Counting on Strong Composition as Identity to Settle the Special Composition Question

Abstract

Strong Composition as Identity (SCAI) is the thesis that necessarily, for any xs and any y, those xs compose y iff those xs are non-distributively identical to y. Some have argued against this view as follows: if some many things are non-distributively identical to one thing, then what's true of the many must be true of the one. But since the many are many in number whereas the one is not, the many cannot be identical to the one. Hence (SCAI) is mistaken. Although I am sympathetic to this objection, in this paper, I present two responses on behalf of the (SCAI) theorist. I also show that once the defender of (SCAI) accepts one of these two responses, that defender will be able to answer The Special Composition Question.

Counting Composites

“…25 6.2. Spencer Spencer [2017] blocks the Counting Argument by providing an alternative analysis of number ascriptions (he doesn't distinguish cardinality and ipseity ascriptions). All number ascriptions are analysed by using predicates at the level of logical form that correspond directly to ordinary-language numerical predicates: 'aa are one thing' is analysed as 'One(aa)'; 'aa are two things' is analysed as 'Two(aa)'; etc.…”

Mereology and Identity

“…Thus, the Benelux, which is composed by Belgium, the Netherlands and Luxembourg, would be identical to them; both the Benelux on the one hand and Belgium, the Netherlands and Luxembourg on the other would be one relative to the concept of a multi-national entity and would be three relative to the concept of a country. These relativisation strategies are usually preferred to a primitivist strategy, according to which the compatibility of different cardinality ascriptions is a primitive, unexplained fact (see Spencer 2017).…”

“…• 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).…”

On relativist approaches to many-one identity

“…Wallace 2011). Another proposal is that we relativize cardinalities to so-called counts (Baxter 1988(Baxter , 2014Spencer 2017). It turns out that, when we think through these accounts of the parameters, no real explanatory progress is made beyond the primitivist view.…”