Implications of Robustness for the Theory of Explanation Mark Povich Philosophy-Neuroscience-Psychology Washington University in St. Louis Question: Are explanations of robustness causal -mechanical explanations? Example: Why are macaque cortical networks robust? Two Views: 1. Explanations of robustness are not causal-mechanical. No mechanism components or their activities are identified, temporal sequence of events is irrelevant [1]. 2. Explanations of robustness are causal-mechanical. They satisfy a principal norm of mechanistic explanation by allowing manipulation and control of the explanandum phenomenon [2]. My Thesis – A Middle Way: Explanations of robustness are “really statistical” [3] but can be accommodated by a generalization of the norms of causal-mechanical explanation. Network Definitions Robustness: The stability of a network property to random deletions of nodes or edges [3]. Common measure: characteristic path length, i.e. average shortest path [5][6][7][8]. Modularity: Network organization characterized by clusters of nodes highly connected to each other (modules or communities), with few connections between clusters. Also called “community structure” [8]. Scale-free: Network organization characterized by a power-law degree distribution: P(k) ~ k -γ where P(k) is the fraction of nodes of degree k [10]. Explanandum: Robustness of macaque cortical networks. Explanans: Scale-free organization [5]. Not Causal-Mechanical, but Really Statistical: Scale-free organization makes robustness “a statistical fact of life” [3]: it follows from the laws of probability that a network with scale-free organization will be robust. The explanandum is neither caused nor constituted by the explanans. Why? Noncausal Dependence and Explanatory Asymmetry: The asymmetric but noncausal dependence involved between our explanandum and explanans is akin to that between realized and realizer or determinable and determinate [11]. This accounts of the intuitive explanatory asymmetry: robustness does not explain scale-free organization. It does not follow from the laws of probability that a robust network will have scale-free organization. Modular networks, for example, are also robust [3]. Generalizing Causal-Mechanical Norms: This account adheres to central norms of causal-mechanical explanation [12] [13] by answering w-questions and allowing manipulation and control. Contra Zednik [2], this does not make explanations of robustness causal-mechanical because manipulations of robustness involve non-ideal interventions [14]. This account is compatible with both ontic and epistemic conceptions of scientific explanation. References: [1] Huneman, Philippe. “Topological Explanations and Robustness in Biological Sciences.” Synthese 177.2 (2010):213-245. [2] Zednik, Carlos. “Are Systems Neuroscience Explanations Mechanistic?” Philosophy of Science (December 2015): 82. [3] Marc Lange (2013). “Really Statistical Explanations and Genetic Drift.” Philosophy of Science 80 (2):169-188. [4] Bullmore, Ed, and Olaf Sporns. “The economy of brain network organization.” Nature Reviews Neuroscience 13.5 (2012): 336-349. [5] Kaiser, M., Martin, R., Andras, P. and Young, M. P. (2007), “Simulation of robustness against lesions of cortical networks.” European Journal of Neuroscience, 25: 3185-3192. [6] Shargel, Benjamin, et al. “Optimization of robustness and connectivity in complex networks.” Physical review letters 90.6 (2003): 068701. [7] Albert, Réka, Hawoong Jeong, and Albert-László Barabási. “Error and attack tolerance of complex networks.” Nature 406.6794 (2000): 378-382. [8] Stam, C. J., et al. "Small-world networks and functional connectivity in Alzheimer's disease." Cerebral cortex 17.1 (2007): 92-99. [9] Sporns, Olaf, and Richard F. Betzel. “Modular brain networks.” Annual review of psychology 67.1 (2015). [10] Newman, Mark. Networks: an introduction. Oxford University Press, 2010. [11] Funkhouser, Eric. "The Determinable Determinate Relation." ‐ Noûs 40.3 (2006): 548-569. [12] Woodward, James. Making Things Happen. Oxford University Press, 2003. [13] Ylikoski, Petri, and Jaakko Kuorikoski. "Dissecting explanatory power." Philosophical Studies 148.2 (2010): 201-219. [14] Romero, Felipe. "Why there isn’t inter-level causation in mechanisms." Synthese (2015): 1-25. Acknowledgments: Thanks to Carl Craver, Philipp Haueis, Eric Hochstein, and Felipe Romero for invaluable comments. Email: mapovich@gmail.com