The Bounds of Logic presents a new philosophical theory of the scope and nature of logic based on critical analysis of the principles underlying modern Tarskian logic and inspired by mathematical and linguistic development. Extracting central philosophical ideas from Tarski’s early work in semantics, Sher questions whether these are fully realized by the standard first-order system. The answer lays the foundation for a new, broader conception of logic. By generally characterizing logical terms, Sher establishes a fundamental result in semantics. Her (...) development of the notion of logicality for quantifiers and her work on branching are of great importance for linguistics. Sher outlines the boundaries of the new logic and points out some of the philosophical ramifications of the new view of logic for such issues as the logicist thesis, ontological commitment, the role of mathematics in logic, and the metaphysical underpinning of logic. She proposes a constructive definition of logical terms, reexamines and extends the notion of branching quantification, and discusses various linguistic issues and applications. (shrink)

1. 1. PROGRAM It will be our aim to reconstruct, with precision, certain views which have been traditionally associated with nominalism and to investigate problems arising from these views in the construction of interpreted formal systems. Several such systems are developed in accordance with the demand that the sentences of a system which is acceptable to a nominalist must not imply the existence of any entities other than individuals. Emphasis will be placed on the constructionist method of philosophical analysis. To (...) follow this method is to introduce the central notions of the subject-matter to be investigated into a system governed by exact rules. For example, the constructionist method of investigating the properties of geometric figures may consist in formulating a system of postulates and definitions which, together with the apparatus of formal logic, generates all necessary truths concerning geometric figures. Similarly, a constructionist analysis of the notion of an individual may take the form of an axiomatic theory whose provable assertions are just those which seem essential to the role played by the concept of an individual in system atic contexts. Such axiomatic theories gain in interest if they are supple mented by precise semantical rules specifying the denotation of all terms and the truth conditions of all sentences of the theory. (shrink)

Quine’s general approach is to treat ontology as a matter of what a theory says there is. This turns ontology into a question of which existential statements are consequences of that theory. This approach is contrasted favourably with the view that takes ontological commitment as a relation to things. However within the broadly Quinean approach we can distinguish different accounts, differing as to the nature of the consequence relation best suited for determining those consequences. It is suggested that Quine’s own (...) narrowly formal account fails. Then a consideration of the necessitation approach championed by Jackson and Lewis shows that it does not do justice to the role of acknowledging consequences in determining rationality. I suggest that an approach which puts a priori consequence as the key relation does a better job. The task of spelling out the nature of a priori consequence is sketched, along with reasons to doubt the adequacy of the double indexing approach to analysing the a priori. The sorts of relations we can stand in to theories which allow us to inherit ontological commitments are touched on with a number of important philosophical strategies for introducing belief-like attitudes which nevertheless avoid ontological commitment. (shrink)

Disagreement over what exists is so fundamental that it tends to hinder or even to block dialogue among disputants. The various controversies between believers and atheists, or realists and nominalists, are only two kinds of examples. Interested in contributing to the intelligibility of the debate on ontology, in 1939 Willard van Orman Quine began a series of works which introduces the notion of ontological commitment and proposes an allegedly objective criterion to identify the exact conditions under which a theoretical discourse (...) signals an assumption of existence. I intend to present the concept of ontological commitment and the Quinean criterion, to expose and evaluate some of the many criticisms to which the criterion has subject and to situate it in the context of Quine’s philosophy. As a product of such analyses, I hope to contribute to the discussion on the application and relevance of the notion of ontological commitment. (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)

The prevailing approach to the problem of the ontological status of mathematical entities such as numbers and sets is to ask in what sense it is legitimate to ascribe a reference to abstract singular terms; those expressions of our language which, taken at face value, denote abstract objects. On the basis of this approach, neo‐Fregean Abstractionists such as Hale and Wright have argued that abstract singular terms may be taken to effect genuine reference towards objects, whereas nominalists such as Field (...) have asserted that these apparent ontological commitments should not be taken at face value. In this article I argue for an intermediate position which upholds the legitimacy of ascribing a reference to abstract singular terms in an attenuated sense relative to the more robust ascription of reference applicable to names denoting concrete entities. In so doing I seek to clear up some confusions regarding the ramifications of such a thin notion of reference for ontological claims about mathematical objects. (shrink)

There are two doctrines for which Quine is particularly well known: the doctrine of ontological commitment and the inscrutability thesis—the thesis that reference and quantification are inscrutable. At first glance, the two doctrines are squarely at odds. If there is no fact of the matter as to what our expressions refer to, then it would appear that no determinate commitments can be read off of our best theories. We argue here that the appearance of a clash between the two doctrines (...) is illusory. The reason that there is no real conflict is not simply that in determining our theories’ ontological commitments we naturally rely on our home language but also (and more importantly) that ontological commitment is not intimately tied to objectual quantification and a reference-first approach to language. Or so we will argue. We conclude with a new inscrutability argument which rests on the observation that the notion of objectual quantification, when properly cashed out, deflates. (shrink)

This paper consists of two parts. Part I contains a precise model-theoretic reconstruction of Quine's criterion for the ontological presuppositions of a theory. Two versions (K1), (K2) of the criterion are elaborated, (K2) being the more adequate one which is shown through a number of theorems for each version. Part II contains a critical discussion of (K2), in particular of the question wether (K2) is a criterion for ontological presuppositions, i.e. for entities existing independently of the theory. Its answer depends (...) on the meaning of the quantifiers used in (K2). It is shown that this meaning, contrary to Quine's opinion, does not commit one to the existence of entities. Quine's criterion is therefore not a criterion for ontological presuppositions of theories. If theories at all presuppose independently existing entities, then it is not by using the standard quantifiers of classical logic. One of the consequences of this result is that there is no need for a free logic, which is shown by discussing a system of Lambert and Meyer. Another consequence is that there is no problem about negative existentials. (shrink)

I propose a way of thinking aboout content, and a related way of thinking about ontological commitment. (This is part of a series of four closely related papers. The other three are ‘On Specifying Truth-Conditions’, ‘An Actualist’s Guide to Quantifying In’ and ‘An Account of Possibility’.).

