Why Philosophers Should Care About Computational Complexity
Scott Aaronson
TL;DR
This paper argues that computational complexity theory offers deep philosophical insights beyond the traditional focus on computability, connecting to issues in the philosophy of mind, epistemology, and the foundations of physics. By emphasizing the polynomial-time versus exponential-time distinction, the Cobham axioms, PAC-learning, and new notions of proof, the work shows how complexity informs questions about knowledge, induction, and AI, and debates around quantum computing and time travel. It surveys key intersections with the Turing Test, logical omniscience, computationalism, and economic rationality, while acknowledging limitations and outlining future research directions. The significance lies in reframing philosophical debates through the lens of resource-bounded computation, highlighting both explanatory power and practical constraints across diverse domains.
Abstract
One might think that, once we know something is computable, how efficiently it can be computed is a practical question with little further philosophical importance. In this essay, I offer a detailed case that one would be wrong. In particular, I argue that computational complexity theory -- the field that studies the resources (such as time, space, and randomness) needed to solve computational problems -- leads to new perspectives on the nature of mathematical knowledge, the strong AI debate, computationalism, the problem of logical omniscience, Hume's problem of induction, Goodman's grue riddle, the foundations of quantum mechanics, economic rationality, closed timelike curves, and several other topics of philosophical interest. I end by discussing aspects of complexity theory itself that could benefit from philosophical analysis.