Connectionism provides hope for unifying work in neuroscience, computer science, and cognitive psychology. This promise has met with some resistance from Classical Computionalists, which may have inspired Connectionists to retaliate with bold, inflationary claims on behalf of Connectionist models. This paper demonstrates, by examining three intimately connected issues, that these inflationary claims made on behalf of Connectionism are wrong. This should not be construed as an attack on Connectionism, however, since the inflated claims made on its behalf have the look of cures for which there are no ailments. There is nothing wrong with Connectionism for its failure to solve illusory problems.