Abstract
Some philosophers assume that our ordinary parts-whole concepts are intuitive and univocal. Moreover, some assume that mereology—the formal theory of parts-whole relations—adequately captures these intuitive and univocal notions. Lewis (Parts of classes. Blackwell, Oxford, 1991: p. 75), for example, maintains that mereology is “perfectly understood, unproblematic, and certain.” Following his lead, many assume that expressions such as ‘is part of’ are (i) univocal, (ii) topic-neutral, and that (iii) compositional monism is true. This paper explores the rejection of (i)–(iii). I argue that our ordinary parts-whole expressions are polysemous; they have multiple distinct, but related, interpretations or meanings. I canvass several criteria by which to test for polysemy, and apply these criteria to some of our parts-whole terminology. I also examine some philosophical examples involving abstracta and abstract parts, which give us additional reasons to think that our parts-whole expressions are polysemous and topic-specific. Yet if so, then compositional pluralism is true.
This is a preview of subscription content, log in via an institution to check access.
Similar content being viewed by others
Notes
At the time, Lewis claimed that his view was a “minority opinion” and that many philosophers “view mereology with the gravest suspicion.” (75) Yet I assume that the tides have shifted since Parts of Classes; most in the literature these days seem to follow Lewis (1991) and assume that mereology and our parts-whole concepts are relatively innocuous and topic-neutral.
Some reserve the terms ‘mereology’ and ‘mereological’ to designate whatever obeys the axioms and principles of formal mereology. Others use these terms more generally, to designate our ordinary thoughts and talk about parts and wholes (and related concepts), regardless of whether those concepts end up obeying formal mereological principles. See Paul (2002: p. 579), e.g. To avoid confusion, I will use ‘parts-whole’ or ‘compositional’ to talk about the (supposed) broader notion(s). I will reserve ‘mereological’ to designate whatever obeys formal classical extensional mereology.
This is a play off of Carnap’s internal and external distinction, although Hofweber disagrees that external questions are meaningless. Hofweber (2009: pp. 275–276) defends the view that the existential quantifier is polysemous by (i) explaining what the two different candidate meanings are (or could be), (ii) showing that depending on which meaning is used or intended, the truth conditions vary. Hofweber maintains that each interpretation has ‘equal standing’ and that neither are dependent on the other for determining truth (one is not a restriction one the other, one is not more ‘strict’ and the other ‘loose’, etc.). Arguably, Hofweber (2009) does not adequately show why the quantifier is polysemous as opposed to homonymous. Nonetheless, his proposed view serves as an example of those who maintain that certain key philosophical terms are polysemous.
According to McDaniel, an expression is pros hen equivocal “just in case it has several senses, each of which is to be understood in terms of some central meaning of that expression.” An expression is analogical “just in case it has a generic sense, which, roughly, applies to objects of different sorts in virtue of those objects exemplifying very different features.” As McDaniel is using these terms, “no expression is both pros hen equivocal and analogical…an expression is pros hen equivocal only if it fails to have a generic sense.” Further, an “expression is polysemous if it has many meanings that are closely related, but these meanings need not be related by way of a central sense or focal meaning…an expression is pros hen equivocal only if it is polysemous only if it is ambiguous, but none of the converses hold.” (2009b: pp. 294–295).
McDaniel (2009b) thinks that there is a generic, univocal sense of ‘is part of’ that can be applied to different kinds of objects, such as material objects and regions of spacetime, which combines with his compositional pluralism (i.e., the view that there is more than one fundamental parthood relation). See also McDaniel (2010: pp. 696–698).
For the moment, I am leaving it open as to what exactly semantic values are. A standard view is to say that semantic values involve a relatively simple word-world mapping from, say, predicates to properties and relations. So predicates such as ‘is part of’, and any variations, would pick out any parthood relation(s), however many there are. While I lean towards this kind of view, I have some reservations, which I’ll discuss more fully in Sect. 5.
