This dissertation is centered around a set of apparently conflicting intuitions that we may have about mathematics. On the one hand, we are inclined to believe that the theorems of mathematics are true. Since many of these theorems are existence assertions, it seems that if we accept them as true, we also commit ourselves to the existence of mathematical objects. On the other hand, mathematical objects are usually thought of as abstract objects that are non-spatiotemporal and causally inert. This makes (...) it difficult to understand how we can have knowledge of them and how they can have any relevance for our mathematical theories. I begin by characterizing a realist position in the philosophy of mathematics and discussing two of the most influential arguments for that kind of view. Next, after highlighting some of the difficulties that realism faces, I look at a few alternative approaches that attempt to account for our mathematical practice without making the assumption that there exist abstract mathematical entities. More specifically, I examine the fictionalist views developed by Hartry Field, Mark Balaguer, and Stephen Yablo, respectively. A common feature of these views is that they accept that mathematics interpreted at face value is committed to the existence of abstract objects. In order to avoid this commitment, they claim that mathematics, when taken at face value, is false. I argue that the fictionalist idea of mathematics as consisting of falsehoods is counter-intuitive and that we should aim for an account that can accommodate both the intuition that mathematics is true and the intuition that the causal inertness of abstract mathematical objects makes them irrelevant to mathematical practice and mathematical knowledge. The solution that I propose is based on Rudolf Carnap's distinction between an internal and an external perspective on existence. I argue that the most reasonable interpretation of the notions of mathematical truth and existence is that they are internal to mathematics and, hence, that mathematical truth cannot be used to draw the conclusion that mathematical objects exist in an external/ontological sense. (shrink)

Esta enciclopédia abrange, de uma forma introdutória mas desejavelmente rigorosa, uma diversidade de conceitos, temas, problemas, argumentos e teorias localizados numa área relativamente recente de estudos, os quais tem sido habitual qualificar como «estudos lógico-filosóficos». De uma forma apropriadamente genérica, e apesar de o território teórico abrangido ser extenso e de contornos por vezes difusos, podemos dizer que na área se investiga um conjunto de questões fundamentais acerca da natureza da linguagem, da mente, da cognição e do raciocínio humanos, bem (...) como questões acerca das conexões destes com a realidade não mental e extralinguística. A razão daquela qualificação é a seguinte: por um lado, a investigação em questão é qualificada como filosófica em virtude do elevado grau de generalidade e abstracção das questões examinadas (entre outras coisas); por outro, a investigação é qualificada como lógica em virtude de ser uma investigação logicamente disciplinada, no sentido de nela se fazer um uso intenso de conceitos, técnicas e métodos provenientes da disciplina de lógica. O agregado de tópicos que constitui a área de estudos lógico-filosóficos é já visível, pelo menos em parte, no Tractatus Logico-Philosophicus de Ludwig Wittgenstein, uma obra publicada em 1921. E uma boa maneira de ter uma ideia sinóptica do território disciplinar abrangido por esta enciclopédia, ou pelo menos de uma porção substancial dele, é extrair do Tractatus uma lista dos tópicos mais salientes aí discutidos; a lista incluirá certamente tópicos do seguinte género, muitos dos quais se podem encontrar ao longo desta enciclopédia: factos e estados de coisas; objectos; representação; crenças e estados mentais; pensamentos; a proposição; nomes próprios; valores de verdade e bivalência; quantificação; funções de verdade; verdade lógica; identidade; tautologia; o raciocínio matemático; a natureza da inferência; o cepticismo e o solipsismo; a indução; as constantes lógicas; a negação; a forma lógica; as leis da ciência; o número. (shrink)

Sellars [1960, ‘Grammar and existence: A preface to ontology’] argues that the truth of a second-order sentence does not incur commitment to there being any sort of abstract entity. This paper begins by exploring the arguments that Sellars offers for the above claim. It then develops those arguments by pointing out places where Sellars has been unclear or ought to have said more. In particular, Sellars's arguments rely on there being a means by which language users could come to understand (...) sentences of a second-order language wherein the truth of second-order existential sentences do not require there to be abstract entities. In addition to this, as Sellars [1979, Naturalism and Ontology] notes, a formal account of quantification is required that does not make use of the apparatus of sequences. Both such a translation of and a formal account of quantification are provided in this article. (shrink)

