Identity in general

The need to identity the same very basic
many cases this conventional

     The same house, though repaired
     The same nation, though new citizens
          The same country, USA, with more states, with different territory

Identity provides way of talking about change.
Some thing changed.
Its properties changed, but it is the same thing
If we didn't make this distinction, talking about change would be impossible

The same x changes. Different properties, same thing

In order to talk about change we need to identify some thing
which has changed, which remains the same thing through that change.
     Here are the roots of talk of substance in ordinary speech.

The same x changes. Different properties of the same substance,
as Descartes would say.