We are interested in the problem of reasoning over very large common sense knowledge bases. When such a knowledge base contains noisy and subjective data, it is important to have a method for making rough conclusions based on similarities and tendencies, rather than absolute truth. We present AnalogySpace, which accomplishes this by forming the analogical closure of a semantic network through dimensionality reduction. It self-organizes concepts around dimensions that can be seen as making distinctions such as "good vs. bad" or "easy vs. hard", and generalizes its knowledge by judging where concepts lie along these dimensions. An evaluation demonstrates that users often agree with the predicted knowledge, and that its accuracy is an improvement over previous techniques.