It is here argued that functionalist constraints on psychology do not preclude the applicability of classic forms of reduction and, therefore, do not support claims to a principled, or de jure, autonomy of psychology. In Part I, after isolating one minimal restriction any functionalist theory must impose on its categories, it is shown that any functionalism imposing an additional constraint of de facto autonomy must also be committed to a pure functionalist--that is, a computationalist--model for psychology. Using an extended parallel (...) to the reduction of Mendelian to molecular genetics, it is shown in Parts II and III that, contrary to the claims of Hilary Putnam and Jerry Fodor, there is no inconsistency between computational models and classical reductionism: neither plurality of physical realization nor plurality of function are inconsistent with reductionism as defended by Ernest Nagel. Employing the results of Part I, the conclusions of Parts II and III are generalized in Part IV to cover any version of functionalism whatsoever; thus, functionalism and reductionism are shown to be consistent. It is urged in conclusion that although a de facto form of autonomy is defensible, there are sound methodological grounds for unconditionally rejecting any principled version of the autonomy of psychology. (shrink)