The goal of neuroeconomics is a mathematical theory of how the brain implements decisions, that is tied to behaviour. This theory is likely to show some decisions for which rational-choice theory is a good approximation (particularly for evolutionarily sculpted or highly learned choices), to provide a deeper level of distinction among competing behavioural alternatives, and to provide empirical inspiration for economics to incorporate more nuanced ideas about endogeneity of preferences, individual difference, emotions, endogeneous regulation of states, and so forth. I also address some concerns about rhetoric and practical epistemology. Neuroscience articles are necessarily speculative and the science has proceeded rapidly because of that rhetorical convention. Single-study papers are encouraged and are necessarily limited in what can be inferred, so the sturdiest cumulation of results, and the best guide forward, comes in review journals which compile results and suggest themes. The potential of neuroeconomics is in combining the clearest experimental paradigms and statistical methods in economics, with the unprecedented capacity to measure a range of neural and cognitive activity that economists like Edgeworth, Fisher and Ramsey daydreamed about but did not have.