Any attempt to explain the mind by building machines with minds must confront the other-minds problem: How can we tell whether any body other than our own has a mind when the only way to know is by being the other body? In practice we all use some form of Turing Test: If it can do everything a body with a mind can do such that we can't tell them apart, we have no basis for doubting it has a mind. But what is everything a body with a mind can do? Turing's original pen-pal version of the Turing Test (the TT) only tested linguistic capacity, but Searle has shown that a mindless symbol-manipulator could pass the TT undetected. The Total Turing Test (TTT) calls instead for all of our linguistic and robotic capacities; immune to Searle's argument, it suggests how to ground a symbol manipulating system in the capacity to pick out the objects its symbols refer to. No Turing Test, however, can guarantee that a body has a mind. Worse, nothing in the explanation of its successful performance requires a model to have a mind at all. Minds are hence very different from the unobservables of physics (e.g., superstrings); and Turing Testing, though essential for machine-modeling the mind, can really only yield an explanation of the body.