contained in the set . But it is not only things that Althea may do that can possibly describe what happens in private sphere. If Bertha punches Althea in the face, for instance, then surely Althea’s this affects private sphere as well. The description of such a state of affairs would thus Althea’s also be contained in the set . Though this understanding of private spheres is not precise just yet §6 below is entirely dedicated to discussing how to interpret this primitive of our model we – – believe it is intuitive enough for the time being. In trying to model perspectival disagreements we say that each individual or sees each social state from his or her unique perspective. More rigorously, for each , perceives define the mapping . We call the mapping individual In words, each perspective function. ’s individual , based on his or her specific perspective function , codes each social state in his or her internal language as a list of descriptions describing what is happening within each private sphere. Here, denotes social state seen from individual specific individual’s ’s perspective. For notational convenience, we will write simply as When (that is, when ), then . this means that individuals and categorize the social world differently. Here, there is perspectival disagreement. Inversely, if (that is, if , then this means that individuals and categorize the social alternative identically. Here, there is no perspectival disagreement. Let denote a profile of individual perspective functions (one perspective function for each individual ), and let be the set of all logically possible profiles of individual perspectives. Though there is a single set of social states , because individuals have different perspective functions, they may perceive these social states quite differently. To account for this, define as the set of all social states seen from individual perspective function . Thus, is how ’s individual perceives the set of social states given his or her perspective.
contained in the set . But it is not only things that Althea may do that can possibly describe what happens in Althea’s private sphere. If Bertha punches Althea in the face, for instance, then surely this affects Althea’s private sphere as well. The description of such a state of affairs would thus also be contained in the set . Though this understanding of private spheres is not precise just yet – §6 below is entirely dedicated to discussing how to interpret this primitive of our model – we believe it is intuitive enough for the time being. In trying to model perspectival disagreements we say that each individual sees or perceives each social state from his or her unique perspective. More rigorously, for each , define the mapping . We call the mapping individual ’s perspective function. In words, each individual , based on his or her specific perspective function , codes each social state in his or her internal language as a list of descriptions describing what is happening within each individual’s private sphere. Here, denotes social state seen from individual ’s specific perspective. For notational convenience, we will write simply as . When (that is, when ), then this means that individuals and categorize the social world differently. Here, there is perspectival disagreement. Inversely, if (that is, if , then this means that individuals and categorize the social alternative identically. Here, there is no perspectival disagreement. Let denote a profile of individual perspective functions (one perspective function for each individual ), and let be the set of all logically possible profiles of individual perspectives. Though there is a single set of social states , because individuals have different perspective functions, they may perceive these social states quite differently. To account for this, define as the set of all social states seen from individual ’s perspective function . Thus, is how individual perceives the set of social states given his or her perspective.