Ontology played a very large role in Quine’s philosophy and was one of his major preoccupations from the early 30’s to the end of his life. His work on ontology provided a basic framework for most of the discussions of ontology in analytic philosophy in the second half of the Twentieth Century. There are three main themes (and several sub-themes) that Quine developed in his work. The first is ontological commitment: What are the existential commitments of a theory? The second (...) is ontological reduction: How can an ontology be reduced to (or substituted by) another? And what is the most economical ontology that can be obtained for certain given purposes? The third is criteria of identity: When are entities of some kind (sets, properties, material objects, propositions, meanings, etc.) the same or different? In this paper I discuss Quine’s development of these three themes and some of the problems that were aised in connection with his work. (shrink)

This paper defends two claims about the criterion of commitment of W.V.O Quine. The first claim is that the criterion can be made extensional. The second is that a proper formulation becomes an analytic truth. We spend a few preliminary sections clarifying our intended notion of ontological commitment. We will not go very far in our investigation of the criterion if we do not distinguish the things a theory postulates, what its adherents, or anybody else, believe in, and which of (...) these entities we have compelling reasons to accept. A look at [Quine 1953] shows that the criterion concerned the postulation of entities by theories, but it is often misread as an attempt to say something about either or. The core of the paper is an exposition of two formulations of the criterion. I first state a schema improving on that of [Scheffler and Chomsky 1959]. The second formulation is a single principle and construes commitment as a relation between theories and predicates: ontological commitment to the entities that satisfy a given predicate. Both criteria are extensional and are formulated for constructional systems, in the sense of [Carnap 1928] and [Goodman 1951], rather than for theories construed as interpreted sets of sentences. This solves a problem raised by [Halvorson 2019]. Their analyticity is substantiated by showing that their most controversial consequences are instances of Tarski’s Convention. (shrink)

At the heart of my pragmatic theory of truth and ontology is a view of the relation between language and reality which I term internal justification: a way of explaining how sentences may have truth-values which we cannot discover without invoking the need for the mystery of a correspondence relation. The epistemology upon which the theory depend~ is fallibilist and holistic ; places heavy reliance on modal idioms ; and leads to the conclusion that current versions of realism and anti-realism (...) are deficient. Just as my theory avoids the need for an epistemic 'given', it avoids the need for a metaphysical 'given' or 'joints'. I offer a view of the nature of philosophy and what it can properly achieve with respect to ontological questions ; since those views lead me to believe that philosophical discussion about what exists should be restricted to 'entities' discussed in non-philosophical contexts, my views on how we should understand claims made about the existence of middle-sized physical objects, theoretical entities in science, and abstract entities in mathematics, give the thesis a schematic completeness. My theory leads me to a conception of inquiry which defends the cognitive status of moral statements whilst being critical of Kantian and utilitarian approaches to morality. Chapter 1 explores the views of my closest philosophical allies: William James and Nelson Goodman. (shrink)

It is persons who are ontologically committed. But a person is not ontologically committed by virtue of his character, his height, his social standing or whatever, but by virtue of the sentences he assents to. Hence we should look to sentences for a criterion of ontological commitment. This is precisely what is done by advocates of what I will call the Referential theory. In this paper I argue that the Referential theory faces serious objections related to the role paraphrase must (...) play in it. I then present a modified Referential theory and go on to discuss certain implications of the modified theory. More precisely, the paper divides up as follows. In §1 I present the Referential theory. In §2 I argue that it is in trouble over paraphrase. In §3 I consider a general objection to the arguments of §2. In §4 I present the modified theory. In §5 I consider the implications of the modified theory for polemic over what there is and for the existence of properties or universals. (shrink)

This paper reexamines an early article by Noam Chomsky and Israel Scheffler concerning the proper formulation and status of Quine's criterion for ontological commitment. ( What is Said to Be,' "Proceedings of the Aristotelian Society", 69, 1958-59; reprinted in Scheffler, "Inquiries".) Somewhat different formulations of the criterion are proposed and their implications explored. It is also argued that Chomsky and Scheffler's views may be seen to foreshadow and lead to some of Quine's later more radical doctrines regarding ontological commitment.

The proper evaluation of a theory's virtues seems to require taking into account what the theory is indirectly or implicitly committed to, in addition to what it explicitly says. Most extant proposals for criteria of theory choice in the literature spell out the relevant notion of implicit commitment via some notion of entailment. I show that such criteria behave implausibly in application to theories that differ over matters of entailment. A recent defence by Howard Peacock of such a criterion against (...) this objection is examined and rejected. I go on to a develop a better proposal on which, roughly speaking, a theory is counted committed to a claim if and only if its best fully explicit extension is explicitly committed to the claim. Such extensions in turn are evaluated by ordinary standards of theory choice adapted to the case of theories assumed to articulate their intended content in a fully explicit fashion. (shrink)