This paper adds a new dimension to the role of scientific knowledge in policy by emphasizing the multivalent character of scientific consensus. We show how the maintained consensus about the quantitative estimate of a central scientific concept in the anthropogenic climate-change field - namely, climate sensitivity - operates as an `anchoring device' in `science for policy'. In international assessments of the climate issue, the consensus-estimate of 1.5°C to 4.5°C for climate sensitivity has remained unchanged for two decades. Nevertheless, during these years climate scientific knowledge and analysis have changed dramatically. We identify several ways in which the scientists achieved flexibility in maintaining the same numbers for climate sensitivity while accommodating changing scientific ideas. We propose that the remarkable quantitative stability of the climate sensitivity range has helped to hold together a variety of different social worlds relating to climate change, by continually translating and adapting the meaning of the `stable' range. But this emergent stability also reflects an implicit social contract among the various scientists and policy specialists involved, which allows `the same' concept to accommodate tacitly different local meanings. Thus the very multidimensionality of such scientific concepts is part of their technical imprecision (which is more than just analytical lack of resolution); it is also the source of their resilience and value in bridging (and perhaps reorganizing) the differentiated social worlds typical of modern policy issues. The varying importance of particular dimensions of knowledge for different social groups may allow cohesion to be sustained amidst pluralism, and universality to coexist with cultural distinctiveness.