Confronting the Liar Paradox is commonly viewed as a prerequisite for developing a theory of truth. In this paper I turn the tables on this traditional conception of the relation between the two. The theorist of truth need not constrain his search for a “material” theory of truth, i.e., a theory of the philosophical nature of truth, by committing himself to one solution or another to the Liar Paradox. If he focuses on the nature of truth (leaving issues of formal (...) consistency for a later stage), he can arrive at material principles that prevent the Liar Paradox from arising in the first place. I argue for this point both on general methodological grounds and by example. The example is based on a substantivist theory of truth that emphasizes the role of truth in human cognition. The key point is that truth requires a certain complementarity of “immanence” and “transcendence”, and this means that some hierarchical structure is inherent in truth. Approaching the Liar Paradox from this perspective throws new light on its existent solutions: their differences and commonalities, their purported ad-hocness, and the relevance of natural language and bivalence to truth and the Liar. (shrink)

During the past few decades, a radical shift has occurred in how philosophers conceive of the relation between science and philosophy. A great number of analytic philosophers have adopted what is commonly called a ‘naturalistic’ approach, arguing that their inquiries ought to be in some sense continuous with science. Where early analytic philosophers often relied on a sharp distinction between science and philosophy—the former an empirical discipline concerned with fact, the latter an a priori discipline concerned with meaning—philosophers today largely (...) follow Willard Van Orman Quine (1908-2000) in his seminal rejection of this distinction. -/- This book offers a comprehensive study of Quine’s naturalism. Building on Quine’s published corpus as well as thousands of unpublished letters, notes, lectures, papers, proposals, and annotations from the Quine archives, this book aims to reconstruct both the nature (chapters 2-4) and the development (chapter 5-7) of his naturalism. As such, this book aims to contribute to the rapidly developing historiography of analytic philosophy, and to provide a better, historically informed, understanding of what is philosophically at stake in the contemporary naturalistic turn. (shrink)

This paper explores the nature of the concept of truth. It does not offer an analysis or definition of truth, or an account of how it relates to other concepts. Instead, it explores what sort of concept truth is by considering what sorts of thoughts it enables us to think. My conclusion is that truth is a part of each and every propositional thought. The concept of truth is therefore best thought of as the ability to token propositional thoughts. I (...) explore what implications this view has for existing accounts of concepts, and argue that truth is a concept unlike any other. (shrink)

Nonclassical theories of truth have in common that they reject principles of classical logic to accommodate an unrestricted truth predicate. However, different nonclassical strategies give up different classical principles. The paper discusses one criterion we might use in theory choice when considering nonclassical rivals: the maxim of minimal mutilation.

In this paper, we offer a brief, critical survey of contemporary work on truth. We begin by reflecting on the distinction between substantivist and deflationary truth theories. We then turn to three new kinds of truth theory—Kevin Scharp's replacement theory, John MacFarlane's relativism, and the alethic pluralism pioneered by Michael Lynch and Crispin Wright. We argue that despite their considerable differences, these theories exhibit a common "pluralizing tendency" with respect to truth. In the final section, we look at the underinvestigated (...) interface between metaphysical and formal truth theories, pointing to several promising questions that arise here. (shrink)

The paper seeks to answer two new questions about truth and scientific change: What lessons does the phenomenon of scientific change teach us about the nature of truth? What light do recent developments in the theory of truth, incorporating these lessons, throw on problems arising from the prevalence of scientific change, specifically, the problem of pessimistic meta-induction?

Millians about proper names typically claim that it is knowable apriori that Hesperus is Phosphorus. We argue that they should claim instead that it is knowable only aposteriori that Hesperus is Hesperus, since the Kripke-Putnam epistemic arguments against descriptivism are special cases of Quinean arguments that nothing is knowable apriori, and Millians have no resources to resist the more general Quinean arguments.

