One of the reasons why so many conflicts tend to be persistent over time is because there are difficulties to understand the perspectives of the opponents. There are, of course, conflicts that are due to the overwhelming interests of some groups over others, and therefore can be explained rationally. But rationality is not able to justify many conflicts, where all players are, in fact, net losers. Cosmopolitanism can help to reduce the frequency, intensity and length of conflicts and of irrational conflicts only. This can be done through a genuine appreciation of the reasons of the other side. Mediators can hopefully induce the conflicting parties to view the problem from the opposite view. Self-determination claims are fundamental in negotiation and decision processes: they often attempts to affirm collective identity and from both sides are not properly assessed rationally. Examples of self-determination claims that have been sorted out peacefully, and other ones where there has not yet been a proper positive adjustment are useful to identify the key aspects which have to be addressed in problem solving.