In Writing the Book of the World, Ted Sider argues that David Lewis’s distinction between those predicates which are ‘perfectly natural’ and those which are not can be extended so that it applies to words of all semantic types. Just as there are perfectly natural predicates, there may be perfectly natural connectives, operators, singular terms and so on. According to Sider, one of our goals as metaphysicians should be to identify the perfectly natural words. Sider claims that there is a (...) perfectly natural first-order quantifier. I argue that this claim is not justified. Quine has shown that we can dispense with first-order quantifiers, by using a family of ‘predicate functors’ instead. I argue that we have no reason to think that it is the first-order quantifiers, rather than Quine’s predicate functors, which are perfectly natural. The discussion of quantification is used to provide some motivation for a general scepticism about Sider’s project. Shamik Dasgupta’s ‘generalism’ and Jason Turner’s critique of ‘ontological nihilism’ are also discussed. (shrink)

This paper is an introduction: in particular, to algebras of relations of various ranks, and in general, to the part of algebraic logic algebraizing quantifier logics. The paper has a survey character, too. The most frequently used algebras like cylindric-, relation-, polyadic-, and quasi-polyadic algebras are carefully introduced and intuitively explained for the nonspecialist. Their variants, connections with logic, abstract model theory, and further algebraic logics are also reviewed. Efforts were made to make the review part relatively comprehensive. In some (...) directions we tried to give an overview of the most recent results and research trends, too. (shrink)

According to ontological nihilism there are, fundamentally, no individuals. Both natural languages and standard predicate logic, however, appear to be committed to a picture of the world as containing individual objects. This leads to what I call the \emph{expressibility challenge} for ontological nihilism: what language can the ontological nihilist use to express her account of how matters fundamentally stand? One promising suggestion is for the nihilist to use a form of \emph{predicate functorese}, a language developed by Quine. This proposal faces (...) a difficult objection, according to which any theory in predicate functorese will be a notational variant of the corresponding theory stated in standard predicate logic. Jason Turner (2011) has provided the most detailed and convincing version of this objection. In the present paper, I argue that Turner's case for the notational variance thesis relies on a faulty metasemantic principle and, consequently, that an objection long thought devastating is in fact misguided. (shrink)

The structuralist conception of metaphysics holds that it aims to uncover the ultimate structure of reality and explain how the world's richness and variety are accounted for by that ultimate structure. On this conception, metaphysicians produce fundamental theories, the primitive, undefined expressions of which are supposed to 'carve reality at its joints', as it were. On this conception, ontological questions are understood as questions about what there is, where the existential quantifier 'there is' has a fundamental, joint-carving interpretation. Structuralist orthodoxy (...) holds that there is exactly one fundamental, joint-carving interpretation that an existential quantifier could have. This orthodox assumption could go wrong--either by there being too few fundamental-quantifier interpretations, or by there being too many. In this dissertation I examine the implications of these non-orthodox options. Someone who thinks there are too many fundamental-quantifier interpretations might think this means standard ontological debates are in some sense defective of 'merely verbal', or she might think instead that the different quantifiers show that there are different 'ways' or 'modes' of being. I argue that the first option runs into problems with a certain sort of realism about logic, but that there is no general problem with the second option, despite its longstanding bad philosophical reputation. I also argue that realism about logic gives us reason to think the dispute between someone who thinks there are many 'modes of being' in this sense and someone who thinks there is just one is not itself verbal. Finally, I turn to the case in which there are no fundamental quantifiers, arguing that it brings with it a host of theoretical problems we could avoid with quantifiers. (shrink)