This paper argues against the realization principle, which reifies the realization relation between lower-level and higher-level properties. It begins with a review of some principles of naturalistic metaphysics. Then it criticizes some likely reasons for embracing the realization principle, and finally it argues against the principle directly. The most likely reasons for embracing the principle depend on the dubious assumption that special science theories cannot be true unless special science predicates designate properties. The principle itself turns out to be false (...) because the realization relation fails the naturalistic test for reality: it makes no causal difference to the world.Footnote11This paper resulted from work done at John Heil's 2006 Mind and Metaphysics NEH Summer Seminar at Washington University in St. Louis. An early version of it was presented in a special symposium on realization at the 2007 meeting of the Southern Society for Philosophy and Psychology. I owe thanks to all the participants in both events for helpful discussions, and I owe particular thanks to Ken Aizawa, Torin Alter, Jason Ford, Carl Gillett, John Heil, Nicholas Helms, Pete Mandik, John Post, Gene Witmer, Michelle Wrenn, Tad Zawidzki, and two anonymous referees for the AJP. (shrink)

Significant issues remain for understanding and evaluating the Quinean critique of the analytic/synthetic distinction. These issues are highlighted in a puzzling mismatch between the common philosophical attitude toward the critique and its broader intellectual legacy. A discussion of this mismatch sets the larger context for criticism of a recent tradition of interpretation of the critique. I argue that this tradition confuses the roles and relative importance of indeterminacy, a priority, and analyticity in the Quinean critique.

We argue that if Stephen Yablo (2005) is right that philosophers of mathematics ought to endorse a fictionalist view of number-talk, then there is a compelling reason for deflationists about truth to endorse a fictionalist view of truth-talk. More specifically, our claim will be that, for deflationists about truth, Yablo’s argument for mathematical fictionalism can be employed and mounted as an argument for truth-theoretic fictionalism.

Isabelle Delpla a écrit une étude critique riche et généreuse de mon ouvrage Les fondements empiriques de la signification. Cette étude regorge d’analyses fines et de critiques subtiles des positions que je défends. Son titre défaitiste ne m’apparaît toutefois pas motivé, et je vais montrer pourquoi ses principales attaques échouent.

True beliefs and truth-preserving inferences are, in some sense, good beliefs and good inferences. When an inference is valid though, it is not merely truth-preserving, but truth-preserving in all cases. This motivates my question: I consider a Modus Ponens inference, and I ask what its validity in particular contributes to the explanation of why the inference is, in any sense, a good inference. I consider the question under three different definitions of ‘case’, and hence of ‘validity’: the orthodox definition given (...) in terms of interpretations or models, a metaphysical definition given in terms of possible worlds, and a substitutional definition defended by Quine. I argue that the orthodox notion is poorly suited to explain what's good about a Modus Ponens inference. I argue that there is something good that is explained by a certain kind of truth across possible worlds, but the explanation is not provided by metaphysical validity in particular; nothing of value is explained by truth across all possible worlds. Finally, I argue that the substitutional notion of validity allows us to correctly explain what is good about a valid inference. (shrink)

Beliefs have what I will call ‘propositional content’. A belief is always a belief that so-and-so: a belief that grass is green, or a belief that snow is white, or whatever. Other things have propositional content too, such as sentences, judgments and assertions. The Standard View amongst philosophers is that what it is to have a propositional content is to stand in an appropriate relation to a proposition. Moreover, on this view, propositions are objects, i.e. the kind of thing you (...) can refer to with singular terms. For example, on the Standard View, we should parse the sentence ‘Simon believes that Sharon is funny’ as: [Simon] believes [that Sharon is funny]; ‘Simon’ is a term referring to a thinking subject, ‘that Sharon is funny’ is a term referring to a proposition, and ‘x believes y’ is a dyadic predicate expressing the believing relation. In this paper, I argue against the Standard View. This is how I think we should parse ‘Simon believes that Sharon is funny’: [Simon] believes that [Sharon is funny]; here we have a singular term, ‘Simon’, a sentence ‘Sharon is funny’, and a ‘prenective’ joining them together, ‘x believes that p’. On this Prenective View, we do not get at the propositional content of someone’s belief by referring to a reified proposition with a singular term; we simply use the sentence ‘Sharon is funny’ to express that content for ourselves. I argue for the Prenective View in large part by showing that an initially attractive version of the Standard View is actually vulnerable to the same objection that Wittgenstein used against Russell’s multiple-relation theory of judgment. (shrink)

