Temporal Parts of Four-Dimensional Objects

1. Temporal Parts of Four-Dimensional Objects Mark Heller Philosophical Studies 46 (1984): 323-334

2. Thesis • Heller defends a new conception of physical objects in which the temporal dimension is part of the three-dimensional physical object.

3. Contradiction View A View B • Objects have three dimensions and persist through time. • (i) There is a physical objects as my body. (obviously true) • (ii) There is physical object in the space that we would typically say is now exactly occupied by all of me other than my left hand. (no so obviously true) • (iii) Physical objects can undergo a loss of parts. (obviously true) • (iv) There cannot be distinct physical objects exactly occupying the same space at the same time. (True) • (v) Identity is transitive. (true)

4. Views A and B Contradictory • A and B are contradictory, so to accept A we have to reject one from (a) – (e). • Heller will demonstrate how his view, which that incorporates the temporal dimension, can avoid this contradiction, because under his view an object can occupy the same space at a given moment in time and still be different and distinguishable.

5. Three-Dimensional Physical Objects Must accept at least one Common sense view • (a) There is no physical objects as my body. • (b) There is no physical object in the space that we would typically say is now exactly occupied by all of me other than my left hand. • (c) No physical object can undergo a loss of parts. • (d) There can be distinct physical objects exactly occupying the same space at the same time. • (e) Identity is not transitive • Thomson accepts (d) • Chisholm accepts (c) • Geach accepts (e)

6. Spacetime Terminology • Temporal part • Temporal slice • Temporal phase • Events • Processes • careers • Phases • Histories

7. 3-dimensional objects in time 4-dimensional objects within time • There is a hunk of matter that endures in (through) time. • If object O begins to exist at T2 and its existence ends at T6, then we say that it existed at these times and any time in-between. • There is a hunk of space time matter. • If object O begins to exist at T2 and its existence ends at T6, then O exists from T2 to T6, and O takes up that region of time.

8. Boundaries 3-dimensional in time 4-dimensional Object within time Object within time Object

9. Four Dimensional Object • A four dimensional object is the material content of a filled region of spacetime. • A spatiotemperal part of such an object is the material content of a sub-region of the spacetime occupied by the whole.

10. Parts of four dimensional objects • A spatiotemporal part is not a set or a process or a way something is at a place and time. • It is what constitutes the object.

11. Spatiotemporal Parts OBJECT O “Temporal sub-region of R, such as S, means spatiotemporal sub-regions that shares all of R’s spatial boundaries within the sub-regions temporal boundaries.” So the spatial boundaries of O at R and S are equal. T0 O T3 Region R T1 T2 Sub-region S

12. Language – 3-Dimensional Picture • “I existed” “I exist now” “I will exist” NOW Whole of me

13. Language – 4-Dimensional Picture • Part of me Part of me Part of me Part of me Part of me Past Past NOW Future Future

14. The Problem of Coincident Entities Golden Ring and Gold • Gold Object G Ring Object R Ring and Gold overlap because they share a temporal part

15. Why 4-Dimensional objects • Only by adopting the 4-dimensional view of objects can we make sense of parts to whole of things within time. • For instance, if I am Bernie NOW and Bernie NOW represents the whole of Bernie, then Bernie tomorrow could not be ME. • Bernie tomorrow has a temporal part that is not part of Bernie NOW, so either we have to admit that (1) Bernie tomorrow is different from Bernie NOW or (2) we have to admit that Bernie NOW is not the whole of Bernie.

16. Objection • The objection to Heller’s view, or shall we say the common argument in favor of the opposing view goes back to the insights of the Greek metaphysicians. • The basic idea revolves around the conception of change: how do things change from on moment to the next? Is an object that is present at one moment (T1) different form the object present at the next moment (T2)? • Is the chalk in my hand at T1 the same or different than the chalk at T2?

17. Objection • We want to say “yes”. • But is they are the same object, then they must have something essential in common. How can this be possible if we already admitted that they are different. • We seem to want to say that, even if the chalk is different and has changed, there is SOME THING that undergoes this change and sustains the sameness or identity of the thing over time.

18. Traditional View • This traditional view implies that there is one thing that endures over time! • If we do not admit this then we would have to admit that there is a NEW thing at each moment in time. But where did this NEW thing come from. • Hence, Thomson’s criticism that temporal parts would come into existence ex nihilo.