The need for representations and computations over their contents in psychological explanations is often cited as both the mark of the genuinely cognitive and a source of skepticism about the reducibility of cognitive theories to neuroscience. A generic version of this anti-reductionist argument is rejected in this paper as unsound, since (i) current thinking about associative learning emphasizes the need for cognitivist resources in theories adequate to explain even the simplest form of this phenomena (Pavlovian conditioning), and yet (ii) the (...) most widely accepted recent theory of associative learning, which utilizes cognitivist resources, has already been reduced to a purely neurophysiological account. Psychoneural reduction of genuinely cognitivist theories is thus already an accomplished scientific fact, despite pronouncements by anti-reductionists about its conceptual impossibility or empirical implausibility. In addition, the specific form of reduction involved in this case (“combinatorial” reduction) provides a promising model for further cognitivist-to-neuroscience theory reductions. (shrink)