Why it isn't syntax that unifies the proposition

Abstract

King develops a syntax-based account of propositions based on the idea that propositional unity is grounded in the syntactic structure of the sentence. This account faces two objections: a Benacerraf objection and a grain-size objection. I argue that the syntax-based account survives both objections, as they have been put forward in the existing literature. I go on to show, however, that King equivocates between two distinct notions of ‘propositional structure’ when explaining his account. Once the confusion is resolved, it is clear that the syntax-based account suffers from both Benacerraf and grain-size problems after all. I conclude by showing that King's account can be revised to avoid these problems, but only if it abandons its motivating idea that it is syntax that unifies the proposition.

Keywords::

• metaphysics of propositions
• semantics
• structured propositions
• syntax
• unity of the proposition

Notes

^1. ‘A proposition, in fact, is essentially a unity, and when analysis has destroyed the unity, no enumeration of constituents will restore the proposition. The verb, when used as a verb, embodies the unity of the proposition, and is thus distinguishable from the verb considered as a term, though I do not know how to give a clear account of the precise nature of the distinction’ (Russell [1903] 2009, 51).

^2. This initial statement of the account will be subject to several refinements as we proceed, along the lines of King's own exposition.

^3. King indicates that MIRROR is subject to a slight qualification, resulting from a later refinement to his account: the additional provision, included within the propositional relation, that R ‘encodes the instantiation function’. Under this refinement, MIRROR is ‘not quite true’ since ‘propositions have an extra bit of structure not had by the sentences expressing them’ (King 2007, 30).

^4. Facts are taken to be individuated independently of their descriptions; for example, ‘o instantiating P’, ‘P being instantiated by o’, ‘o standing in the instantiation relation to P’ are descriptions of the same fact (King 2007, 63–64, note 69).

^5. King refers here to acquaintance with the proposition ‘qua proposition’ (2007, 52). My terminology of ‘acquaintance with the proposition qua content’ is intended to preserve the primacy that King's terminology imputes to this mode of acquaintance.

^6. King's explanation of how PR-2 comes to inherit its significance from R is briefly discussed in the next section.

^7. They call these, respectively, the ‘plain propositional fact’ and the ‘augmented propositional fact’; SWIMS-1 is the ‘diminished propositional fact’.

^8. I put the term ‘propositional relation’ in scare-quotes here because the propositional relation is by definition that which binds the constituents together into the proposition. If on the correct account, SWIMS-2 were identified as the proposition, then PR-2 would indeed be the propositional relation. But here the proposal under consideration is that SWIMS-2 is merely the proto-proposition; the genuine propositional relation on this story would be PR-3 (the propositional relation of the SWIMS-3 account), which itself includes as a component that PR-2 encodes instantiation. Similar comments apply to the discussion of PR-1 below.

^9. I ignore here the possibility that considerations of simplicity might break the tie in favor of SWIMS-2.5.

^10. See, e.g., Collins (2007), Hanks (2009), and Speaks (2011).

^11. This is in a personal communication cited by King (2013a, 769).

^12. King's response to Burgess' objection is more nuanced than this remark suggests; see King (2013a, 769–773).

^13. I omit discussion of another version of the grain-size objection, which is based on the observation that it seems possible to substitute syntactic variants of embedded that-clauses without changing the truth conditions of the overall expression. See King (2007, 95–98; 2013a, 768–769).

^14. Note that SSSS only requires that syntactically identical sentences express structurally identical propositions. It does not itself require MIRROR, the claim that propositional structure is identical to syntactic structure. See King (2013a, 775).

^15. King develops the argument in a different way from the presentation provided here, but the underlying idea is the same. See King (2013a, 774–777).

^16. While to my knowledge, this challenge to King's account has not appeared anywhere in print, a very similar challenge is put forward in an unpublished paper by Speaks (2011, 8–9). In Speaks' example, the English sentence ‘John loves Jane’ is contrasted with the Reverse-English sentence ‘Jane loves John’, which has identical truth conditions.

^17. This follows the diagram from King (2007, 54).

^18. There is a subtlety here, because on King's account, the instruction provided by the syntactic relation will refer to the basic propositional constituents obliquely, that is, via the syntactic positions of the lexical items that designate them, and the instructions' reference to complex properties will therefore be oblique in a corresponding way. I ignore this complication here for ease of exposition.

^19. At least this is true on the SWIMS-1 model. Since the account of SWIMS-2 introduces the additional component that R encodes instantiation, that fact will have some additional structure, which as King admits, makes MIRROR-F subject to a ‘slight qualification’ (King 2007, 54, note 59). Since as we've seen, for R to ‘encode instantiation’ is actually for R to bear some complicated relation to the conceptual-intentional systems that receive it, one might wonder whether the additional component actually introduces a lot of hidden complexity into the fact SWIMS-2, making the qualification to MIRROR-F not so slight after all. See note 3.

^20. Note, however, that this is not because the syntactic structure of the sentence is more fine-grained than the content-structure of the proposition. In the case under consideration, the shared content-structure is precisely as fine-grained as the two syntactic structures.

^21. While the proposal that King's account be amended so as to existentially generalize over particular syntactic relations has not to my knowledge appeared anywhere in print, it has been suggested in an unpublished paper by Speaks (2011, 9).

^22. I would like to thank David Hunter and Gurpreet Rattan for very helpful comments on an earlier version of this paper.

Additional information

Notes on contributors

Logan Fletcher

Logan Fletcher is a doctoral candidate in philosophy at the University of Maryland, College Park. His primary research interests are in philosophy of mind, philosophy of cognitive science, and aesthetics. His current research focuses on the epistemology of visual proofs in mathematics.