Human experts in scientific fields routinely work with evidence that is noisy and untrustworthy, heuristics that are unproven, and possible conclusions that are contradictory. We present a fully implemented AI system, Calvin, for cosmogenic isotope dating, a domain that is fraught with these difficult issues. Calvin solves these problems using an argumentation framework and a system of confidence that uses two-dimensional vectors to express the quality of heuristics and the applicability of evidence. The arguments it produces are strikingly similar to published expert arguments. Calvin is in daily use by isotope dating experts.