Our thoughts are meaningful. We think about things in the outside world; how can that be so? This is one of the deepest questions in contemporary philosophy. Ever since the 'cognitive revolution', states with meaning-mental representations-have been the key explanatory construct of the cognitive sciences. But there is still no widely accepted theory of how mental representations get their meaning. Powerful new methods in cognitive neuroscience can now reveal information processing in the brain in unprecedented detail. They show how the brain performs complex calculations on neural representations.