This essay argues that deflationism is incompatible with the phenomenon of referential indeterminacy. This puts the deflationist in the difficult position of having to deny the possibility of what otherwise seems like a manifest and theoretically important phenomenon. Section 1 provides background on deflationism. Section 2 considers an intuitive argument by Stephen Leeds to the effect that deflationism precludes RI; the essay argues that this argument does not succeed. The rest of the essay presents its own, distinct argument for the (...) incompatibility of deflationism and RI. Section 3 argues that direct RI—RI that is not simply a derivative of some other, nonreferential instance of indeterminacy—is strictly incompatible with deflationism. Section 4 considers a couple of different ways the deflationist might try to achieve indirect RI—via indeterminate identity and indeterminate synonymy—and argues that each is unsatisfactory. (shrink)

Ignacio Jane has argued that second-order logic presupposes some amount of set theory and hence cannot legitimately be used in axiomatizing set theory. I focus here on his claim that the second-order formulation of the Axiom of Separation presupposes the character of the power set operation, thereby preventing a thorough study of the power set of infinite sets, a central part of set theory. In reply I argue that substantive issues often cannot be separated from a logic, but rather must (...) be presupposed. I call this the logic-metalogic link. There are two facets to the logic-metalogic link. First, when a logic is entangled with a substantive issue, the same position on that issue should be taken at the meta- level as at the object level; and second, if an expression has a clear meaning in natural language, then the corresponding concept can equally well be deployed in a formal language. The determinate nature of the power set operation is one such substantive issue in set theory. Whether there is a determinate power set of an infinite set can only be presupposed in set theory, not proved, so the use of second-order logic cannot be ruled out by virtue of presupposing one answer to this question. Moreover, the legitimacy of presupposing in the background logic that the power set of an infinite set is determinate is guaranteed by the clarity and definiteness of the notions of all and of subset. This is also exactly what is required for the same presupposition to be legitimately made in an axiomatic set theory, so the use of second-order logic in set theory rather than first-order logic does not require any new metatheoretic commitments. (shrink)

According to the logical pluralism of Beall and Restall, there are several distinct relations of logical consequence. Some critics argue that logical pluralism suffers from what I call the collapse problem: that despite its intention to articulate a radically pluralistic doctrine about logic, the view unintentionally collapses into logical monism. In this paper, I propose a contextualist resolution of the collapse problem. This clarifies the mechanism responsible for a plurality of logics and handles the motivating data better than the original (...) view. It is a major improvement that should be embraced by all logical pluralists. (shrink)

Is understanding epistemic in nature? Does a correct account of what constitutes understanding of a concept mention epistemological notions such as knowledge, justification or epistemic rationality? We defend the view that understanding is epistemic in nature – we defend epistemological conceptions of understanding. We focus our discussion with a critical evaluation of Tim Williamson's challenges to epistemological conceptions of understanding in The Philosophy of Philosophy. Against Williamson, we distinguish three kinds of epistemological conceptions and argue that Williamson's arguments succeed against (...) only the most heavily committed kind, and leave the less heavily committed kinds untouched. Further, we argue that Williamson's elaboration of lessons from his arguments point in a direction opposite of his own conclusions and give vivid articulation and support to epistemological conceptions. We suggest also that skepticism about Williamson's larger metaphilosophical conclusions – according to which understanding plays no special role in the epistemology of philosophy – may be in order. (shrink)

Logic isn’t special. Its theories are continuous with science; its method continuous with scientific method. Logic isn’t a priori, nor are its truths analytic truths. Logical theories are revisable, and if they are revised, they are revised on the same grounds as scientific theories. These are the tenets of anti-exceptionalism about logic. The position is most famously defended by Quine, but has more recent advocates in Maddy, Priest, Russell, and Williamson. Although these authors agree on many methodological issues about logic, (...) they disagree about which logic anti-exceptionalism supports. Williamson uses an anti-exceptionalist argument to defend classical logic, while Priest claims that his anti-exceptionalism supports nonclassical logic. This paper argues that the disagreement is due to a difference in how the parties understand logical theories. Once we reject Williamson’s deflationary account of logical theories, the argument for classical logic is undercut. Instead an alternative account of logical theories is offered, on which logical pluralism is a plausible supplement to anti-exceptionalism. (shrink)

The mereological predicate ‘is part of’ can be used to define the predicate ‘is identical with’. I argue that this entails that mereological theories can be ideologically simpler than nihilistic theories that do not use the notion of parthood—contrary to what has been argued by Ted Sider. Moreover, if one accepts an extensional mereology, there are good philosophical reasons apart from ideological simplicity to give a mereological definition of identity.

