Inscrutability of Reference as a Result of Quine’s Structuralism

In his later writings Quine is increasingly explicit about the fact that his view of language is, in a certain sense, structuralistic. Structuralist interpretations of non-empirical, especially mathematical theories are now commonplace, but this chapter argues that Quine’s thought experiment with radical translation can be interpreted as showing that even empirical theories cannot be anchored in reality so firmly as to evade the same structuralist nature. Therefore, this peculiar form of structuralism extends to all our theories––the terms of all of them are best seen as meaning not definite substances, but nodes in certain structures. Moreover, radical translation shows––or purports to show––that the structure behind any natural language allows for some non-trivial ‘automorphisms’––that mapping the meaning of rabbit on that of undetached rabbit part, provided we make an appropriate remapping of many other meanings, does not change the language. Inscrutability of reference is then only a direct consequence.

Quine on Ontological Commitment in Light of Predicate-Functor Logic

Quine is renowned for offering a criterion of ontological commitment in terms of the values of bound variables. Simultaneously, however, Quine had a long-standing interest in formal systems that dispense with variables and quantifiers that permit variables to be explained away. The chapter seeks to resolve this often-neglected tension in a way that is sensitive to Quine’s allegiance to first-order logic, but is somewhat relaxed about the connection between semantics (/truth) and ontology.

A New Look at Quine on Set Theory

This chapter first argues that while there are solid objections to be raised to Quine’s view, certain widespread arguments against result from overly crude and uncharitable interpretations of Quine. It then turns to the question of what kind of evidence it would take for a Quinean naturalist to change their mind about certain theses, such as the size of the set theoretic universe. It argues that Quineans might be moved to embrace further set-theoretic ontology in the light of the mathematical utility of large cardinals, and potentially even the ‘multiverse’ position on set theory.

On What Exists

Quine’s criterion of theoretical ontological commitment is subject to a variety of interpretations, all of which save one yield incorrect verdicts. Moreover, the interpretation that yields correct verdicts is not what Quine meant. Instead the intended criterion unfairly imputes ontological commitments to theories that lack those commitments and fails to impute commitments to theories that have them. Insofar as Quine’s criterion is interpreted so that it yields only correct verdicts, it is trivial and of questionable utility. Moreover, the correct criterion invokes analyticity, a notion that Quine spent most of his life tirelessly combating. This yields a dilemma for Quinean philosophy: either his criterion of ontological commitment is incorrect, or else Quine is committed to a traditional philosophical notion that he emphatically rejected as disreputable.

Quine’s Structural Holism and the Constitutive A Priori

Recent work on the structure of scientific theories has assigned a significant role to a priori principles in the formulation of scientific theories. For example, Michael Friedman has argued that theories possess an asymmetrical structure, with mathematical and logical principles presupposed in the very formulation of empirical laws. He further argues that Quine’s depiction of human knowledge as a ‘web of belief’, cannot capture this structure nor the constitutive role played by a priori principles in enabling the formulation of empirical statements and laws. This chapter argues that properly understood Quine’s ‘structural holism’ can capture this asymmetrical structure of scientific theories, but fails to address Friedman’s concern with constitutive a priori principles as coordinating the abstract mathematical component of scientific theories with sensible experience. However, once this difference is located in their different perspectives on scientific theories, the chapter argues that their views be seen as complementary rather than opposed.

The Ontogeny of Quine’s Ontology

Quine’s philosophical views did not emerge fully formed in the 1930s; rather, they changed over the seven decades he was philosophically active. This chapter investigates two episodes in Quine’s ontological development: his engagement with Pythagoreanism (an Appendix with new primary sources is included), and his conversion from nominalism to Platonism about mathematics. These two topics might seem completely distinct. However, although they could conceivably be treated separately, this chapter treats them together by considering the role clarity plays in both these episodes. Quine’s changing views about the theoretical virtue of clarity, and which particular things are clear and which are not, help explain his ontological development. In particular, the chapter offers a new hypothesis about the causes of Quine’s conversion from nominalism to realism, in which his views about clarity play an essential role.

Quine’s Non-ontological Structuralism (and Mine)

In ‘Structure and Nature’ Quine advocates a ‘global ontological structuralism’, one that sees all objects, even nonmathematical ones, as positions or nodes in a structure. The term ‘ontological’ here is misleading and would be better deleted. For Quine is no ontological structuralist; in the same paper he makes it clear that he is not proposing a structuralist ontology or even an ontological doctrine in which structures are eliminated in favour of systems instantiating them. Resnick’s own mathematical structuralism evolved from a sui generis ontological form to a Quinean non-ontological form. In this chapter Resnick discusses the evolution of Quine’s structuralism and how it shaped his own.

Quine on Ontology

This chapter presents a section-by-section discussion of chapter 7 of W. V. Quine’s Word and Object, ‘Ontic Decision’. After outlining Quine’s earlier thinking about ontology, it considers his handling of the subject in the chapter––his most careful treatment of ontology in his ‘classical’ period––and comments on how he downplayed the importance of the issue in later works. Among the topics examined are his qualms about nominalism, his plumping for physical objects and sets, his insistence on the difference between concrete general terms and abstract singular terms, his argument that ‘attribute’ and ‘proposition’ are no more referential than ‘sake’ and ‘mile’, his handling of ideal objects such as infinitesimals and geometrical objects, his analysis of ‘ordered pair’, ‘natural number’, and other notions that require paraphrasing rather than elimination, his view of semantic ascent and how he views the philosophical project. Throughout the chapter attends to Quine’s emphasis on science, not common sense.

Quine vs. Quine

How does Quine fare in the first decades of the twenty-first century? This chapter examines a cluster of Quinean theses that are especially fruitful in meeting some of the current challenges of epistemology and ontology. These theses offer an alternative to the traditional bifurcations of truth and knowledge into factual and conceptual-pragmatic-conventional, the traditional conception of a foundation for knowledge, and traditional realism. To make the most of Quine’s ideas, however, we have to take an active stance: accept some of his ideas and reject others, sort different versions of the relevant ideas, sharpen or revise some of the ideas, connect them with new, non-Quinean ideas, and so on. As a result the chapter pits Quine against Quine, in an attempt to identify those Quinean ideas that have a lasting value and sketch potential developments.

Introduction

This introduction discusses the development of Quine’s system over time and the centrality of structure to it. It explains the contributions made in this volume to our understanding of Quine’s thought on structure and ontology, especially with respect to philosophical logic, philosophy of language, history of philosophy, mathematics, philosophy of time, and set theory. Chapters by Michael Resnik, Frederique Janssen-Lauret and Fraser MacBride, John Collins, Jaroslav Peregrin, and Paul Gregory explore whether Quine’s structuralism is epistemological, language-based, or ontological. Greg Frost-Arnold, Robert Sinclair, and Gary Kemp and Andrew Lugg explore Quine’s views on structure from a historical point of view. Nathan Salmón, Gila Sher, Marianna Antonutti Marfori, and Natalja Deng consider Quine’s views on the structure of logic, language, and theories in relation to contemporary philosophy, specifically ontology, the philosophy of logic and mathematics, philosophy of set theory, and philosophy of time.