Temporal Parts

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'Temporal Parts' are used in contemporary metaphysics. Some metaphysicists believe objects have temporal parts as well as spatial parts (such as hands, feet, legs etc.). A temporal part would thus be something like the first year of my life, or all of a table from between 10.00am on June 21st 1994 to 11.00pm July 23rd 1996. Originally it was argued that those who believe in temporal parts believe in perdurantism, that persisting objects are wholes composed entirely of temporal parts. This view was contrasted with endurantism which was taken to be the claim that objects are 'wholly present' at any one time (thus not having temporal parts at different times). This claim is still common place but philosophers like Ted Sider believe that even endurantists should accept temporal parts.

Not everyone was happy with the definition by analogy from above: some philosophers, such as Peter van Inwagen argued that even given the definition by analogy, they still had no real idea what a temporal part was meant to be (1981: 133), whilst others have felt that whether temporal parts existed or not is merely a verbal dispute (Eli Hirsch holds this view). So there has been work on giving a more specific definition. Gallois surverys some of them (Gallois 1998: 256). The early attempts included identifying temporal parts with ordered pairs of times and objects, but (a) it seems relatively unproblematic that temporal parts exist given the definition and (b) ordered pairs seem unsuitable to play the role that perdurantists demand, such as being parts of persisting wholes (how can a set be a part of a material object?). Later perdurantists identified persisting objects with events, and as events unproblematically had temporal parts (such as the first and second halves of a football match) it was imagined that persisting objects could unproblematically have temporal parts. There was a reluctance from many to identify objects with events, and this definition has long since fallen out of fashion.

Of the definitions closest to those commonly used in the literaute, the earliest was Thomson

x is a cross-sectional temporal part of y =df (∃T)[y and x exist through T & no part of x exists outside T & (∀t)(t is in T ⊃ (∀P)(y exactly occupies P at t ⊃ x exactly occupies P at t))] (Thomson 1983: 207).

Later Sider tries to combat fears by endurantists that they cannot understand what a temporal part by defining it in terms of 'part at a time', a relation that the endurantist should accept (unlike parthood simpliciter which an endurantist may say makes no sense given that all parts are had at a time: although see McDaniel (2004) 146-7, where he argues that even endurantists should accept the notion). He gives the following definition (the use of which has become wide-spread)

x is an instantaneous temporal part of y at instant t =df (i) x is a part of y; (ii) x exists at, but only, at t; and (iii) x overlaps every part of y that exists at t. (Sider 2001: 60).

Sider also gives an alternative definition that presentism is compatible with, using the tensed operators 'WILL' and 'WAS':

x is an instantaneous temporal part of y =df (i) x is a part of y; (ii) x overlaps every part of y; (iii) it is not the case that WILL (x exists); (iv) it is not the case that WAS (x exists). (Sider 2001: 71).

It is worth noting that whilst it is Sider's definition that is most commonly used, Zimmerman - troubled by the demand for instants (which may not exist in a gunky space-time that is such that every region has a sub-region) - gives the following:

x is a temporal part of y throughout T =df (i) x exists during and only during T; (ii) for every subinterval T* of T, there is a z such that (a) z is a part of x, and (b) for all u, u has a part in common with z during T* if and only if u has a part in common with y during T*; and (iii) y exists at times outside of T. (Zimmerman 1996: 122)

[edit] References

• Gallois, A. 1998. Occasions of Identity. Oxford, Clarendon Press.
• McDaniel, K. 2004. Modal Realism with Overlap from Lewisian Themes: The Philosophy of David K. Lewis ed. Frank Jackson and Graham Priest. Oxford, Clarendon Press.
• Sider, T. 2001. Four-Dimensionalism. Oxford: Clarendon Press.
• Thomson, J. 1983. Parthood and Identity Across Time. The Journal of Philosophy 80:4, p. 201-20.
• van Inwagen, P. 1981. The Doctrine of Arbitrary Undetatched Parts. Pacific Philosophical Quarterly, 62, p. 123-37.
• Zimmerman, D. 1993. Persistence and Presentism. Philosophical Papers 25:2, p. 115-26.