In her examination of the problem of identity and its fractal character H. Arendt makes an important step towards a more profound understanding of the thinking Self. Her objective is evident - it is her effort to eliminate the negative effects of the so called identifying monism resulting in mass hysterias. Arendt argues, that the thinking Self is never identical with itself, therefore the definition of subjectivity itself should be seen from the perspective of the difference between the Self and the statments about the Self. For Arendt it means opening the Self, so far shut off in his private cell of the only belief, that it is the Self, who produces the subjectivity. The fractal version of subjectivity represents an open universe of freely chosen responsibility ensuring that there is the only correspondence between the Self and the statments about the Self, namely the correspondence based on knowing the price, paid for it by every Self. And that means tolerating the differences, produced by mind as the thinking Self, differences by which we are constantly being negatively determined. Contrary to identifying monism, however, this determination is not a militant one.