Prior Analytics by the Greek philosopher Aristotle and Laws of Thought by the English mathematician George Boole are the two most important surviving original logical works from before the advent of modern logic. This article has a single goal: to compare Aristotle's system with the system that Boole constructed over twenty-two centuries later intending to extend and perfect what Aristotle had started. This comparison merits an article itself. Accordingly, this article does not discuss many other historically and philosophically important aspects (...) of Boole's book, e.g. his confused attempt to apply differential calculus to logic, his misguided effort to make his system of ‘class logic’ serve as a kind of ‘truth-functional logic’, his now almost forgotten foray into probability theory, or his blindness to the fact that a truth-functional combination of equations that follows from a given truth-functional combination of equations need not follow truth-functionally. One of the main conclusions is that Boole's contribution widened logic and changed its nature to such an extent that he fully deserves to share with Aristotle the status of being a founding figure in logic. By setting forth in clear and systematic fashion the basic methods for establishing validity and for establishing invalidity, Aristotle became the founder of logic as formal epistemology. By making the first unmistakable steps toward opening logic to the study of ‘laws of thought’—tautologies and laws such as excluded middle and non-contradiction—Boole became the founder of logic as formal ontology.… using mathematical methods … has led to more knowledge about logic in one century than had been obtained from the death of Aristotle up to … when Boole's masterpiece was published.Paul Rosenbloom 1950. (shrink)

Particle indistinguishability has always been considered a purely quantum mechanical concept. In parallel, indistinguishable particles have been thought to be entities that are not properly speaking objects at all. I argue, to the contrary, that the concept can equally be applied to classical particles, and that in either case particles may (with certain exceptions) be counted as objects even though they are indistinguishable. The exceptions are elementary bosons (for example photons).

W. V. Quine famously argues that though all knowledge is empirical, mathematics is entrenched relative to physics and the special sciences. Further, entrenchment accounts for the necessity of mathematics relative to these other disciplines. Michael Friedman challenges Quine’s view by appealing to historicism, the thesis that the nature of science is illuminated by taking into account its historical development. Friedman argues on historicist grounds that mathematical claims serve as principles constitutive of languages within which empirical claims in physics and the (...) special sciences can be formulated and tested, where these mathematical claims are themselves not empirical but conventional. For Friedman, their conventional, constitutive status accounts for the necessity of mathematics relative to these other disciplines. Here I evaluate Friedman’s challenge to Quine and Quine’s likely response. I then show that though we have reason to find Friedman’s challenge successful, his positive project requires further development before we can endorse it. (shrink)

One logic or many? I say—many. Or rather, I say there is one logic for each way of specifying the class of all possible circumstances, or models, i.e., all ways of interpreting a given language. But because there is no unique way of doing this, I say there is no unique logic except in a relative sense. Indeed, given any two competing logical theories T1 and T2 (in the same language) one could always consider their common core, T, and settle (...) on that theory. So, given any language L, one could settle on the minimal logic T0 corresponding to the common core shared by all competitors. That would be a way of resisting relativism, as long as one is willing to redraw the bounds of logic accordingly. However, such a minimal theory T0 may be empty if the syntax of L contains no special ingredients the interpretation of which is independent of the specification of the relevant L-models. And generally—I argue—this is indeed the case. (shrink)

Carl Hempel introduced what he called "Craig's theorem" into the philosophy of science in a famous discussion of the "problem of theoretical terms." Beginning with Hempel's use of 'Craig's theorem," I shall bring out some of the key differences between Hempel's treatment of the "problem of theoretical terms" and Carnap's in order to illuminate the peculiar function of Wissenschaftslogik in Carnap's mature philosophy. Carnap's treatment, in particular, is fundamentally antimetaphysical—he aims to use the tools of mathematical logic to dissolve rather (...) solve traditional philosophical problems—and it is precisely this point that is missed by his logically-minded contemporaries such as Hempel and Quine. (shrink)

