Determinism, Counterpredictive Devices, and the Impossibility of Laplacean Intelligences

In a famous passage drawing implications from determinism, Laplace introduced the image an intelligence who knew the positions and momenta of all of the particles of which the universe is composed, and asserted that in a deterministic universe such an intelligence would be able to predict everything that happens over its entire history. It is not, however, difficult to establish the physical possibility of a counterpredictive device, i.e., a device designed to act counter to any revealed prediction of its behavior. What would happen if a Laplacean intelligence were put into communication with such a device and forced to reveal its prediction of what the device would do on some occasion? On the one hand, it seems that the Laplacean Intelligence should be able to predict the device's behavior. On the other hand, it seems like that device should be able to act counter to the prediction. An examination of the puzzle leads to clarification of what determinism does (and does not) entail, with some insights about various other things along the way.