Clearly we can differentiate between different-location-same-time and different-location-different-time. Two things in different-location-same-time are different things. Two things different-location-different-time may be same thing or may be different thing depending on the path through time. Your mathematical style of abstraction in thinking about identity will only be useful at explaining the real world if it is matched to real world processes, and does not ignore important real world insights.
In fact my goal was to get rid of mathematical definitions of identity and move to instrumental definition. That is the definition of identity depends of the goal I am solving and identity itself is not a thing that actually exists but a supportive term. That is why we have problems this it.
Basically, there is two types of question where we need notion of “identity”:
1) What I will experience in the next moment? (first-eye view)
2) Is it the same person? (third-eye view)
Clearly we can differentiate between different-location-same-time and different-location-different-time. Two things in different-location-same-time are different things. Two things different-location-different-time may be same thing or may be different thing depending on the path through time. Your mathematical style of abstraction in thinking about identity will only be useful at explaining the real world if it is matched to real world processes, and does not ignore important real world insights.
In fact my goal was to get rid of mathematical definitions of identity and move to instrumental definition. That is the definition of identity depends of the goal I am solving and identity itself is not a thing that actually exists but a supportive term. That is why we have problems this it.
Basically, there is two types of question where we need notion of “identity”:
1) What I will experience in the next moment? (first-eye view) 2) Is it the same person? (third-eye view)