Michael Dummett has argued that a formal semantics for our language is inadequate unless it can be shown to illuminate to our actual practice of speaking and understanding. This paper argues that Frege’s account of the semantics of predicate expressions according to which the reference of a predicate is a concept (a function from objects to truth values) has exactly the required characteristics. The first part of the paper develops a model for understanding the distinction between objects and concepts as (...) an ontological distinction. It argues that, ontologically, we can take a Fregean function to be generated by a property detection device that can register for any object the presence or absence of that property. This provides a direct connection between the semantics of sentences and the structure of perceptual judgment. The second part of the paper deals with arguments that have been mounted against the coherence of Frege’s semantics. It argues that some of these are question begging, while others are correct in so far as Frege’s claim is untenable if we assume that the syntactic categories singular term and predicate are primary, and the ontological categories are simply projections of these syntactic categories. However, the objections dissipate once we recognize that an independent ontological characterization of the distinction is available. (shrink)

In this paper I argue against the commonly received view that Kripke's formal Possible World Semantics (PWS) reflects the adoption of a metaphysical interpretation of the modal operators. I consider in detail Kripke's three main innovations vis-à-vis Carnap's PWS: a new view of the worlds, variable domains of quantification, and the adoption of a notion of universal validity. I argue that all these changes are driven by the natural technical development of the model theory and its related notion of validity: (...) they are dictated by merely formal considerations, not interpretive concerns. I conclude that Kripke's model theoretic semantics does not induce a metaphysical reading of necessity, and is formally adequate independently of the specific interpretation of the modal operators. (shrink)

This paper formulates a general epistemological argument against what I call non-causal realism, generalizing domain specific arguments by Benacerraf, Field, and others. First I lay out the background to the argument, making a number of distinctions that are sometimes missed in discussions of epistemological arguments against realism. Then I define the target of the argument—non-causal realism—and argue that any non-causal realist theory, no matter the subject matter, cannot be given a reasonable epistemology and so should be rejected. Finally I discuss (...) and respond to several possible responses to the argument. In addition to clearing up and avoiding numerous misunderstandings of arguments of this kind that are quite common in the literature, this paper aims to present and endorse a rigorous and fully general epistemological argument against realism. (shrink)

Can one combine Davidsonian semantics with a deflationary conception of truth? Williams argues, contra a common worry, that Davidsonian semantics does not require truth-talk to play an explanatory role. Horisk replies that, in any event, the expressive role of truth-talk that Williams emphasizes disqualifies deflationary accounts—at least extant varieties—from combination with Davidsonian semantics. She argues, in particular, that this is so for Quine's disquotationalism, Horwich's minimalism, and Brandom's prosententialism. I argue that Horisk fails to establish her claim in all three (...) cases. This involves clarifying Quine’s understanding of a purely referential occurrence; explaining how Davidsonians can avail themselves of a syntactic treatment of lexical ambiguity; and correcting a common misreading of Brandom (answering along the way an objection offered by Künne as well). (shrink)

The paper is concerned with Quine's substitutional account of logical truth. The critique of Quine's definition tends to focus on miscellaneous odds and ends, such as problems with identity. However, in an appendix to his influential article On Second Order Logic, George Boolos offered an ingenious argument that seems to diminish Quine's account of logical truth on a deeper level. In the article he shows that Quine's substitutional account of logical truth cannot be generalized properly to the general concept of (...) logical consequence. The purpose of this paper is threefold: first, to introduce the reader to the metamathematics of Quine's substitutional definition of logical truth; second, to make Boolos' result accessible to a broader audience by giving a detailed and self-contained presentation of his proof; and, finally, to discuss some of the possible implications and how a defender of the Quinean concepts might react to the challenge posed by Boolos' result. (shrink)

This introductory chapter provides a summary of the contributions to the volume, as well as some critical remarks.

