For Husserl, intersubjectivity means the condition whereby I maintain the assumption that the world as it presents itself to me is the same world as it presents itself to you, not because you can ‘read my mind’ but because I assume that if you were in my place you would see it the way I see it. This is captured by the notion of Platzwechsel, that is, ‘trading places’ or ‘place exchange’, which is made possible by empathy (see also De Bergoffen, 1996: 54; Depraz, 2001: 173; Schutz, 1962).4 (..) the idea is not that we simultaneously come to the same understanding of any given situation (although this can happen), but that we have, to start, the possibility of exchanging places, of seeing the world from the point of view of the Other. Intersubjectivity is thus an existential condition that can lead to a shared understanding – an important achievement in its own terms – rather than being itself such an understanding. This is made clear in the following passage where Husserl states that nature itself is an intersubjective reality. This does not mean that we have a mutual understanding of nature but that nature, by being something we share with other beings, can be one of the conditions for us to come to a shared understanding of the world at large (what he calls here ‘things and people’).
'Nature is an intersubjective reality and a reality not just for me and my companions of the moment but for us and for everyone who can come to a mutual understanding with us about things and about other people. There is always the possibility that new spirits enter into this nexus; but they must do so by means of their Bodies, which are represented through possible appearances in our consciousness and through corresponding ones in theirs.'(Husserl, 1989: 91)

(Alessandro Duranti "Husserl, Intersubjectivity and Anthropology")

Despite the fact that we see the world with different clarity and from a different point of view and therefore that for each of us things have a different physical appearance – I might see one side of a car while you might see the other side – I assume that we end up with the same objective world (Husserl, 1998: 55–6; 1969: 233).6 For Husserl, this common world is an accomplishment that is made possible first of all by empathy (Einfühlung), understood as the primordial experience of participating in the actions and feeling of another being without becoming the other (Husserl, 1969: 233; Stein, 1989). This kind of empathetic (and hence non-rational, non-cognitive) understanding of Others comes out of our exposure to their bodies moving and acting in ways that we recognize as similar to the ways in which we would act under similar circumstances.

(Alessandro Duranti "Husserl, Intersubjectivity and Anthropology")