The Ship of Theseus paradox, the teletransportation paradox, the Water-H2O paradox, so on and so forth, they are all identity paradoxes. They arise if you take abstract identity too literally, as if Theseus’s ship or “you” actually exist as an autonomous thing-in-itself in the real world. These kinds of paradoxes arise because it mistakes abstract identity for a physical thing in the world, when it identity is not real to begin with.
If identity is real, then it is a real, physical property some systems possess. My cat would possess the property of the identity of “cat,” but my cup of coffee would not. Of course, my cat did not exist forever, so it could not have had that property forever, and so there must be a definite moment in time when it acquires this property. Not just in time, but also in space: there must be unambiguous boundaries between where my “cat” begins and where it ends.
This is what Friedrich Engels largely tried to point out in his book “Dialectics of Nature,” that whenever you try to draw these boundaries in time and space, you quickly realize how ambiguous they are, how it is not actually possible to draw “hard-and-fast” lines separating things in the real world. Whenever you investigate an object more closely, you find that the boundaries between it and everything else disappear.
Abstract identity is better understood as a high-level abstraction created by humans. Reality does not contain autonomous things-in-themselves like cats, chairs, “you,” ships, etc, each understood as an autonomous object conceivable as existing in itself with unambiguous boundaries between itself and everything else.
Reality, to quote Jocelyn Benoist, just is what it is. It does not care how you label it, or even if you label it at all. These labels are socially constructed means by which we break up reality into smaller chunks in order for us to more easily discuss it as a social process, and the labels, the identity, does not possess any sort of real existence. They are all normative.
Indeed, to some extent, it has always been both necessary and proper for man, in his thinking, to divide things up, and to separate them, so as to reduce his problems to manageable proportions; for evidently, if in our practical technical work we tried to deal with the whole of reality all at once, we would be swamped…However, when this mode of thought is applied more broadly…then man ceases to regard the resulting divisions as merely useful or convenient and begins to see and experience himself and his world as actually constituted of separately existent fragments…fragmentation is continually being brought about by the almost universal habit of taking the content of our thought for ‘a description of the world as it is’. Or we could say that, in this habit, our thought is regarded as in direct correspondence with objective reality. Since our thought is pervaded with differences and distinctions, it follows that such a habit leads us to look on these as real divisions, so that the world is then seen and experienced as actually broken up into fragments.
— David Bohm, “Wholeness and the Implicate Order”
