This paper argues that the goals people have when reasoning determine their own norms of reasoning. A radical descriptivism which avoids norms never worked for any science; nor can it work for the psychology of reasoning. Norms as we understand them are illustrated with examples from categorical syllogistic reasoning and the "new paradigm" of subjective probabilities. We argue that many formal systems are required for psychology: classical logic, non-monotonic logics, probability logics, relevance logic, and others. One of the hardest challenges is working out what goals reasoners have and choosing and tailoring the appropriate logics to model the norms those goals imply.
Keywords: classical logic; heterogeneity of human reasoning; nonmonotonic reasoning; normativity; probabilistic reasoning; reasoning goals; reasoning norms; syllogisms.