Persistence and qualitative change

The metaphysical idea of and object persisting over time brings rise to a lot of debate on how we can properly identify a thing as it experiences qualitative change over time. The main issue that arises when talking about persistence over time is whether we can identify the initial thing we are observing as a different entity as time progresses and it undergoes qualitative change. For example is some thing we identify as “x”, that goes through a qualitative change at time T1, the same as the thing “x” at time T2 after the change was implemented. There are many different views on this topic and I will introduce three of them and then select the one I think is most probable. The first view is the standard view which states that an object “x” persisting through time exist entirely at both T1 and T2 regardless of qualitative change. This view in my opinion is not very strong it seems as if it aims to just disregard what we know about change and the implication of logical conditions. I refuse to believe that an object can both change and be the same thing as it was before. Using the rusting of iron we can clearly see that the item “iron” clearly has a different set of inherent properties at two different points in time. At T1 it is not rusted and at T2 it is rusted the change in color, texture, and even chemical composition leads me to believe that we are simply talking about two different items. This clearly violates the principal of non-contradiction. The other two theories do a better job to cleverly avoid this problem. The next theory is the temporal parts theory which states that an object that persist form time T1 through T2, while undergoing qualitative change, are both parts of a whole that extends through all time. Using the rusting of iron as an example again the initial un-rusted iron is only apart of the iron being