Amongst philosophers and cognitive scientists, modularity remains a popular choice for an architecture of the human mind, primarily because of the supposed explanatory value of this approach. Modular architectures can vary both with respect to the strength of the notion of modularity and the scope of the modularity of mind. We propose a dilemma for these modularity approaches, no matter how they vary along these two dimensions. First, if a modular architecture commits to the informational encapsulation of modules, as it is the case for modularity theories of perception, then modules are on this account impenetrable.However, we argue that there are genuine cases of the cognitive penetrability of perception and that these cases challenge any strong, encapsulated modular architecture of perception.Second, many recent massive modularity theories weaken the strength of the notion of module, while broadening the scope of modularity. These theories do not require any robust informational encapsulation, and thus avoid the incompatibility with cognitive penetrability.However, the weakened commitment to informational encapsulation greatly weakens the explanatory force of the approach and, ultimately, is conceptually at odds with the core of modularity.Amongst philosophers and cognitive scientists, modularity remains a popular choice for theorizing the human mind at some broad level of architecture. Jerry Fodor (1983), who was influential in establishing the concept of a module, writes: "One day . . . Merrill Garrett made what seems to me to be the deepest remark that I have yet heard about the psychological mechanisms that mediate the perception of speech. 'What you have to 1 This work was thoroughly collaborative and the paper thoroughly co-authored-the order of authors was chosen randomly.2 remember about parsing is that basically it's a reflex.'" (Dedication). Reflexes are quick, inflexible, involuntary responses to stimuli, and Fodorian modules are like reflexes. In its most general form, the modularity hypothesis consists in viewing the human mind, or at least part of it, as a configuration of quick specialized mental mechanisms, or subsystems, that are dissociable, and that typically operate over a distinct domain of information.There are compelling theoretical and empirical motivations for this approach.Theoretically, modularity nicely accommodates adaptationist and other evolutionary explanations of mental phenomena. It also provides materials for a simple explanation of important empirical data, including a wide range of behavioural dissociations, as well as the speed and robustness of processing enjoyed by the human mind. Most broadly, modularity provides an intuitive framework for characterizing the relations between brain structures and particular perceptual and cognitive functions.Although it is sometimes misrepresented as doing precisely this, Fodor's pioneering discussion of the concept did not involve a definition of 'module'. (Fodor 1983; see also Coltheart 1999). Fodor did, however, provide a l...