Varzi does admit that the ‘part’ concept that mereology is about “does not have an exact counterpart in ordinary language.” But then he—in line with others in the literature—appeals to how we use parts-whole concepts in English to justify and explain various philosophical positions about our mereological concepts.
Simons (1987) talks about different ‘senses’ of part but does not explicitly defend the view that such expressions are polysemous.
Thanks to an anonymous referee for raising this point.
According to McDaniel: “Analogous features are something akin to disjunctive properties, but they aren’t merely disjunctive. Analogous features enjoy a kind of unity that merely disjunctive features lack: they are, to put it in medieval terms, unified by analogy.” (2010: p. 696).
McDaniel (ibid.) focuses primarily on analogous features, relations, or properties, but seems sympathetic with views where ‘existence’ and ‘being’ are analogous expressions, or ambiguous in ordinary language. Yet he also admits that one can be an ontological pluralist without thinking that that ordinary English reflects this. (2010: p. 692).
I said it should be no surprise. But I did not say it necessarily follows. It may be that there is—in general—a hook-up between our words and the world. But as I mention above (footnote 8), I’m not ready to make that commitment here. This is in part because I think the evidence for whether our parts-whole terminology is polysemous holds independently of whatever semantic theories we accept, or what we take semantic values to be. More on this in Sect. 5.
Sider (2001: p. 61).
Paul (2002: p. 578).
“I fully accept the argument of Chisholm and Geach for the conclusion that the idea of a temporal part is incoherent. I simply do not understand what these things are supposed to be, and I do not think this is my fault. I think that no one understands what they are supposed to be, though of course plenty of philosophers think they do.” van Inwagen (1981(1997 reprint: p. 202)) Elsewhere: “…though I think that color blue and I both exist, I am unable to form a sufficiently general conception of parthood to be able to conceive of an object that has me and a color as parts.” van Inwagen (1987: p. 35).
Thanks to an anonymous referee for raising this point.
“Both the parthood relation defined on regions and the relation defined on facts is two-placed. One could say that there is one perfectly natural relation that is exemplified by both regions and facts. But note that the logic of this relation is ugly… but systematically ugly: when applied to objects of one ontological category, it behaves in one way, but when applied to objects of another ontological category, it behaves in a radically different way. The ‘‘logic’’ of parthood is most naturally expressed as a disjunctive list of two disjoint axiom systems, each such that the variables are restricted to objects of the relevant kinds. Parthood is systematically variably axiomatic. This is a bad way for a perfectly natural relation to behave: its behavior looks disjunctive at worst, less than uniform at best…Instead, there are three perfectly natural topic-specific parthood relations, one for regions, one for material objects, and one for facts.” (ibid.: pp. 699–700).
An object is mereological simple iff it has no parts. If all abstracta are mereologically simple, then it is misleading (at best) to say that our parts-whole terminology is topic-neutral with respect to concreta and abstracta—i.e., parts-whole terminology would only apply to abstracta vacuously.
Where H = a Tinkertoy house on the shelf at 1:15, W = the fusion of the Tinkertoys on the shelf at 1:15, and W’ = the wood on the shelf at 1:15.
Thanks to an anonymous referee for raising this point.
McDaniel (2013).
First, we might distinguish fundamental parthood relations by the category of things that participate in them: one for material objects, one for spacetime, one for facts, one for structure-making relations, one for classes or sets, haecceities, or abstracta generally, etc. These relations might otherwise be the same—they might obey the same rules (e.g., classical mereology—they are both transitive, unique, universal), they might all be 2-placed, have the same logical form etc. Alternatively, the different relations might differ with respect to their logical form. Material objects may have a 3-place parthood relations, relative to regions of spacetime, for examples, whereas regions of spacetime have a 2-place parthood relation. Third, they might obey different (but partially overlapping) axioms. If our part-whole talk in ordinary language is indeed polysemous as argued above, this might be a tempting option since it would explain how these relations are “different but related,” which would in turn explain the linguistic data. Etc.
References
Fine, K. (2010). Towards a theory of part. Journal of Philosophy, 107, 559–589.
