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According to the received view in the literature on homonymy and polysemy representation, there is a difference between how polysemes and homonyms are represented in our mental lexicons. More concretely, the received view holds that whereas the meanings associated with a homonymous expression are (mentally) represented in separate lexical entries, the meanings associated with a polysemous expression are represented together in a single lexical entry. It is usually argued that this is the picture that is supported by the growing body of empirical evidence coming from psycholinguistics. Empirical studies of ambiguity processing and resolution consistently show that polysemous expressions enjoy various processing advantages compared to homonyms, and the received view is generally taken to be required in order to explain these results. The aim of this paper is not only to show that this is not the case but also, and more fundamentally, that the received view falls far short of explaining the available data to a sufficient degree. As a result, the received view is caught up in an explanatory dilemma that I dub the Continuum Puzzle. I then claim that the best way to escape this puzzle is to give up the received view’s core thesis in favor of an alternative view consistent with the empirical evidence. Reaching such an alternative will require rejecting the following pervasive but ill-motivated assumption: Differences in ambiguity processing and resolution can only be explained by there being some corresponding differences in the architecture of our mental lexicons.