Anti-naturalistic critics of Unity of Science have often tried to establish a fundamental difference between social and physical science on the grounds that research in the social field (unlike physical research) seems to interfere with the original situations so as to make accurate predictions impossible. A 'social' prediction may, e.g., itself influence the course of events so that the prediction proves false. H. A. Simon has dealt with such effects of predictions in a well-known article. Drawing on a mathematical theorem, (...) Brouwer's so-called fixed-point theorem, he claims to prove that reactions to published predictions can be accounted for so that appropriately adjusted predictions can avoid being self-destructive. The present article is an attempt to show that Simon's use of the Brouwer theorem is misplaced, and that his proof does not parry the anti-naturalistic argument. Indeed, the burden of his proof is not really of a mathematical, but, it is argued, of a 'protosociological' kind. In conclusion, the article points to the fundamental inadequacy of a frame of reference which makes the 'interference' or 'reaction' effects due to people's having access to social knowledge appear strange or eccentric: as some kind of marginal irregularity causing trouble in the philosophy of (social) science. (shrink)