Mereological endurantism and being a whole at a time: reply to Costa

ABSTRACT

Damiano Costa has recently offered a novel mereological definition of endurantism based on the idea that for an object to be wholly present at a time is for it to be a whole at that time. In this paper, I argue that Costa’s is not a definition of endurantism, since the idea that every object is a whole at every time it exists can be accepted by endurantists and perdurantists alike.

KEYWORDS:

• Three-dimensionalism
• wholly present
• mereology
• persistence
• time

Acknowledgements

Many thanks to an anonymous referee for this Journal.

Disclosure statement

No potential conflict of interest was reported by the author(s).

Notes

1 For an overview of this debate see, for instance, Crisp and Smith (2005).

2 See, among others, Sattig (2006), Eagle (2016), Gilmore (2018), and Leonard (2018).

3 So, for instance, a definition of endurantism employing a (non-mereologically defined) notion of constitution—as the alternative definitions that Costa (2020, 9) himself offers—doesn’t count as purely mereological in this sense.

4 As it will become clear below, my criticism applies also to the other purely mereological definitions of endurantism provided by Costa, namely those he calls ‘Whole presence 1’ (p. 6) and ‘Whole presence 2’ (pp. 7-8). Instead, the definitions he calls ‘Whole presence for constitution theorists’ (p. 9) and ‘Whole presence for time traveller’s (p. 10) are not purely mereological and are, thus, beyond the scope of this paper.

5 Notice that in what follows I will take times to be instants rather than intervals of time.

6 I am here relying on the following principles concerning the notions of exact, weak, and entire location: (WL) x is weakly located at r if and only if there is a region s such that x is exactly located at s and r overlaps s. (ENL) x is entirely located at r if and only if there is a region s such that x is exactly located at s and s is part of r (see Parsons 2007, 204–205).

7 Namely: (i) exact location is unique; (ii) x exists at t if only if x is weakly located at t; (iii) x is weakly located at t if and only if x’s exact location overlaps t; (iv) x is entirely located at t if and only if x’s exact location is part of t.

8 This notion of proper-part-at-t is defined as follows: $x{<}_t^{C}y{=}_{df}x{\le }_t^{C}y\wedge x\ne y$

9 This notion of overlap-t is defined as follows: $O_t^{C}xy{=}_{df}\mathrm{\exists }z(z{\le }_t^{C}x\wedge z{\le }_t^{C}y)$

10 Notice that (5) can be shown to follow from (3) even without assuming (PPT) and allowing, thus, persisting objects to be part of themselves at times at which they exist. In fact, if the entity c that we are supposing to be part-at-t of both a and b is identical to a it still follows that b overlaps-at-t some of the proper parts-at-t of a. We are assuming that a has proper parts-at-t. Let d any of these proper parts-at-t of a. By (P@T_C-2), d exists only at t. By Conditional Reflexivity* d is thus part-at-t of itself. However, by Transitivity* d is also a part-at-t of b, so that d is indeed a proper part-at-t of a that overlaps-at-t b.

11 Notice, furthermore, that (no matter how they may define the atemporal notion of parthood in terms of their primitive temporal one) also Costa’s endurantists appear to be committed to rejecting the idea that persisting objects are identical to atemporal sums of proper parts they have at any time of their persistence. Suppose, in fact, that a is a persisting object that exists both at time T1 and at time T2. Let the bb be the proper parts-at-T1 of a and the cc be the proper parts-at-T2 of a. Following Costa’s notion of part-at-a-time (according to which if x is a part-at-t of y, then x exists only at t; see above), we have both that all of the bb and their parts exists only at T1 and that all of the cc and their parts exists only at T2. If a was an atemporal sum of both the bb and the cc it would follow from the definition of atemporal sum (see (Sum) above) that each of the bb overlaps some of the cc and that each of the cc overlaps some of the bb. This is, however, impossible given that every part of the bb exists only at T1 and every part of the cc exists only at T2.

Additional information

Funding

This work was supported by the Deutsche Forschungsgemeinschaft under [grant number 448954791] (project title ‘The Structure of Fundamentality’) and the Ministerio de Ciencia y Innovación under [grant number RYC2019-026416-I].