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Morphology induction is a subproblem of important tasks like automatic learning of machine-readable dictionaries and grammar induction. Previous morphology induction approaches have relied solely on statistics of hypothesized stems and affixes to choose which affixes to consider legitimate. Relying on stem-and-affix statistics rather than semantic knowledge leads to a number of problems, such as the inappropriate use of valid affixes ("ally" stemming to "all"). We introduce a semantic-based algorithm for learning morphology which only proposes affixes when the stem and stem-plus-affix are sufficiently similar semantically. We implement our approach using Latent Semantic Analysis and show that our semantics-only approach provides morphology induction results that rival a current state-of-the-art system.