The metaphysics of propositional constituency

Abstract

In this paper, I criticize Structured Propositionalism, the most widely held theory of the nature of propositions according to which they are structured entities with constituents. I argue that the proponents of Structured Propositionalism have paid insufficient attention to the metaphysical presuppositions of the view – most egregiously, to the notion of propositional constituency. This is somewhat ironic, since the friends of structured propositions tend to argue as if the appeal to constituency gives their view a dialectical advantage. I criticize four different approaches to providing a metaphysics of propositional constituency: set-theoretic, mereological, hylomorphic, and structure-making. Finally, I consider the option of taking constituency in a deflationary, metaphysically ‘lightweight’ sense. I argue that, though invoking constituency in a lightweight sense may be useful for avoiding the ontological problems that plague the ‘heavyweight’ conception, it no longer proffers a dialectical advantage to Structured Propositionalism.

Keywords::

• propositions
• structure
• mereology
• Russell
• Frege

Notes

^1. Thanks to John Keller, Michael Rea, Jeff Speaks, Marian David, and the editors of this journal for helpful comments on earlier drafts of this paper.

^2. I've substituted ‘proposition’ for ‘Objective’, the typical translation of Meinong's ‘Objectiv’ – his favored term for states of affairs and propositions (the objects of thought). Cf. Alvin Plantinga: ‘What exactly, or even approximately, is this relationship being a constituent of? Do we know or even have reason to suspect that propositions have constituents’ (1983, 164)?

^3. Prominent structured propositionalists include Scott Soames, Nathan Salmon, Jeffrey King, Mark Richard, David Braun, Peter Hanks, Kent Bach, and Jason Stanley. Prominent historical structured propositionalists include Bernard Bolzano, Gottlob Frege, Bertrand Russell, and G. E. Moore.

^4. I'll drop the reference to context in what follows.

^5. Linguists sometimes use the term ‘semantic value’ to mean reference. However, it is often used in a more neutral way to pick out whatever the relevant type(s) of meaning is (are). Here I use it to pick out, at the sentential level, propositions, and at the sub-sentential level, whatever kind of meaning contributes to the propositions expressed.

^6. Single quotes function as both corner quotes and mention quotes throughout. Double quotes function as scare quotes.

^7. I'm using Frege's terminology here, where concepts are reference-level semantic values associated with predicate expressions. Concepts are not semantic-values at the level of sense and, thus, are not constituents of propositions.

^8. In Keller, 2012, I evaluate arguments for SP from semantic compositionality, logic, and direct reference theory.

^9. Jeff Speaks suggested the helpful labels ‘metaphysically heavyweight’ and ‘metaphysically lightweight’: see Speaks (with Jeff King and Scott Soames) (forthcoming).

^10. Many structured propositionalists consider the critique in Soames, 1987 to have dealt a deathblow to PW. I will not discuss the details of this well-known argument here, but the gist of it is that sets of worlds are not fine-grained enough to play one of the fundamental propositional roles: objects of belief. If, for example, a necessarily true proposition is the set of all possible worlds, then, given that belief is a dyadic relation between a believer and a proposition, anyone who believes one necessary truth thereby believes all necessary truths. Thus, a kindergartener, by virtue of believing that 2+2 = 4, also believes that arithmetic is incomplete. Proponents of PW, of course, have responded to this objection, and it is worth noting that many linguists still accept PW. However, some famous proponents of PW, e.g., Robert Stalnaker and David Chalmers, have made a significant concession to the SPist's criticism by countenancing structured intensions in their account of propositional attitudes. See Stalnaker, 2012 and Chalmers, 2006.

^11. Even on David Lewis' famous, but controversial, mereological account of sets, it is their subsets, rather than their members, that are parts of a set. See Lewis, 1991. But see Kit Fine, 2010 for defense of the less common view that takes a set's members to be its parts.

^12. Proponents of Primitivism include Bealer, 1998, Merricks, 2009, Plantinga, 1974 and van Inwagen, 2004. This view (or something similar) is also referred to as the “primitive-entity theory” (Jubien, 2001), “Magical Ersatzism” (Lewis, 1986), and “Unsound Abstractionism” (van Inwagen, 1986).

^13. Soames, 2010 and Jubien, 2001 make similar claims. And see Richard, 1990, 34 for a closely related criticism. Also, see David Lewis' criticism of Magical Ersatzism in Lewis, 1986, 174–191.

