Although belief in the existence of mental modules of some form is widespread among cognitive researchers, neurally sophisticated researchers commonly resist the view that cognitive processing involves modules that are functionally independent of one another. Moreover, within the past few years, at least three noted researchers (Fodor, Kosslyn and Uttal) have called into serious question the existence of distinct modules in broad areas of human cognition. This paper offers a defence of the existence of functionally independent modules, which, though spatially distributed, communicate via traditionally conceived input/output channels. This defence proceeds: (i) by showing that the anti-modularity arguments of Fodor, Kosslyn and Uttal are not compelling; (ii) by presenting theoretically-grounded reasons why any connectionist is committed, via the most basic tenets of connectionism, to accepting the existence of functionally independent modules; (iii) by presenting holistically inclined connectionists with a novel challenge, namely, to demonstrate that a single, holistic network could display strong levels of generalization as a side-effect of multiple, previously acquired skills. In the course of these arguments, I examine a recent generalization challenge posed by Phillips (2000, Connection Science, 12: 1-19) to eliminative connectionists.