations to structural causal models: The deterministic case. In
*Proceedings of the 29th Annual Conference on Uncertainty in Artificial Intelligence*(pp. 440–448).Google Scholar - Pearl, J. (2000).
*Causality: Models, reasoning, and inference*. Cambridge: Cambridge University Press.Google Scholar - Plis, S., Danks, D., & Yang, J. (2015). Mesochronal structure learning. In
*Uncertainty in artificial intelligence*(Vol. 31, pp. 702–711).Google Scholar - Sokol, A. (2013). On martingales, causality, identifiability, and model selection. University of Copenhagen Ph.D. Dissertation.Google Scholar
- Spirtes, P., Glymour, C., & Scheines, R. (2000).
*Causation, prediction, and search*. Cambridge, MA: MIT Press.Google Scholar - Voortman, M., Dash, D., & Druzdzel, M. J. (2010). Learning why things change: The difference-based causality learner. In
*Proceedings of the 26th Annual Conference on Uncertainty in Artificial Intelligence*(pp. 641–650).Google Scholar - Weber, M. (2016). On the incompatibility of dynamical biological mechanisms and causal graphs.
*Philosophy of Science*,*83*, 959–971.CrossRefGoogle Scholar - Woodward, J. (2003).
*Making things happen: A theory of causal explanation*. Oxford: Oxford University Press.Google Scholar

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