| Gaia: | <p>This work is closely tied to the metaphysical and formal work of David Lewis on modality. First, to Lewis’ reduction of modality in terms of his modal realism and mature counterpart machinery. Second, to Lewis’ 1968 formal account (and its subsequent developments) employing a notion of counterparthood, an account that is detachable from Lewis’ full-blooded metaphysics. This work is primarily an examination of both of these accounts, as well as five other formal accounts that, inspired by Lewis’ work, employ a notion of counterparthood.</p>
<p>The thesis divides into four chapters. The first chapter presents Lewis' reduction of modality in terms of his modal realism and mature counterpart machinery. It includes a presentation of an account that I take to be a straightforward regimentation of Lewis' sketch of joint possibilities in 1986.</p>
<p>The second chapter considers certain issues for this account. These concern existence, the combination of existence and iterated modality, and ``contingent identity". The chapter ends with a discussion of alternatives to the machinery employed by the account.</p>
<p>The third chapter begins with a presentation and discussion of Lewis' 1968 formal account. That account employs formal machinery to deliver counterpart characterisations of natural language modal claims. First, Lewis presents a formal first-order theory, counterpart theory. Second, Lewis provides a method for translating natural language modal claims into sentences of the language of counterpart theory. This process has two steps. First, Lewis assumes a regimentation of natural language modal claims into sentences of ``the language of quantified modal logic". Second, Lewis provides a translation scheme that maps sentences of this language of quantified modal logic to sentences of the language of counterpart theory.</p>
<p>This combination of (i) a theory and (ii) a translation scheme (that maps sentences of the language of quantified modal logic to sentences of the language of counterpart theory) generates a semantics for the language of quantified modal logic. Given this, I turn to a more foundational matter in the final part of the third chapter: comparing the usual direct model-theoretic approach and this indirect approach (presenting a theory and translation scheme) to presenting a semantics for a formal language.</p>
<p>The fourth chapter raises issues for five formal accounts in the literature that in some way appeal to a notion of counterparthood: Hazen's 1977 stipulational semantics; Russell's 2013 counterpart semantics; Bacon's 2014 counterpart semantics; Graff Fara's 2008 relative-sameness semantics; and Meyer's 2013 counterpart account.</p>
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