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...

According to the so-called strong variant of Composition as Identity (CAI), the Principle of Indiscernibility of Identicals can be extended to composition, by resorting to broadly Fregean relativizations of cardinality ascriptions. In this paper we analyze various ways in which this relativization could be achieved. According to one broad variety of relativization, cardinality ascriptions are about objects, while concepts occupy an additional argument place. It should be possible to paraphrase the cardinality ascriptions in plural logic and, as a consequence, relative counting requires the relativization either of quantifiers, or of identity, or of the is one of relation. However, some of these relativizations do not deliver the expected results, and others rely on problematic assumptions. In another broad variety of relativization, cardinality ascriptions are about concepts or sets. The most promising development of this approach is prima facie connected with a violation of the so-called Coreferentiality Constraint, according to which an identity statement is true only if its terms have the same referent. Moreovereven provided that the problem with coreferentiality can be fixedthe resulting analysis of cardinality ascriptions meets several difficulties.

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The paper pinpoints certain unrecognized difficulties that surface for recombination and duplication in modal realism when we ask whether the following inter-world fixity claims hold true: 1) A property is perfectly natural in a world iff it is perfectly natural in every world where it is instantiated; 2) Something is mereologically atomic in a world iff all of its duplicates in every world are atomic. In connection to 1), the hypothesis of idlers prompts four variants of Lewis’s doctrine of perfectly natural properties, all deemed unsatisfactory for the purposes of duplication and recombination. By means of 2), instead, we show that the principle of recombination does not countenance the atomicity or non-atomicity of duplicates; but it should, because it is genuinely possible that: a) something, which is atomic, is non-atomic; and b) something, which is non-atomic, is atomic. In discussing 1) and 2), the paper substantiates a tension in Lewis’s metaphysics between modal intuitions and the reliance on the natural sciences.