Quasi-truth in quasi-set theory (Q1840965)

The first four sections of this paper present some of the work of da Costa and collaborators. First we are introduced to the notion of ``quasi-truth'', founded on the notion of ``partial structures'', and the intuition that a quasi-true sentence does not necessarily describe, in an appropriate way, the whole domain to which it refers but only an aspect of it; the one modelled by the relevant partial structure (p. 37). Next follows an analysis of ``quasi-set theory'', apparently developed to express ``Schrödinger logic'', a ``two-sorted type-theoretic logic in which the concept of identity is applicable to formulas of one sort''. Here the predicates \(m(x)\), `\(x\) is a micro-object', is to be distinguished from \(M(x)\), `\(x\) is a macro-object', and although ``\(m\)-atoms are not subject to the concept of identity'', a weaker notion of `indistinguishability' (an equivalence relation) is defined for them. In section 4 a notion of ``quasi-truth in quasi-set theory'' is sketched, apparently adapting a notion of Bueno and de Souza. The earlier analysis of partial structures is applied to derive notions of ``quasi-satisfaction'' in ``quasi-models'', essentially along Tarskian lines. Finally, in the last section of the paper the author discusses the application of the preceding analysis to van Fraassen's modal interpretation of quantum mechanics, claiming that it may lead to a ``modal and empiricist'' approach to quantum mechanics.