It is now more than a half-century since the Physical Symbol Systems Hypothesis (PSSH) was first articulated as an empirical hypothesis. More recent evidence from work with neural networks and cognitive architectures has weakened it, but it has not yet been replaced in any satisfactory manner. Based on a rethinking of the nature of computational symbols -- as atoms or placeholders -- and thus also of the systems in which they participate, a hybrid approach is introduced that responds to these challenges while also helping to bridge the gap between symbolic and neural approaches, resulting in two new hypotheses, one that is to replace the PSSH and other focused more directly on cognitive architectures.

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