Composition, Indiscernibility, Coreferentiality

Abstract

According to strong composition as identity (CAI), the logical principles of oneone and plural identity can and should be extended to the relation between a whole and its parts. Otherwise, composition would not be legitimately regarded as an identity relation. In particular, several defenders of strong CAI have attempted to extend Leibniz's Law to composition. However, much less attention has been paid to another, not less important feature of standard identity: a standard identity statement is true iff its terms are coreferential. We contend that, if coreferentiality is dropped, indiscernibility is no help in making composition a genuine identity relation.To this aim, we analyse as a case study Cotnoir's theory of general identity (Cotnoir, 2013), in which indiscernibility is obtained thanks to a revisionary semantics and true identity statements are allowed to connect non-coreferential terms. We extend Cotnoir's strategy for indiscernibility to the relation of comaternity, and we show that, neither in the case of composition nor in that of comaternity, indiscernibility contibutes to show that they are genuine identity relations. Finally, we compare Cotnoir's approach with other versions of strong CAI endorsed by Wallace, Bøhn, and Hovda, and canvass the extent to which they violate coreferentiality. The comparative analysis shows that, in order to preserve coreferentiality, strong CAI is forced to adopt a non-standard semantic treatment of the singular/plural distinction.approaches to strong CAI fail or manage to extend it to composition. We focus on those versions of strong CAI that are conservative with respect to the features of standard identityi and aim to show that these features can be extended to composition, making it a legitimate identity relation. Thus, we leave henceforth Baxter's revisionary rejection of Leibniz's Law aside. Our complaint against these approaches is that, while they devote so many efforts to extend Leibniz's Law to composition, they fail to pay due attention to coreferentiality: an identity statement is true iff its terms have the same referent.This feature of standard identity should be extended by the backers of strong CAI to composition. If a relational predicate is allowed to combine two terms standing for different things in a true statement, then it does not express a genuine identity relation. And if that relational predicate expresses composition, then composition cannot be legitimately regarded as an identity relation. Thus, coreferentialty should be seen as a constraint on the debate on strong CAI:Coreferentiality Constraint The terms of a true identity statement must be coreferential.The Coreferentiality Constraint is never explicitly discussed by the defenders of strong CAI, and some strategies to extend Leibniz's Law to composition risk leading to an open violation of the Coreferentiality Constraint. In order to make clear the import of this constraint and to see how it happens that strong CAI risks violating it, we consider Aaron Cotnoir's recent theory of general ide...

Composition and Relative Counting

“…In this set-theoretical framework, the two subject terms of "the Netherlands, Belgium, and Luxembourg are three" and "The molecules are three" (in spite of also being the terms of a true GI statement) are not coreferential. By contrast, in the hyperpluralist version of GI we sketched in Carrara and Lando (2016), the two terms are coreferential.…”

“…Does this mean that GI cannot be applied as such to any case of so-called gunk, that is to entities such that all their proper parts always have further proper parts? In Carrara and Lando (2016) we raised a different objection against GI. We argued that Cotnoir's set-theoretical approach violates the following semantic requirement on genuine identity statements:…”

“…In Carrara and Lando (2016) we spelt out many details of Cotnoir's violation of the Coreferentiality Constraint, and showed that GI could be amended, and thus made compliant with it, if the terms of GI statements were hyperplurals, instead of denoting sets. 32 The idea is that both "the Netherlands, Belgium, and Luxembourg" and "Benelux" would denote plurally the mereological atoms in Benelux, but at different levels of plurality; also "the molecules" would denote those same atoms at the same level of "the Netherlands, Belgium, and Luxembourg", but would group (in a non-very clear sense) them differently.…”

Contingent composition as identity

“…In § 5 we argue that the only way to make sense of CAI on the background of the broadly Kripkean view of modality we assume is to relativize also identity to possible worlds, and to formulate the resulting variety of CAI (CCAI) in terms of this relativized form of identity. In § 6 we discuss the resulting distinction between the world-relative identity which 1 (Carrara & Lando 2016, 2017, (Lando 2017, Appendix).. composition would be on the one hand, and standard identity on the other. In § 7 we present an important objection to CCAI, according to which CCAI would be ad hoc.…”

“…It does not matter from the viewpoint of which world we look at it. 7 (Carrara and Lando 2016) discusses the impact of the special semantic treatment of the identity predicate on CAI.…”