Hawthorne, J., & Lepore, E. (2011). On words. The Journal of Philosophy, 108, 447–485.
Hofweber, T. (2009). Ambitious, yet modest, metaphysics. In D. Chalmers, D. Manley & R. Wasserman (Eds.), Metametaphyiscs: New essays in the foundations of ontology. Oxford: Oxford University Press.
Koslicki, K. (2008). The structure of objects. Oxford: Oxford University Press.
Leonard, H. S., & Goodman, N. (1940). The calculus of individuals and its uses. The Journal of Symbolic Logic, 5(2), 45–55.
Lewis, D. (1991). Parts of classes. Oxford: Blackwell.
McDaniel, K. (2004). Modal realism with overlap. Australasian Journal of Philosophy, 82(1): 137–152. Reprinted in Lewisian Themes (eds.) Frank Jackson and Graham Priest. Oxford University Press 2004.
McDaniel, K. (2009a). Structure-making. Australasian Journal of Philosophy, 87(2), 251–274.
McDaniel, K. (2009b). Ways of being. In D. Chalmers, D. Manley, & R. Wasserman (Eds.), Metaphysics. Oxford: Oxford University Press.
McDaniel, K. (2010). Return to the analogy of being. Philosophy and Phenomenological Research, 81(3), 688–717.
McDaniel, K. (2013). Degrees of being. Philosophers’ Imprint, 13(19), 1–18.
McDaniel, K. (2014). Compositional pluralism and composition as identity. In A. J. Cotnoir & D. L. M. Baxter (Eds.), Composition as identity. Oxford: Oxford University Press.
Mellor, D. H. (2006). Wholes and parts: The limits of composition. South African Journal of Philosophy, 25, 138–145.
Paul, L. A. (2002). Logical parts. Nous, 36(4), 578–596.
Sharvy, R. (1980). A more general theory of definite descriptions. The Philosophical Review, 89(4), 607–624.
Sider, T. (2001). Four-dimensionalism: An ontology of persistence and time. Oxford: Oxford University Press.
Simons, P. (1987). Parts: A study in ontology. Oxford: Clarendon Press.
Sweetser, E. E. (1990). From etymology to pragmatics: Metaphorical and cultural aspects of semantic structure., Cambridge studies in linguistics 54 Cambridge: Cambridge University Press.
Thomson, J. J. (1983). Parthood and identity across time. The Journal of Philosophy, 80(4), 201–220.
Van Inwagen, P. (1981). The doctrine of arbitrary undetached parts, Pacific Philosophical Quarterly, 62, 123–137. Reprinted in Material Constitution: A Reader (ed.) Rea, Michael C. (1997) Rowman and Littlefield Publishers, INC.
Van Inwagen, P. (1987). When are objects parts? Philosophical Perspectives, 1: 21–47. Reprinted in Kim et al. 2011.
Varzi, A. (2016) Mereology. The Stanford Encyclopedia of Philosophy (Winter 2016 Edition), Edward N. Zalta (ed.), https://plato.stanford.edu/archives/win2016/entries/mereology/.
Vienbahn, E., & Vetter, B. (2016). How many meanings for ‘may’? The case for modal polysemy. Philosophers’ Imprint, 16(10), 1–26.
Wallace, M. (2014). Composition as identity, modal parts, and mereological essentialism. In A. J. Cotnoir & D. L. M. Baxter (Eds.), Composition as identity. Oxford: Oxford University Press.
Wallace, M. (forthcoming). The lump sum: A theory of modal parts. Philosophical Papers.
Author information
Authors and Affiliations
Corresponding author
Additional information
Publisher's Note
Springer Nature remains neutral with regard to jurisdictional claims in published maps and institutional affiliations.
Rights and permissions
About this article
Cite this article
Wallace, M. The polysemy of ‘part’. Synthese 198 (Suppl 18), 4331–4354 (2021). https://doi.org/10.1007/s11229-019-02088-x
Received:
Accepted:
Published:
Issue Date:
DOI: https://doi.org/10.1007/s11229-019-02088-x