Real wholes, real parts: Mereology without algebra

Journal of Philosophy

Volumn 103, Issue 12, 2006, Pages 597-613

  Simons, Peter ^a  

^a UNIVERSITY OF LEEDS   (United Kingdom)

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[No Author keywords available]

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EID: 60950203939     PISSN: 0022362X     EISSN: 19398549     Source Type: Journal    
DOI: 10.5840/jphil2006103122     Document Type: Review

References (30)

1. Whitehead, An Enquiry Concerning the Principles of Natural Knowledge (New York: Cambridge, 1919; 2nd ed., 1925).
2. The objects of Whitehead's mereology in Principles are called"events." I shall ignore this terminology and speak throughout of"objects." What Whitehead himself calls an "object" is notan event but a continuant constituted by a suitable sequence of events. By 1929Whitehead had moved his mereology from events to the regions they occupy. See Peter M. Simons, "Whitehead und die Mereologie, " in Michael Hampe and Helmut Maaßen, eds., Die Gifford Lectures und ihre Deutung. Materialien zu Whiteheads Prozess und Realität, Band 2 (Frankfurt: Suhrkamp, 1991), pp.369-88;
3. translation: "Whitehead and Mereology, " in Guillaume Durand and Michel Weber, eds., Les principes de la connaissance naturelle d'Alfred North Whitehead: Alfred North Whitehead's Principles of Natural Knowledge (Frankfurt:Ontos, 2007), pp. 215-33.
4. It is surprising how many ontologists - unlike Leśniewski - failto distinguish between a collection of many individuals and the one individualthey compose, if they do: for example, D.L.M. Baxter, "Many-One Identity, " Philosophical Papers, XVII (1988): 193-216;
5. David Lewis, Parts of Classes (Cambridge: Blackwell, 1990), pp. 81-87.
6. Leśniewski, Collected Works (Boston: Kluwer, 1992), p. 135 (Axiom III).
7. Tarski, "Zur Grundlegung der Boole'schen Algebra I, " Fundamenta Mathematicae XXIV (1935): 177-98;
8. revised English translation: "On the Foundations of Boolean Algebra, " in his Logic, Semantics, Metamathematics (New York: Oxford, 1956;2nd ed., Indianapolis: Hackett, 1983), pp. 320-41.
9. See Simons, Parts (New York: Oxford, 1987), p. 35.
10. Leśniewski, Collected Works, pp. 207ff.
11. Partly as transmitted through Henry S. Leonard and Nelson Goodman, "The Calculus of Individuals and Its Uses, " Journal of Symbolic Logic, V (1940): 45-55.
12. This position is actually upheld by J. Krupp, "Mereological Nihilism: Quantum Atomism and the Impossibility of Material Constitution, "Axiomathes (forthcoming),
13. and considered possible and unrefuted in Gideon Rosen and Cian Dorr, "Composition as Fiction, " in Richard Gale, ed., The Blackwell Guide to Metaphysics (Malden, MA: Blackwell, 2002), pp. 151-74. Such negative andsceptical positions have to face the Moorean objection that we seem to know justby looking that some objects are parts of other objects. This is not arefutation of course, but it puts the onus of proof on them. Krupp has tocontend that when I seem to see my finger as part of my hand I am hallucinating(since there are no such objects as my finger or my hand).
14. Van Inwagen, Material Beings (Ithaca: Cornell, 1990).
15. J.T.J. Szrednicki and Z. Stachniak, eds., S. Leśniewski's Lecture Notes in Logic (Boston: Kluwer, 1988), pp. 109ff.,
16. C. Lejewski, "Consistency of Leśniewski's Mereology, "Journal of Symbolic Logic, XXXIV (1969): 321-28.
17. For such attempts, see Simons, Parts, pp. 330ff.
18. Lewis, Parts of Classes;
19. Sider, Four-Dimensionalism: An Ontology of Persistence and Time (New York: Oxford, 2001).
20. The problem of vague objects is a different problem. An object is vagueif it is unclear what its parts are - for example, the sun - cf. Simons, "Does the Sun Exist? The Problem of Vague Objects, " in Tom Rockmore, ed., Proceedings of the XX World Congress of Philosophy, Volume II: Metaphysics(Bowling Green, OH: Philosophy Documentation Center, 1999), pp. 89-97. But thesun clearly exists: it is not a borderline case of existence.
21. This in a nutshell is the argument of Kathrin Koslicki, "The Crooked Path from Vagueness to Four-Dimensionalism, " Philosophical Studies, CXIV(2003): 107-34.
22. Cf. Simons, "The Universe, " Ratio, XVI (2003): 236-50.
23. Denying multicategorial composition means denying states of affairs, atleast on those conceptions where a state of affairs is literally composed ofindividuals and a universal. This is no burden for those who deny states ofaffairs. Those who have states of affairs in their ontology are unlikely to beheld back from accepting them by a Verbot on intercategorial composition. If, as I do, one accepts a trope-bundle theory of substance (Simons, "Particularsin Particular Clothing: Three Trope Theories of Substance, " Philosophy and Phenomenological Research, LIV (2004): 553-76) then it would appear that anobject composed wholly of things from one category, namely the category TROPE, can be of another category, namely the category SUBSTANCE. If that is right, then there is at least one kind of category-crossing composition, and the Verboton category-crossing composition is wrong. This is a good argument, but for adifferent conclusion. It is a good reason to deny that there is a categorialdistinction between tropes and substances. Tropes and substances both belongtogether in a single category, that of individual THING. Without going intodetails here, there are a number of solid metaphysical advantages todown-grading the substance/trope distinction to an intracategorial one.
24. Simons, "Extended Simples: A Third Way between Atoms and Gunk, "The Monist, LXXVII (2004): 371-84.
25. On the importance of cavities, see Roberto Casati and Achille Varzi, Holes and Other Superficialities (Cambridge: MIT, 1994).
26. On different kinds of artefact part and the problems of discrepancy, see Simons and Charles W. Dement, "Aspects of the Mereology of Artifacts, "in Roberto Poli and Simons, eds., Formal Ontology (Boston: Kluwer, 1996), pp.255-76.
27. For example, the Gene Ontology: http://www.geneontology.org.
28. That they usually are not is the justified complaint of Barry Smith, "Beyond Concepts: Ontology as Reality Representation, " in Varzi and Laure Vieu, eds., Formal Ontology and Information Systems (Amsterdam: IOS, 2004), pp. 73-84.
29. A mereologist who has remained quietly unfazed by algebra is David Sanford: see his "The Problem of the Many, Many Composition Questions, and Naive Mereology, " Noûs, XXVII (1993): 219-28;
30. and "Temporal Parts, Temporal Portions, and Temporal Slices: An Exercise in Naive Mereology, " Acta Analytica, XV (1996): 21-33.