In this paper, I examine Quine's views on the epistemology of logic. According to Quine's influential holistic account, logic is central in the “web of belief” that comprises our overall theory of the world. Because of this, revisions to logic would have devastating systematic consequences, and this explains why we are loath to make such revisions. In section1, I clarify this idea and thereby show that Quine actually takes the web of belief to have asymmetrical internal structure. This raises two (...) puzzles. First, as I show in section 2, Quine's mature thoroughly naturalized view has it that logic is simply obvious, and this is explains why we do not typically consider revising it. While Quine presents this naturalized view as a way to make good on his earlier metaphor of centrality in a web of belief, I argue that the resources of Quine's naturalized epistemology cannot adequately explain why we are reluctant to revise logic. And, Quine seems to recognize this point himself. In light of this, I explain in section 3 how Quine can allow that our overall scientific theory has systematic structure in a way that is consistent with his naturalistic strictures. Second, the asymmetrical internal structure of the web of belief seems to be inconsistent with its being a holistic web at all. I defuse this problem in section 4 by showing how Quine distinguishes between structural and confirmational considerations. I close by using this distinction to show how Quine's view can evade Michael Friedman’s criticisms, and allow for important methodological distinctions between areas of the web of belief. (shrink)

In this paper we explain our pretense account of truth-talk and apply it in a diagnosis and treatment of the Liar Paradox. We begin by assuming that some form of deflationism is the correct approach to the topic of truth. We then briefly motivate the idea that all T-deflationists should endorse a fictionalist view of truth-talk, and, after distinguishing pretense-involving fictionalism (PIF) from error- theoretic fictionalism (ETF), explain the merits of the former over the latter. After presenting the basic framework (...) of our PIF account of truth-talk, we demonstrate a few advantages it offers over T-deflationist accounts that do not explicitly acknowledge pretense at work in the discourse. In turning to the Liar Paradox, we explain how the quasi-anaphoric functioning that our account attributes to truth-talk provides a diagnosis of the Liar Paradox (and other instances of semantic pathology) as having no content—in the sense of not specifying any of what we call M-conditions. At the same time, however, we vindicate the intuition that we can understand liar sentences, thereby avoiding one standard objection to “meaningless strategy” responses to the Liar Paradox. With this diagnosis in place, we then, by way of treatment, introduce a new predicate, ‘semantically defective’, and show how the explanation we give for its application allows for a consistent, yet revenge-immune, (dis)solution of the Liar Paradox, and semantic pathology generally. (shrink)

In this paper, I articulate and argue for a new truthmaker view of ontological commitment, which I call the “General Truthmaker View”: when one affirms a sentence, one is ontologically committed to there being something that makes true the proposition expressed by the sentence. This view comes apart from Quinean orthodoxy in that we are not ontologically committed to the things over which we quantify, and it comes apart from extant truthmaker views of ontological commitment in that we are not (...) ontologically committed to the truthmakers of our sentences. (shrink)

Why should one think Frege's definition of the ancestral correct? It can be proven to be extensionally correct, but the argument uses arithmetical induction, and that seems to undermine Frege's claim to have justified induction in purely logical terms. I discuss such circularity objections and then offer a new definition of the ancestral intended to be intensionally correct; its extensional correctness then follows without proof. This new definition can be proven equivalent to Frege's without any use of arithmetical induction. This (...) proves, without any use of arithmetical induction, that Frege's definition is extensionally correct and so answers the circularity objections. (shrink)

Bob Hale’s distinguished record of research places him among the most important and influential contemporary analytic metaphysicians. In his deep, wide ranging, yet highly readable book Necessary Beings, Hale draws upon, but substantially integrates and extends, a good deal his past research to produce a sustained and richly textured essay on — as promised in the subtitle — ontology, modality, and the relations between them. I’ve set myself two tasks in this review: first, to provide a reasonably thorough (if not (...) exactly comprehensive) overview of the structure and content of Hale’s book and, second, to a limited extent, to engage Hale’s book philosophically. I approach these tasks more or less sequentially: Parts I and 2 of the review are primarily expository; in Part 3 I adopt a somewhat more critical stance and raise several issues concerning one of the central elements of Hale’s account, his essentialist theory of modality. (shrink)

