I will discuss two ways of responding to Cartesian arguments for global skepticism about the external world.  In an earlier paper ("The Matrix as Metaphysics") I argued that Cartesian hypotheses such as the evil demon hypothesis, the brain-in-a-vat hypothesis, and the Matrix hypothesis are not in fact skeptical hypotheses: if these hypotheses are correct, most of our ordinary beliefs are still true.  This response is often assimilated to Hilary Putnam's appeal to semantic externalism to defuse external-world skepticism, whereby brains in vats are held to refer to whatever causes their experiences.  I will argue that Putnam's externalist response fails because it requires an implausible global externalism.  I will argue instead for a response to skepticism driven by an underlying structuralism (akin to structural realism in the philosophy of science).  On this line, Cartesian hypotheses are non-skeptical hypotheses because they share the structure of our ordinary hypotheses about the external world.