Plessner not only formulates a theory of positionality here but also a principle of how to construct this theory with respect to empirical research, a principle he calls the "deduction of the categories of life". This is described in the literature as "reflexive deduction". With reference to Plessner's methodology of theory construction I unfold a new understanding of his theory of the shared world. At present, there are two understandings of the shared world. The traditional understanding of the shared world is primarily concerned with relativizing particular individual selves, whose boundedness to their own standpoint is devalued by the we-form. I call this SWU-1. SWU-1 is not developed in accordance with the principle of reflexive deduction. The second understanding of the shared world, on the other hand, is developed, in accordance with that principle, as a reflexive turning upon the factual state of existing in relationships of touch. This leads to a different understanding of the shared world, which I call SWU-2, or the social undecidedness relation. Such an understanding of the shared world forces us to also reconsider our understanding of the inner and outer worlds.