Temporal Parts and Four-Dimensionalism
How is some object, O, the same object over time if, at different times, it has different properties? Imagine that at some time, t1, O is bent, while at some future time, t2, O is straight. How are we able to say that the same object persists from t1 to t2? Consider Leibniz' law:
Leibniz's Law: Objects x and y are identical only if they have exactly the same properties.
If O is bent at t1 and straight at t2, then it does not have the same properties at those times, and, consequently, it would seem that it is not the same object at t2 that it was at t1.
Temporal Parts Theory (Four-Dimensionalism)
Temporal parts theory claims to offer a solution to this puzzle. Consider your body. Your body has spatial parts; a nose, arms, ears, etc. Although these parts are different from one another, together they compose your body. Your body is not identical to any one of your parts. Rather, it is the composite of your parts. Similarly, temporal parts theory argues that an object has temporal parts. Temporal parts theorists envision time as being an additional, fourth dimension to space (hence, temporal parts theory is often called four-dimensionalism). Thus, an object is both spatially and temporally extended.
Imagine viewing time from a God's-eye perspective. You would see a spacetime worm with a spacetime part at t1 where O is bent and a spacetime part at t2 where O is straight. O at t1 and O at t2 are temporal parts of O. That is to say, O at t1 and O at t2 are "spacetime subregions" that are merely aggregates of an entire spacetime "worm." O would be the composite of the spacetime subregions of O -- t1, t2,...tn -- but would not be wholly identical to any one spacetime part, no more than any part of your body is identical to you. Mark Heller writes, "A four-dimensional object is the material content of a filled region of space-time. A spatiotemporal part of such an object is the material content of a subregion of the space-time occupied by the whole" [1].
By permitting temporal parts into their ontology, temporal parts theorists claim to answer the challenge of Leibniz' law to persistence over time. They do so, however, by envisioning time as a fourth dimension to the three dimensions of space, positing subregions of spacetime as parts of larger subregions. Since O is a spacetime composite of spacetime parts, no absurdities seem to accrue by O's parts having different properties at different times.
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Footnotes:
[1] Heller, Mark. "The Ontology of Physical Parts." Metaphysics: Contemporary Readings. Ed. Michael J. Loux. Abingdon: Routledge, 2001. Print.
Leibniz's Law: Objects x and y are identical only if they have exactly the same properties.
If O is bent at t1 and straight at t2, then it does not have the same properties at those times, and, consequently, it would seem that it is not the same object at t2 that it was at t1.
Temporal Parts Theory (Four-Dimensionalism)
Temporal parts theory claims to offer a solution to this puzzle. Consider your body. Your body has spatial parts; a nose, arms, ears, etc. Although these parts are different from one another, together they compose your body. Your body is not identical to any one of your parts. Rather, it is the composite of your parts. Similarly, temporal parts theory argues that an object has temporal parts. Temporal parts theorists envision time as being an additional, fourth dimension to space (hence, temporal parts theory is often called four-dimensionalism). Thus, an object is both spatially and temporally extended.
Imagine viewing time from a God's-eye perspective. You would see a spacetime worm with a spacetime part at t1 where O is bent and a spacetime part at t2 where O is straight. O at t1 and O at t2 are temporal parts of O. That is to say, O at t1 and O at t2 are "spacetime subregions" that are merely aggregates of an entire spacetime "worm." O would be the composite of the spacetime subregions of O -- t1, t2,...tn -- but would not be wholly identical to any one spacetime part, no more than any part of your body is identical to you. Mark Heller writes, "A four-dimensional object is the material content of a filled region of space-time. A spatiotemporal part of such an object is the material content of a subregion of the space-time occupied by the whole" [1].
By permitting temporal parts into their ontology, temporal parts theorists claim to answer the challenge of Leibniz' law to persistence over time. They do so, however, by envisioning time as a fourth dimension to the three dimensions of space, positing subregions of spacetime as parts of larger subregions. Since O is a spacetime composite of spacetime parts, no absurdities seem to accrue by O's parts having different properties at different times.
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Footnotes:
[1] Heller, Mark. "The Ontology of Physical Parts." Metaphysics: Contemporary Readings. Ed. Michael J. Loux. Abingdon: Routledge, 2001. Print.
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