Explanations of cognitive behavior often appeal to computations over representations. What does it take for a system to implement a given computation over suitable representational vehicles within that system? We argue that the language of causality -- and specifically the theory of causal abstraction -- provides a fruitful lens on this topic. Drawing on current discussions in deep learning with artificial neural networks, we illustrate how classical themes in the philosophy of computation and cognition resurface in contemporary machine learning. We offer an account of computational implementation grounded in causal abstraction, and examine the role for representation in the resulting picture. We argue that these issues are most profitably explored in connection with generalization and prediction.

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