^14. See Benacerraf, 1965 for the original exposition of this problem as applied to a set-theoretic treatment of numbers, and see Jubien, 2001 and Soames, 2010 for an application of this problem to propositions.

^15. See, among many others, Bealer, 1998 and Jubien, 2001. David Lewis was famously unmoved by this objection to his set-theoretic construal of propositions. See Lewis, 1979.

^16. This problem is also discussed in Bealer, 1998 and, in somewhat different terms, in Soames, 2010.

^17. Cf. Soames, 2010, 91–92.

^18. See Braun, 2005 (especially fn. 6), King, 2007, Soames, 2010, and Hanks, 2011.

^19. Leonard and Goodman, 1940. Tillman and Fowler, 2012 argue for the claim that propositional constituents must be understood as propositional parts (see pp. 528–529), but they also reject CEM.

^20. Typically, a principle of strong or weak supplementation (and/or various fusion principles) is added to the three core axioms, though there is disagreement among theorists of CEM about which principle(s) to add. See Paul Hovda, 2009 for discussion. The arguments of this paper only rely on the three core axioms.

^21. See, e.g., Lewis, 1991 and Koslicki (Forthcoming).

^22. Braun, 1993 seems to think proposition's structure is itself a part. This view provides a way to distinguish the propositions Maggie loves John and John loves Maggie, but has other problems, which I briefly discuss in §2.4.

^23. Frege took note of this problem in an undated letter to Jourdain (see Gabriel et al., 1980: 79). See Gilmore (Forthcoming) for fuller discussion.

^24. If you do not like Carl, substitute another part of Socrates.

^25. Cf. Gilmore (forthcoming: 6), who calls this the ‘acquaintance argument’.

^26. Frege presents two brief versions of the compositionality argument, one in “Compound Thoughts” (1923/1984) and one in “Logic in Mathematics” (1914/1979). Russell presents a similar argument in The Philosophy of Logical Atomism (1918/1956), but for structured facts, not structured propositions. For detailed discussion of Frege's and Russell's compositionality arguments, see Keller, 2012 and Lorraine Juliano Keller and John A. Keller (Forthcoming).

^27. Couldn't the SPist avoid this problem simply by denying that propositions have any constituents other than the semantic values of the parts of the sentences that express them? That move would certainly solve the problem at hand, but at the cost of begging the question. If constituents are supposed to be parts in the mereological sense, then the presumption is that the notion of parthood being invoked obeys the axioms of CEM. By those axioms, the proper parts of a proposition include the proper parts of its proper parts, thus Carl is a (proper) part of Socrates is wise.

^28. It's in general very plausible that, if abstract objects have parts, they have them essentially. Given that propositions are abstracta, propositional part essentialism would follow from this more general principle. Gilmore also discusses this ‘essentialist’ principle in his forthcoming: 7.

^29. But see Gilmore (Forthcoming) for a sophisticated attempt to reconcile Russellianism with Transitivity. It would take me too far afield to discuss Gilmore's interesting solution in detail here, but let me just quickly note two potential problems with his approach. Gilmore's solution involves invoking a four-place parthood relation and positing slots at different ‘locations’ in propositions (see pp. 17–24). Here are a couple of prima facie objections. First, construing parthood as a four-place relation seems like cheating, and should only be done as a last resort (akin to positing relative identity to “solve” the puzzles about identity). And second, I find the notion of location applied to abstract objects obscure. If an object is not extended, in what sense can we speak of different locations in it? Invoking the notion of location seems (to me) not to illuminate the application of ‘part-whole’ terminology to propositions, but to obfuscate it further. I think this sort of “solution” just points to the depth of the difficulty of applying an idiom designed for material objects to abstracta.

^30. See Simons, 2003 and Varzi, 2006.

^31. Alvin Plantinga applies this worry specifically to singular Russellian propositions in Plantinga, 1983.

^32. It may be objected that because the proposition itself is abstract, it has no location. But this objection seems to beg the question. If, in general, objects that have material parts are located where there parts are, what makes propositions the exception?

^33. See also Künne, 2008.

^34. This is the line that Varzi favors.

^35. But see Kit Fine op cit. for a defense of the view that the members of a set are its parts. It should be noted that Fine's view is committed to the claim that there are different fundamental parthood relations and, thus, is a form of compositional pluralism.

^36. Cf. Künne, 2008, 226–230.

