1. Convictions are always convictions held by a certain person. However, we can also speak of common convictions held by different people, and of one and the same conviction being shared by different people. But then we are actually talking about the proposition each of these persons believes to be the respective content of their convictions, not (only) the proposition of being convinced experienced by the persons concerned. In other words, what we are talking about is the proposition A which

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... believed to be true by both X and Y, and not the propositions that X believes A or that Y believes A, respectively (in symbols: B(X,ÊA) and B(Y,ÊA)). The same goes for common knowledge. All the fact that X and Y have certain common convictions and common knowledge means is that for certain propositions A it holds that A is the content of the (correct) convictions expressed by B(X,ÊA) and B(Y,ÊA).