Leithart
Time and change are persistent puzzles in metaphysics. How can something be “the same” when all of its properties have changed?
A number of philosophers defend a “four-dimensional” metaphysics that incorporates temporal change into the very definition of an object. For four-dimensionalists, things have not only spatial but also temporal “parts,” and the thing is the sum of both sorts of parts.
Theodore Sider ( Four-Dimensionalism: An Ontology of Persistence and Time (Mind Association Occasional Series) 
Many “philosophers prefer instead to regard objects as ‘three-dimensional,’ as ‘enduring’, as being ‘wholly present’ at all times at which they exist. Consider the regions of space I occupy throughout my life. According to three-dimensionalists, these regions are not occupied by distinct instantaneous objects, but are rather occupied successively by the entire persisting object.” Four dimensionalists speak instead of “perdurance”: “a perduring object is ‘spread out’ over a region of spacetime, whereas an enduring object ‘sweeps through’ a region of spacetime, the whole of the object occupying the region’s subregions at different times” (3).
Sider thinks that four-dimensionalism is able to deal with traditional difficulties in ontology. Leibniz’s law, he notes, says that ” x = y only if x and y have all the same properties.” He agrees, but suggests that Leibniz’s law “seems to prohibit anything’s surviving any change.” A haircut changes a person from “Longhair” to “Shorthair,” and if Leibniz is correct these seem to be distinct entities. The person is not the same before and after the haircut.
Four-dimensionalists deal with the mystery of haircuts differently: “Leibniz’s Law does indeed imply that there are two distinct objects with different properties involved: a temporal part, which we may call ‘Longhair’, and a distinct temporal part, ‘Shorthair’. Longhair is my temporal part before the haircut, and does not survive the haircut; Shorthair is my temporal part after the haircut, and did not exist before the haircut. But it does not follow that I do not survive the haircut, for I am not identical to Longhair, nor am I identical to Shorthair. I am a sum of temporal parts that includes both Longhair and Shorthair, and survive the haircut in virtue of including each as parts. Change over time for the four-dimensionalist is thus a matter of dissimilarity between successive temporal parts”” (4).
He uses the illustration of a sculptor forming a statue from a lump of clay one Tuesday morning to deal with the problem of objects occupying the same space. The lump and statue share many properties – mass, location, atomic structure. But there are obvious differences: The lump has the property of “existing on Monday” that the status does not share. They are not entirely identical, but they are in many ways exactly alike. How can two things apparently occupy the same space.
Four-dimensionalists dissolve the issue with the notion of temporal parts: “At any given time it is only a temporal part of a spacetime worm that is wholly present. Thus it is only temporal parts of Statue and Lump that are wholly present at the time of coincidence. How can these temporal parts both fit into a single region of space? Because ‘they’ are identical. Statue and Lump are of course not identical, for Lump has temporal parts on Monday that are not shared by Statue. It is only their temporal parts on Tuesday (and subsequent days) that are identical. That is, Statue and Lump share a single temporal part on Tuesday” (5-6).
He resolves the problem of the ship of Theseus this way: “A four-dimensionalist regards the world as a world of stages. Acceptance of four-dimensionalism is plausibly accompanied by acceptance of another metaphysical principle, the principle of unrestricted mereological composition according to which, for any objects, there exists such a thing as the mereological sum, or fusion of those objects—a larger object that contains those objects as parts. According to this principle, any group of objects has a sum, even a group of objects that is very scattered . . . . once unrestricted composition is accepted, any set of stages has a sum, even sets of stages that are not unified in any particularly interesting way. The world is therefore populated by a host of continuing spacetime worms, of which we name, think of, and quantify over a small minority.”
Whether we say that the Ship of Theseus is identical to the replacement or the planks that are removed, we are dealing with some sort of “spacetime worm”: There is the “replacement worm” and ‘the original planks worm’ the worm that consists, at any moment, of the stages of all and only the original planks of The Ship of Theseus. This worm is co-located with The Ship of Theseus at the beginning of the process, and is co-located with Planks at the end of the process; it might be thought of as the ‘quantity of planks’ of which the original Ship of Theseus and Planks are made.” Whether the ship is the replacement ship or the planks depends on our concept of ship. Four-dimensionalism dissipates the metaphysical problem and leaves a conceptual issue (8-10).
I’m sure there are problems here, but any effort to include temporality and change into the definition of created things is worth exploring.
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