Modalising Plurals

When the Necessity of Identity (NI) is combined with Composition as Identity (CAI), the contingency of composition (CC) is at risk. In the extant literature, either NI is seen as the basis for a refutation of CAI or CAI is associated with a theory of modality, such that: either NI is renounced (if counterpart theory is adopted); or CC is renounced (if the theory of modal parts is adopted). In this paper, we investigate the prospects of a new variety of CAI, which aims to preserve both NI and CC. This new variety of CAI (CCAI, Contingent Composition as identity) is the quite natural product of the attempt to make sense of CAI on the background of a broadly Kripkean view of modality, such that one and the same entity is allowed to exist at more than one possible world. CCAI introduces a worldrelative kind of identity, which is different from standard identity, and claims that composition is this kind of world-relative identity. CCAI manages to preserve NI and CC. We compare CCAI with Gibbard's and Gallois' doctrines of contingent identity and we show that CCAI can be sensibly interpreted as a form of Weak CAI, that is of the thesis that composition is not standard identity, yet is significantly similar to it.

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“…See (Uzquiano 2011) for some objections. (Hewitt 2012) has explicitly defended the minority thesis that ≺ is contingent.…”

Section: From World-relative Fusion To World-relative Identitymentioning

confidence: 99%

Contingent composition as identity

Carrara

Lando

2018

Synthese

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“…79 Hewitt (2012) argues that PL1 is false. As he points out, however, PL1 does hold for "rigid" pluralities.…”

Section: An Axiomatisation Of Msstmentioning

confidence: 99%

Modal Structuralism and Reflection

Roberts

2018

The Review of Symbolic Logic

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Modal structuralism promises an interpretation of set theory that avoids commitment to abstracta. This article investigates its underlying assumptions. In the first part, I start by highlighting some shortcomings of the standard axiomatisation of modal structuralism, and propose a new axiomatisation I call MSST (for Modal Structural Set Theory). The main theorem is that MSST interprets exactly Zermelo set theory plus the claim that every set is in some inaccessible rank of the cumulative hierarchy. In the second part of the article, I look at the prospects for supplementing MSST with a modal structural reflection principle, as suggested in Hellman (2015). I show that Hellman’s principle is inconsistent (Theorem 5.32), and argue that modal structural reflection principles in general are either incompatible with modal structuralism or extremely weak.

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“…Likewise, if Vladimir were one of some people, these people would not be Barack and Michelle but some other people. Modal rigidity has, admittedly, been challenged as an interpretation of the ordinary, English plural idiom in full generality (see Hewitt ). But for present purposes, we would, if necessary, be content simply to stipulate the rigidity.…”

Section: The Higher‐order Logic Of Potential Infinitymentioning

confidence: 99%