Perdurance, endurance, and 'havingh a property atemporally'

In this section, I present very summarily the two views on persistence and change that I want to consider, paying special attention to their shared feature mentioned above. Let me first make clear what I understand by"persistence","change" and"theories of persistence". Following Lewis (1986), I say that an object x persists iff x exists at different times. And I say that x changes with respect to a property P iff x exemplifies P at some time and fails to do so at some other time in which x exists. Theories of persistence for a domain of objects O are intended to explain how objects in O persist, i.e. in virtue of which facts they manage to exist at different times. This explanation must be compatible with a coherent account of what it is for these objects to exemplify different properties at different times, and thus with a coherent account of change. Consider for instance a banana that is wholly green at a time t1 and wholly yellow at some later time t2. This banana persists from t1 to t2 and has different colour properties at each of these times, thereby changing with respect to colour. Theories of persistence are intended to explain in virtue of which facts all these claims about the banana are true