Composition and Relative Counting

Abstract

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.

On relativist approaches to many-one identity

“…In this case, any remaining appeal to relativization and the postulation of the parameters needs to be motivated on different grounds. For example, one might hope that the relativization can do some theoretical work in providing an alternative analysis of cardinality ascriptions and hence improve on the primitivist approach to them (for a critical discussion of such accounts however, see Carrara and Lando 2017). Without any independent motivation, the relativizations are theoretical danglers.…”

“…This is a key challenge to any composition as identity view. The challenge is underwritten by what Carrara and Lando (2017) call the numerical discernibility argument (where uu is a constant picking out a plurality) 1 :…”

Mereology and Identity

“…• it is far from clear which concepts are suitable for the role of property relativisers (see Koslicki (1997) about this problem); • the relativization of cardinality ascriptions to concepts makes it difficult (or outright impossible) to paraphrase them in logical terms (Spencer 2017;Carrara and Lando 2017); • some of the most promising strategies to extend the Indiscernibility of Identicals to composition risk relying on questionable presuppositions, such as atomism (Cotnoir 2013, fn. 13).…”

“…This proposal, which Azzano rejects, has been defended inHawley (2010).4 SeeCarrara and Lando (2017) for a general analysis of the relativisation strategies.…”

Baxter and Cotnoir on Composition as Identity

“…One problem with moderate relativism is that it requires major changes in plural logic (see Sider 2007, 68-9, andCarrara andLando 2017). Numerical predicates of the form 'to be n (in number)' can be defined in terms of the plural predicate 'is one of' (see Yi 2006, 246, and2014, 175).…”