The Ship of Theseus
The Ship of Theseus is a paradox coming from Ancient Greece. It asks whether a ship is still the same ship if every part of it is replaced. An even older version asks whether grandfather's axe is still the same axe if both the blade and the handle are replaced at different times. A modern version is: if you gradually replace the keyboard, screen, mouse, and all the other components of a computer, then is it still the same computer? Apparently, most cells in our body are replaced every ten years or so, but does that mean we are no longer the same person?
What about the self? We tend to think that we are like a rock over which flows the river of experience, leaving us unchanged. Yet we do change. But do we change so much that, at some point, we are a different person altogether?
Another example is photography. Is a photo that has been enhanced or altered in Photoshop still a "true" document, or does the edit falsify it, and if so, where do we draw the line?
Generally speaking, nothing stays the same; everything changes, if only gradually and minutely. Our bodies age every second. Yet in practical terms, these minuscule changes are only of academic interest.
A more meaningful criterion of sameness or change is whether a given thing is "effectively the same", ie has not changed in a sense that has practical consequences. So both the ship and the axe are better considered as new, since they are made up of new, not old and presumably damaged materials.
Although naming and categorising are essential human activities, they should never be confused with the reality they refer to and seek to define. The map is not the territory. If there is a problem with the application of names, eg with deciding whether to apply the label "new" or not, that is not a big surprise. It is a mapping problem. Reality is complex, amorphous and paradoxical. It is under no obligation to fit neatly into the categories we humans have created.
To determine whether a thing is still the "same" thing, we should first ask what a "thing" is. A thing is no more and no less than an object of thought. The article on things explains this in detail. It hardly matters whether we regard the axe as the same or not, since only our mental model changes. Our decision has no effect on reality. Given that we already know about the replacements, our judgement that it is new does not tell us anything useful about the axe. All it does is alter the way that we think about the axe. Indeed, none of our naming games have any effect on what they classify and analyse.
At best, our use of names gives us an illusory sense of security that we know and understand the world around us.