Scientific procedures are widely expected to be unbiased, in the sense that they do not single out one specific set of claims about which they yield false results more often than about others. This assumed feature of the practices of science can be called procedural objectivity. The author argues that attempts to analyze procedural objectivity on the level of individual rationality fail. The appropriate balance of inductive risks for each scientific investigation hinges upon value judgments for which no binding, 'neutral' standard can be derived from universal principles. He makes the case that the perspective of social epistemology offers a much more promising approach to establish a substantial conception of procedural objectivity. The author examines two genuinely social elements of the sciences' procedural objectivity. One consists in conventional standards, which are adopted by research communities in order to facilitate epistemic trust and which impose constraints on methodological choices that affect the balance of inductive risks. The other is constituted by the plurality of approaches within research communities and the mechanism of mutual criticism. Procedural objectivity in science thus becomes understandable as a social phenomenon.