Abstract
A theory of temporal mereology is formulated in which the principles of Existence and of Uniqueness of Composition hold. The theory is consistent both with a three-dimensionalist ontology and with the change of parts, that is, with the view that at least one object has distinct parts at distinct times. Some interesting consequences of the theory joined with the change of parts, taken as an axiom, are proven. It is usually held that certain well known ontological puzzles must be solved either by adopting a four-dimensionalist ontology or by restricting some mereological principles. Here a solution to those puzzles is stated, which allows to keep all mereological principles in their generality, without adopting a four-dimensionalist ontology. The solution is achieved by denying the persistence of some of the entities involved, along the “Chrysippean” lines advocated by M. Burke and M. Rea. Although good reasons for this move are provided, some problems of the solution are also highlighted and tentatively answered.
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- 1.
Sums may be taken to exist in time, even if they are conceived as set-like, while existence in time for (certain) sets is not so clear. It is clear instead that if sets do not exist in time, it does not make sense to speak of their change of elements.
- 2.
As in, for example, [22]. Relativization to time is not always a natural move. We do not claim that a temporal parameter should be introduced for all predicates.
- 3.
Alternatively, “x is one of the X”/“a is one of the X” can be taken as the result of applying the predicate “is one of” to an individual variable/individual constant and to a plural variable. In this case “is one of” expresses a multigrade relation between one entity and one or more entities. The introduction of the predicate “is one of” enables us to adopt the expressions “each one of the X” as an abbreviation for “each entity x that is one of the X”, “some of the X” as an abbreviation of “some entity x that is one of the X”, and “at least one of the X” as an abbreviation of “at least an entity x that is one of the X”.
- 4.
Assuming the following form of the second order comprehension:
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If there is an x such that \(\varPhi(x)\), there are X such that x is one of the X if and only if Φ(x).
where Φ(x) is a well formed formula and X does not occur in it, and taking the temporal parameter as fixed, anti-symmetry of parthood does not need to be explicitly stated. It follows from Axioms 1, 2 and Axiom 6 below.
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- 5.
This is a common thesis in the framework of temporal mereology (see e.g., [22, p. 215]). It entails that Caesar (assuming that he does not exist anymore) is presently not a part of itself. This consequence might sound odd, but it immediately follows from the plausible view that no material object is now a part of a presently non-existing object.
- 6.
- 7.
There are various versions of Uniqueness of Composition, or mereological extensionality. Their relations are highlighted by Varzi [27]. We state here the most standard version.
- 8.
For the sake of simplicity, we take subsets of the domain, not pluralities of entities of the domain, as values of the second order variables. It would be possible, but much more complicated, to provide a full plural semantics for a second order language.
- 9.
It is an apparent empirical truth that some things change their parts. However, taking this truth as empirical does not imply that it cannot be contested. Here it will be assumed as an axiom, without dealing with the question of its justification.
- 10.
The story is really an adaptation of a medieval puzzle, Animal est pars animalis (see [28]), but analogous puzzles have haunted philosophers at least since Plato. A cat, Tibbles, her tail, Tail, and the rest of her body, Tib, are considered at a certain time, say t 1. Later on, Tibbles’s tail is cut. Soon after, say at t 2, it appears that Tibbles has the same parts, and so is the same, as Tib.
- 11.
- 12.
Thanks to an anonymous referee for this example.
- 13.
The analogy is partial because of the set-theoretical nature of geometrical entities. Moreover, the alleged vagueness of boundaries, which also affects fully integrated wholes, might make this analogy to appear too strong a simplification of the difference between Tibbles and Tib. However, it might be claimed that the degree of vagueness of entities that are not fully integrated wholes is higher in a quite intuitive sense, which could probably be further specified in some way.
- 14.
Other more or less formal ideas concerning unity and its ground are expressed in recent literature. See, for example, [8, 9, 13, 14, 21, 24]. In contrast to what was done in these writings, we pursue the idea that no entity is devoid of unity, while accepting the mereological axiom of Existence of Composition and avoiding to choose among the main ontological options.
- 15.
Simons [21] provides some case studies of natural wholes. However, he argues against the use of the notion of a kind of whole in the explication of what a whole is and prefers to raise the general question of what requirements a relation must satisfy in order to give rise to wholes. It should be said that Simons does not accept Existence of Composition in its full generality.
- 16.
Survival as a mere brain appears to be physiologically impossible or, at least, highly unlikely, since to survive a brain needs a continuous exchange with the body at a chemical level (see e.g., [2]). But even if it were possible to simulate this exchange by employing a suitably designed device, it might be argued that, after the device is in function, the whole organism persists at least in part as (a certain portion of) such a device.
- 17.
- 18.
18 Alternatively, the portion of clay might be thought of as an entity obtained by means of an equivalence relation. The portion of clay just bought and the statue are both composed, respectively at 9 am and at 2 pm, by the same disjoint minimal parts of clay. The corresponding equivalence class could be identified with the portion of clay regarded as an amount without any qualification. From this point of view the portion of clay might be conceived as the materialization of an abstract entity.
- 19.
