Abstract
Weatherson (The Philosophical Quarterly, 53, 481–501 2003) argues that whoever accepts classical logic, standard mereology and the difference between vague objects and any others, should conclude that there are no vague objects. Barnes and Williams (Pacific Philosophical Quarterly, 90, 176–187 2009) claim that a supporter of vague objects who accepts classical logic and standard mereology should recognize that the existence of vague objects implies indeterminate identity. Even though it is not clearly stated, they all seem to be committed to the assumption that reality is ultimately constituted by mereological atoms. This assumption is not granted by standard mereology which instead remains silent on whether reality is atomic or gunky; therefore, I contend that whoever maintains classical logic, standard mereology and the difference between vague objects and any others, is not forced to conclude with Weatherson that there are no vague objects; nor is she compelled to revise her point of view according to Barnes and Williams’s proposal and to accept that the existence of vague objects implies indeterminate identity.
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Notes
See for example Lewis ([3], p. 74): “These axioms [i.e. Transitivity, Unrestricted Composition and Uniqueness of Composition] do not settle all questions that can be raised in the language of mereology. Does Reality consist entirely of atomless gunk? Entirely of atoms? Or some of each? […] the basic axioms of mereology are silent about which of these hypotheses are true.”
It may be useful to note that McGee and McLaughlin’s definition is made in terms of “atoms”, while mereology is neutral with respect to there being mereological atoms or atomless gunk. For someone looking for a more neutral presentation of K(+) and K(-), I propose to substitute the occurrences of “atoms” with “parts” in McGee and McLaughlin’s definition quoted in the text. I am indebted to an anonymous referee for highlighting the importance of distancing myself from McGee and McLaughlin’s definition.
It may be useful to note moreover that K(+) and K(-) are vague objects. Although K(+) determinately includes Sparky, while K(-) determinately excludes it, they share the vagueness of K for all the other parts except Sparky.
2) is a rewording of Weatherson’s principle: “if for all x other than Sparky, x is part of y iff x is part of z, then if Sparky is part of both y and z, or part of neither y nor z, then y and z coincide” (Weatherson [8], p. 491). It is quite important to note that Weatherson’s principle includes “for all x other than Sparky” and not “for all x not identical to Sparky”. According to the Oxford English Dictionary, “other” means “existing besides, or distinct from, that already mentioned or implied; further, additional”. This is relevant because a part of Sparky is obviously not identical to Sparky, but it is not other than Sparky; therefore, according to Weatherson, the domain of the universal quantifier is restricted to everything that is neither Sparky nor part of Sparky.
Weatherson [8] takes into consideration some variants of assumption 3) and presents a different argument taking into consideration one of these variants. I will not consider any of these variants because my claim is independent of assumption 3).
It may be tempting to believe that Barnes and Williams could easily propose another argument (not parasitic on problematic assumptions of Weatherson’s argument) for the thesis that vague objects imply indeterminate identity. Here is a proposal of such an argument by a referee: (1) Either Sparky is part of K or it is not (assumption - EM); (2) If Sparky is part of K, then K = K+ (from Weatherson’s argument and not under discussion); (3) If Sparky is not part of K, then K ≠K+ (as Sparky is part of K + by definition and not of K by the antecedent of the conditional); (4) Either K = K+ or K ≠K+ (by Constructive Dilemma from 1, 2 and 3). The argument is valid and sound up to this point. Then, if it is assumed that: (5) it is indeterminate which disjunct holds [in (4)]; it follows that it is indeterminate whether K = K+. As I see it, (5) presupposes what is argued for, i.e. that there is indeterminate identity. A supporter of vague objects who believes that identity is a determinate relation would not accept (5), she would probably say that K ≠K+ is true and K = K+ false.
By the way, Sparky is assumed by Weatherson to be an electron. And it is not clear weather an electron is a mereological atom.
An even better formulation is the following: “if two things have the same parts, setting aside Sparky, then they coincide if and only if every part of Sparky that is part of one is part of the other, and vice versa.” I am indebted to Achille Varzi for suggesting this to me. I stick to 2*) in the text because it better suits the second step (i.e. [2]) of Weatherson’s argument.
References
Barnes, E., & Williams, J. R. G. (2009). Vague Parts and Vague Identity. Pacific Philosophical Quarterly, 90, 176–187.
Casati, R., & Varzi, A. C. (1999). Parts and Places. The Structure of Spatial Representation. Cambridge Massachusetts: The MIT Press.
Lewis, D. K. (1991). Parts of Classes. Oxford, Cambridge Massachusetts: Basil Blackwell.
McGee, V. (1997). Kilimanjaro. Canadian Journal of Philosophy, supp, 23, 141–163.
McGee, V., & McLaughlin, B. (2000). The Lessons of the Many. Philosophical Topics, 28, 129–151.
Simons, P. (1987). Parts. A Study in Ontology. Oxford: Clarendon Press.
Varzi, A. C. (2014). Mereology. The Stanford Encyclopedia of Philosophy (Fall 2014 Edition), Edward N. Zalta (ed.) http://plato.stanford.edu/archives/fall2014/entries/mereology/.
Weatherson, B. (2003). Many Many Problems. The Philosophical Quarterly, 53, 481–501.
Acknowledgments
I presented this work at different stages of its elaboration in Torino, Macerata, Bergamo, Milano (Università Cattolica and Università degli Studi di Milano) and Warwick (Joint Session of the Aristotelian Society and Mind). I thank everyone who reacted to my work with questions and objections, I am particularly indebted to Andrea Bottani, Aldo Frigerio, Alessandro Giordani, Hykel Hosni, Andrea Iacona, Diego Marconi, Francesco Orilia, Thomas Sattig, Nicholas J. J. Smith, Alfredo Tomasetta, Giuliano Torrengo, Achille Varzi and two anonymous referees.
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Paganini, E. Vague Objects within Classical Logic and Standard Mereology, and without Indeterminate Identity. J Philos Logic 46, 457–465 (2017). https://doi.org/10.1007/s10992-016-9407-9
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DOI: https://doi.org/10.1007/s10992-016-9407-9