An argument against nominalism

Abstract

Nominalism in formal ontology is still the thesis that the only acceptable domain of quantification is the first-order domain of particulars. Nominalists may assert that second-order well-formed formulas can be fully and completely interpreted within the first-order domain, thereby avoiding any ontological commitment to second-order entities, by means of an appropriate semantics called "substitutional". In this paper I argue that the success of this strategy depends on the ability of Nominalists to maintain that identity, and equivalence relations more in general, is first-order and invariant. Firstly, I explain why Nominalists are formally bound to this first-order concept of identity. Secondly, I show that the resources needed to justify identity, a certain conception of identity invariance, are out of the nominalist's reach.

Substance metaphysics is incompatible with the causal closure of the metaphysical realm

“…Accordingly, "particulars", "tropes", "facts", "events", "well-defined (abstract or concrete) objects" are From the formal standpoint, substances are first order and invariant entities, namely they are self-identical and context-independent in the precise sense offered by primitive equivalence relations (reflexive, symmetrical, and transitive relations). Metaphysics and ontologies that assume the validity of the Classical Theory of Identity (CTI) (Arenhart et al 2019;Catren 2022, Ferrari 2022a, 2022b, French and Krause 2006) are example of this trend. 3 Despite being relational, even first order structures can be considered as (abstract) substances 4 because, as Rodin (2007Rodin ( , 2011Rodin ( , 2017 tells us, in defining structures, primitive first order isomorphisms play an analogous role of primitive equivalences, in that they preserve the structural organization.…”

“…Particulars, as cases of substances, are invariant entities and, as such, they are defined by equivalence relations like the relation of identity -as well as a resemblance relations or even other sorts of relations like isomorphic functions. Within allegedly monistic frameworks, particulars like particles are characterized by something of the sort of the CTI, a first order theory according to which entities are self-identical (∀x = x) and context- Yet, according to my previous works (Ferrari 2022a(Ferrari , 2022b in formal ontology, it is arguably impossible to obtain a consistent monistic (non-dualistic) ontology from the assumptions of CTI or something analogous and, equivalently, of only one domain of primitive first order invariant entities, like (abstract or concrete) objects and particulars, and even when conceived as bundles of tropes (cf. Campbell 1990).…”

“…The present paper develops a rather complex but specific argument in three steps. First, from a result due to Ferrari (2022aFerrari ( , 2022b it is argued that monistic substance metaphysics cannot preserve the ontological closure of the intended first order ontology. In other words, it is argued that monistic substance metaphysics cannot fix once and for all their own domain of existence or, equivalently, that they cannot restrict the meaning of what exists to what belongs to the intended or standard domain.…”

“…Número XXVI -Volume I -julho de 2023 https://periodicos.ufjf.br/index.php/eticaefilosofia ISSN: 1414-3917 e-ISSN: 2448-2137 Rodin (2007Rodin ( , 2011Rodin ( , 2017 and Heller (2016) (cf. also Ferrari, 2022aFerrari, , 2022b) may help to understand that (any) Kim's argument (against emergence or against the introduction of new information in a system) should have been assessed in these models rather than in the extensional ones.…”