19 See note 18 above. It might be objected that, intuitively enough, portions of stuff may lose a minimal amount of matter without passing out of existence. And this entails—so the objection goes—that singular reference to portions, as ordinarily understood, is never eliminable in favor of plural reference to their components. We are not too impressed by this objection. Of course, we may speak of “the same portion” even if what we have is not, strictly speaking, the same portion. Like many empirical notions, our usual concept of a portion is vague. For instance, the view that portions survive the lost of a minimal part is obviously the first step of a soritical series. But in the same vein, we may also speak of the “same components” at different times even if the components have not, strictly speaking, remained the same. As far as ordinary understanding is concerned, it appears that vagueness affects both the singular reference to a portion and the plural reference to its components, contrary to what the objection assumes. Moreover, vagueness is a notoriously delicate issue, and not specifically involved in the puzzles we are discussing.
- 20.
Something similar to what was said above (note 18) of the portion of clay could be said of the piece of yarn, even though in a somewhat more complex manner. The piece of yarn might be thought of as an entity got by means of an equivalence relation. The unraveled piece of yarn, the sweater, and the hat are all composed, at the appropriate times, by the same disjoint connected parts linearly ordered. The corresponding equivalence class could be identified with the piece of yarn. From this point of view also the piece of yarn (without any qualification) might be conceived as the materialization of an abstract entity.
- 21.
References
Baker, Lynne Rudder. 2000. Persons and Bodies: A Constitution View. Cambridge, UK: Cambridge University Press.
Berlucchi, Giovanni. 2009. “Identità personale, corpo, mente e cervello.” In Filosofia della medicina. Modelli, metodo, cura ed errori, edited by P. Giaretta, A. Moretto, G. Gensini, and M. Trabucchi, 613–29. Bologna: Il Mulino.
Boolos, George. 1984. “To Be Is to Be the Value of a Variable (or to Be Some Values of Some Variables).” The Journal of Philosophy 81:430–49.
Burke, Michael. 1980. “Cohabitation, Stuff and Intermittent Existence.” Mind 89:391–405.
Burke, Michael. 1994. “Dion and Theon: An Essentialist Solution to an Ancient Puzzle.” The Journal of Philosophy 91:129–39.
Burke, Michael. 1996. “Tibbles the Cat: A Modern Sophisma.” Philosophical Studies 84:63–74.
Gibbard, Allan. 1975. “Contingent Identity.” Journal of Philosophical Logic 4:187–221.
Guarino, Nicola and Christopher Welty. 2000. “Identity, Unity, and Individuation: Towards a Formal Toolkit for Ontological Analysis.” In Proceedings of ECAI-2000: The European Conference on Artificial intelligence, edited by W. Horn, 219–23. Amsterdam: IOS Press.
Hawley, Katherine. 2001. How Things Persist. Oxford: Oxford University Press.
Johnston, Mark. 1992. “Constitution Is Not Identity.” Mind 101:89–105.
Lewis, David. 1991. Parts of Classes. London: Blackwell.
Lowe, Edward Jonathan. 1998. “On the Identity of Artifacts.” The Journal of Philosophy 80:220–32.
Lowe, Edward Jonathan. 1998. “Entity, Identity and Unity.” Erkenntnis 48:191–208.
Lowe, Edward Jonathan. 2003. “Identity, Individuality, and Unity.” Philosophy 78:321–36.
Noonan, Harold. 1999. “Tibbles the Cat—Reply to Burke.” Philosophical Studies 95:215–18.
Olson, Eric. (Winter 2008). “Personal identity.” In The Stanford Encyclopedia of Philosophy, edited by Edward N. Zalta. http://plato.stanford.edu/archives/win2008/entries/identity-personal.
Rea, Michael. 1995. “The Problem of Material Constitution.” The Philosophical Review 104:525–52.
Rea, Michael. 2000. “Constitution and Kind Membership.” Philosophical Studies 97:169–93.
Sidelle, Alan. 2002. “Is There a True Metaphysics of Material Objects?” Philosophical Issues 12:118–45.
Simons, Peter. 1987. Parts: A Study in Ontology. Oxford: Clarendon Press.
Simons, Peter. 2006. “Real Wholes, Real Parts: Mereology Without Algebra.” The Journal of Philosophy 103:597–613.
Thomson, Judith Jarvis. 1983. “Parthood and Identity Across Time.” The Journal of Philosophy 80:201–20.
Thomson, Judith Jarvis. 1998. “The Statue and the Clay.” Noûs 32:149–73.
Van Inwagen, Peter. 1990. Material Beings. Ithaca, NY: Cornell University Press.
Van Inwagen, Peter. 2006. “Can Mereological Sums Change Their Parts?” The Journal of Philosophy 103:614–30.
Varzi, Achille. 2000. “Mereological Commitments.” Dialectica 54:283–305.
Varzi, Achille. 2008. “The Extensionality of Parthood and Composition.” The Philosophical Quarterly 58:108–33.
Wiggins, David. 1968. “On Being in the Same Place at the Same Time.” The Philosophical Review 77:90–95.
Wiggins, David. 1980. Sameness and Substance. Oxford: Blackwell.
Wiggins, David. 2001. Sameness and Substance Renewed. Cambridge, UK: Cambridge University Press.
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Giaretta, P., Spolaore, G. (2012). A Mereology for the Change of Parts. In: Trobok, M., Miščević, N., Žarnić, B. (eds) Between Logic and Reality. Logic, Epistemology, and the Unity of Science, vol 25. Springer, Dordrecht. https://doi.org/10.1007/978-94-007-2390-0_13
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