In a preceeding question I have asked about the foundations of rational reasonning. It seems the concept of identity plays a key role. However "identity" is not observed in the real world: our mind creates identities.
For example if you see a simple blue pencil, turn your head and go back to the pencil, you say "these are the same". If the pencil has changed a little bit when you turn your head back you might think it is a different pencil or just forget about the difference and keep thinking it is the same. The reason why and the condition in which you should foreget about the difference in the second case is the purpose of my question:
when and why would you say that two things are the same?
Side Note: It seems to me that the identity is created to connect two events that we percieve. This creation is made possible because the identity is not modifying our system of representations. Creating identities is always a reduction, a simplification of the objective truth but it is very important to create identities to fit the real world into our mind and make it possible to think about.