Dorr et al.

No abstract

The identity predicate can be defined using second-order quantification: a ¼ b ¼ df 8FðFa $ FbÞ. Less familiarly, a dyadic sentential operator analogous to the identity predicate can be defined using third-order quantification: ' ¼ df 8XðX' $ X Þ, where X is a variable of the same syntactic type as a monadic sentential operator. With this notion in view, it is natural to ask after general principles governing its application. More grandiosely, how fine-grained is reality? I will argue that reality is not structured in anything like the way that the sentences we use to talk about it are structured. I do so by formulating a higher-order analogue of Russell's paradox of structured propositions. I then relate this argument to the Frege-Russell correspondence. When confronted with the alleged paradox, Frege agreed that reality was not structured, but maintained that propositions (i.e. thoughts) were structured all the same. Russell replied that his paradox showed Frege's theory of structured thoughts to be inconsistent, to which Frege replied that Russell's argument failed to heed the distinction between sense and reference. Most recent commentators have sided with Russell. In defense of Frege, I establish the consistency of one version of his rejoinder. I then consider and reject some ways of resisting the argument against a structured conception of reality. I conclude that, if propositions are structured, this is because they correspond not to distinctions in reality, but rather to ways in which those distinctions can be represented. 1. Against structure I will work in a higher-order language with variables p, q,. .. of the same syntactic type as sentences and X, Y,. .. of the same syntactic type as monadic sentential operators. I will assume the following two standard principles of higher-order logic 1 :-CONV Ƚ'=p $ ðpÈÞ', where ' is free for p in È 9-INTRO Ƚt=v ! 9vÈ, where t is free for v in È and has same syntactic type as v

This paper is a study of higher-order contingentism -the view, roughly, that it is contingent what properties and propositions there are. We explore the motivations for this view and various ways in which it might be developed, synthesizing and expanding on work by Kit Fine, Robert Stalnaker, and Timothy Williamson. Special attention is paid to the question of whether the view makes sense by its own lights, or whether articulating the view requires drawing distinctions among possibilities that, according to the view itself, do not exist to be drawn. The paper begins with a nontechnical exposition of the main ideas and technical results, which can be read on its own. This exposition is followed by a formal investigation of higher-order contingentism, in which the tools of variable-domain intensional model theory are used to articulate various versions of the view, understood as theories formulated in a higher-order modal language. Our overall assessment is mixed: higher-order contingentism can be fleshed out into an elegant systematic theory, but perhaps only at the cost of abandoning some of its original motivations.