Nikolaj Jang Lee Linding Pedersen

The neo-Fregean account of arithmetical knowledge is centered around the abstraction principle known as Hume’s Principle: for any concepts X and Y , the number of X ’s is the same as the number of Y ’s just in case there is a 1–1 correspondence between X and Y . The Caesar Problem, originally raised by Frege in §56 of Die Grundlagen der Arithmetik , emerges in the context of the neo-Fregean programme, because, though Hume’s Principle provides a criterion of identity for objects falling under the concept of Number–namely, 1–1 correspondence—the principle fails to deliver a criterion of application. That is, it fails to deliver a criterion that will tell us which objects fall under the concept Number, and so, leaves unanswered the question whether Caesar could be a number. Hale and Wright have recently offered a neo-Fregean solution to this problem. The solution appeals to the notion of a categorical sortal. This paper offers a reconstruction of their solution, which has the advantage over Hale and Wright’s original proposal of making clear what the structure of the background ontology is. In addition, it is shown that the Caesar Problem can be solved in a framework more minimal than that of Hale and Wright, viz . one that dispenses with categorical sortals. The paper ends by discussing an objection to the proposed neo-Fregean solutions, based on the idea that Leibniz’s Law gives a universal criterion of identity. This is an idea that Hale and Wright reject. However, it is shown that a solution very much in keeping with their own proposal is available, even if it is granted that Leibniz’s Law provides a universal criterion of identity.

Traditional theories of truth – such as the correspondence theory – are monist in character. All propositions, regardless of subject-matter, are true in the same way (if true). Recently, this view has been called into question by alethic pluralists (most notably Crispin Wright and Michael Lynch). According to the pluralist, the nature of truth varies across domains. Pluralists try to motivate their position by appealing to the following principle: for any domains D1 and D2, if the metaphysical constitutions of respectively D1 and D2 differ, then D1-propositions and D2-propositions are true in different ways (if true). The aim of the paper isto present a monist challenge to this principle. The gist of the challenge is this: even if metaphysical pluralism (i.e. the antecedent) is granted, truth can be given a uniform account within a correspondence framework. The basic argument is this: every domain that the alethic pluralist is interested in is truth-apt. But any domain that deals in truth-apt propositions likewise deals in facts – after all, it seems a mere platitude that facts are what makes propositions true (if true). Once facts are admitted, the monist can argue as follows: a proposition is true if, and only if, it corresponds to reality. Now, a proposition corresponds to reality if, and only if, it represents reality correctly – and a proposition represents reality correctly if, and only if, what is says is a fact, or is the case. However, since the notion of fact is available for any truth-apt domain, a proposition – whatever its (truth-apt) domain – can be taken to be true if, and only if, it corresponds to reality. Thus, metaphysical pluralism does not imply alethic pluralism.