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▼a My dissertation combines work in the history of analytic philosophy with contributions to contemporary metaphysics and philosophy of language. I argue for a new view about the function of philosophical disagreements concerning existence questions, called "ontological expressivism". The view distinguishes between ordinary and ontological existence claims, and says that ontological existence claims do not serve to describe the world, but express mental states that are in important respects like desires. This view is inspired by Rudolf Carnap's views about ontology, which have been enormously influential, but-I think-have so far not been very well understood. In Chapters 1 and 2, I develop a new interpretation of Carnap. In Chapter 3, I present ontological expressivism. In chapter 4, I relate my view on the meaning of existence claims to current debates concerning generality relativism (i.e., the view that every domain of quantification can always be expanded).Carnap is known as a great anti-metaphysician, since he argues that metaphysicians debate misguided questions (Carnap, 1950). He thinks that ontological questions, such as the question of whether numbers exist, can be understood in two ways. First, this question can be understood as internal to the framework of mathematics. Understood in this way, its answer is "yes". This answer can, moreover, be trivially read off the "rules of the framework" and is therefore analytic (p. 209). Ontologists presumably do not mean to debate this trivial question. Alternatively, ontologists could be asking whether numbers exist in an external sense of this question, where what is at stake is the existence of numbers in a framework independent sense (p. 209). But, Carnap argues, this external question would be "non-cognitive" (p. 210). Either way, there is no philosophically interesting question with regard to the existence of numbers. However, even though something about what Carnap says seems to be deeply and importantly correct, "it all seems to vanish when one tries to get clear just what it is" (Field, 1984, p. 662).In Chapter 1 (on "Carnap's Noncognitivism about Ontology"), I provide a new interpretation of Carnap's views on ontology. I draw attention to Carnap's distinction between purely external statements, which are independent from all frameworks, and pragmatic external statements, which concern which framework one should adopt, and argue that the latter express noncognitive mental states. Specifically, I propose that Carnapian "frameworks" are systems of rules for the assessment of "statements", which are utterances of ordinary language sentences. Pragmatic external statements express noncognitive dispositions to follow only certain such rules of assessment. For instance, "numbers exist" understood as a pragmatic external statement expresses a disposition to assess statements using only rules according to which this statement is to be assessed as correct. This disposition is "noncognitive" since it does not describe the world as being one way rather than another and therefore has no truth-value.I motivate this interpretation from two different angles. First, my noncognitivist interpretation contrasts with popular "language-pluralist" accounts, as endorsed by Yablo (1998), Price (2009), Hirsch (2011), Thomasson (2015), Eklund (2016), and others, according to which frameworks simply are interpreted languages. In Chapter 1, I argue that language-pluralist interpretations cannot explain why Carnap thought that he was able to reconcile empiricism with the acceptance of abstract entities, which was one of his most fundamental ambitions. This gives my interpretation a certain comparative advantage. Second, in Chapter 2 (on "Carnap's Defense of Impredicative Definitions"), I discuss the role of Carnap's distinction between internal and external statements for his early views on the foundations of mathematics. Impredicative definitions-definitions that refer in the defining clause to what they define-play a central role in logic and mathematics. Carnap's contemporaries commonly thought that a theory of the real numbers needs to make essential use of impredicative definitions. But the use of impredicative definitions also raises thorny metaphysical questions. Due to influential arguments by Ramsey (1926) and Godel (1944), it is often thought that an impredicative definition does not have its intended meaning unless the property it defines already exists. Carnap opposes this dominant view. He maintains in The Logical Syntax of Language (1934) that accepting impredicative definitions amounts to choosing a "form of language". This view is an early precursor of his later, more general claim that referring to abstract entities amounts to accepting a linguistic framework. In Chapter 2, I explain Carnap's defense of impredicative definitions in its historical context. Explaining this hitherto neglected part of history allows me to pin down otherwise elusive aspects of his thought. (Abstract shortened by ProQuest). |