^37. One might object that hylomorphism is not a theory of parts and wholes, and hence, is not a rival to CEM. One reason for this would be that the notion of constituent that is employed in hylomorphism is different than the notion of part (not just as it is employed in CEM – of course this is a different notion, otherwise they would not be rival theories – but in its ordinary use). However, as Johnston, 2006 presents the view, hylomorphism is intended to be a rival to CEM (see, in particular, p. 688).

^38. For example, Kit Fine, 1999, 2010, Kathrin Koslicki, 2008, and Mark Johnston, 2006.

^39. Laws of nature are states-of-affairs with no particulars as constituents. See McDaniel, 2009, 259.

^40. To be precise, a proposition cannot have only a single part that is a property or relation, but they can be composed of only properties and/or relations (e.g. the proposition Blue is a color). Gappy propositions and propositional radicals are structured propositions with “missing” constituents. See Braun, 1993 and 2005 and Bach, 2006. On Braun's view, gappy propositions are expressed by sentences containing empty names (e.g., ‘Vulcan is a planet’ expresses a proposition with an empty place or “gap” where the semantic value of the name ‘Vulcan’ should be, as modeled by the ordered pair < {}, is a planet>).

^41. Cf. Soames, 2010. 28–32 for a closely related point.

^42. ‘Consider the structural property of being (just) two electrons, a property possessed by all two-member collections of electrons. We cannot say that this property involves the same universal, being an electron, taken twice over, because a universal is one, not many’ (Armstrong, 1978, 69–70).

^43. See McDaniel, 2009, 254–255 for fuller discussion of the claim that the structure-making account is a form of compositional pluralism.

^44. Note that some philosophers who enthusiastically endorse Millianism have expressed reservations about Direct Reference (DR) Theory (famously, Kripke 1979). Also, DR Theory is, confusingly, commonly presented in (at least) two different ways in the literature, one of which entails SP and the other of which is compatible with the non-existence of propositions. Explaining the different formulations would distract from the main thread of this paper, so I'd rather avoid it here – but see Keller, 2012 for an in-depth discussion.

^45. Some Millians are skeptical about propositions (e.g. Kripke 1979 and Wettstein, 2004). Also, some Millians are propositionalists but emphatically not Russellians (e.g. van Inwagen, 1986, 2004).

^46. One might think that the difference between a name and a co-referential rigid description can be explained by an appeal to de jure rigidity, where an expression is de jure rigid if its rigidity is due to the rules of the language (Kripke 1972, 21n). However, this will not work for rigid descriptions of the form ‘the actual F’, since the rigidity of this type of description is due to the rules of the language (viz. the semantics of ‘actual’); thus they are, like names, de jure rigid.

^47. Of course, an important semantic difference between (F) and (B), considered as sentence-types, is that (B) may express different propositions in different possible contexts, whereas (F) plausibly cannot. If one believes in sentential characters, one might put it this way: holding the characters of (F) and (B) fixed, (F) has a stable content across possible contexts, whereas the content of (B) may shift (e.g., consider an utterance of (B) in a world where some obscure German mathematician distinct from Frege writes the Begriffsschrift). I'm interested here in how one might account for the difference in the propositions expressed by actual world tokens of (F) and (B). Thanks to the editors of this journal for pointing out the need for more clarity about this issue.

^48. As I mentioned above, this is a view that Kripke and some other Millians reject, since they are skeptics about propositions. My remarks in this section are intended only for Millian propositionalists, not all of whom are friendly towards SP.

^49. Though ‘the even prime’, unlike ‘the actual author of the Begriffsschrift’, is only de facto (not de jure) rigid.

^50. Cf. Schiffer, 2011 and Hofweber, 2005.

^51. Cf. Almog, 1986.

^52. In this review of Michael Tye's Consciousness Revisited, Fodor criticizes Tye's appeal to an analogy with Russellian propositions as part of a defense of his thesis that experiences have parts.

^53. Some propositionalists reject SP largely because of their worries about the apparent threat that object-dependent propositions pose to serious actualism. Thus, the ability to accommodate object-dependence will not appeal to such propositionalists. For discussion of this problem, see Plantinga, 1983, 1985, Fine, 1985, David, 2009, and Speaks (Forthcoming).

Additional information

Notes on contributors

Lorraine Keller

Lorraine Juliano Keller is a recent PhD from the University of Notre Dame whose dissertation critically evaluates the theory of structured propositions. She currently teaches at Niagara University