I propose a comprehensive account of negation as a modal operator, vindicating a moderate logical pluralism. Negation is taken as a quantifier on worlds, restricted by an accessibility relation encoding the basic concept of compatibility. This latter captures the core meaning of the operator. While some candidate negations are then ruled out as violating plausible constraints on compatibility, different specifications of the notion of world support different logical conducts for negations. The approach unifies in a philosophically motivated picture the following (...) results: nothing can be called a negation properly if it does not satisfy Contraposition and Double Negation Introduction; the pair consisting of two split or Galois negations encodes a distinction without a difference; some paraconsistent negations also fail to count as real negations, but others may; intuitionistic negation qualifies as real negation, and classical Boolean negation does as well, to the extent that constructivist and paraconsistent doubts on it do not turn on the basic concept of compatibility but rather on the interpretation of worlds. (shrink)

The five English words—sentence, proposition, judgment, statement, and fact—are central to coherent discussion in logic. However, each is ambiguous in that logicians use each with multiple normal meanings. Several of their meanings are vague in the sense of admitting borderline cases. In the course of displaying and describing the phenomena discussed using these words, this paper juxtaposes, distinguishes, and analyzes several senses of these and related words, focusing on a constellation of recommended senses. One of the purposes of this paper (...) is to demonstrate that ordinary English properly used has the resources for intricate and philosophically sound investigation of rather deep issues in logic and philosophy of language. No mathematical, logical, or linguistic symbols are used. Meanings need to be identified and clarified before being expressed in symbols. We hope to establish that clarity is served by deferring the extensive use of formalized or logically perfect languages until a solid “informal” foundation has been established. Questions of “ontological status”—e.g., whether propositions or sentences, or for that matter characters, numbers, truth-values, or instants, are “real entities”, are “idealizations”, or are “theoretical constructs”—plays no role in this paper. As is suggested by the title, this paper is written to be read aloud. -/- I hope that reading this aloud in groups will unite people in the enjoyment of the humanistic spirit of analytic philosophy. (shrink)

When we use a directly referential expression to denote an object, do we incur an ontological commitment to that object, as Russell and Barcan Marcus held? Not according to Quine, whose regimented language has only variables as denoting expressions, but no constants to model direct reference. I make a case for a more liberal conception of ontological commitment—more wide-ranging than Quine’s—which allows for commitment to individuals, with an improved logical language of regimentation. The reason for Quine’s prohibition on commitment to (...) individuals, I argue, is that his choice of regimented language is heavily informed by his holist epistemology, in which objects are introduced via a description of their explanatory role. But non-holists can coherently attempt to commit to individuals using directly referential expressions, modelled in a formal language as constants. While holding on to the insight that a logical language is a helpful medium for ontology, I propose instead a more permissive language of regimentation, one expanded to permit the use of constants to record attempts to commit to individuals, which allows us to make sense of non-holist theories with alternative name-based or name-and-variable-based criteria of ontological commitment as well as Quinean theories. (shrink)

I here defend a theory consisting of four claims about ‘property’ and properties, and argue that they form a coherent whole that can solve various serious problems. The claims are (1): ‘property’ is defined by the principles (PR): ‘F-ness/Being F/etc. is a property of x iff F’ and (PA): ‘F-ness/Being F/etc. is a property’; (2) the function of ‘property’ is to increase the expressive power of English, roughly by mimicking quantification into predicate position; (3) property talk should be understood at (...) face value: apparent commitments are real and our apparently literal use of ‘property’ is really literal; (4) there are no properties. In virtue of (1)–(2), this is a deflationist theory and in virtue of (3)–(4), it is an error theory. (1) is fleshed out as a claim about understanding conditions, and it is argued at length, and by going through a number of examples, that it satisfies a crucial constraint on meaning claims: all facts about ‘property’ can be explained, together with auxiliary facts, on its basis. Once claim (1) has been expanded upon, I argue that the combination of (1)–(3) provides the means for handling several problems: they help giving a happy-face solution to what I call the paradox of abstraction , they form part of a plausible account of the correctness of committive sentences, and, most importantly, they help respond to various indispensability arguments against nominalism. (shrink)

Take a correct sequent of formal logic, perhaps a simple logical truth, like the law of excluded middle, or something with premises, like disjunctive syllogism, but basically a claim of the form \.Γ can be empty. If you don’t like my examples, feel free to choose your own, everything I have to say should apply to those as well. Such a sequent attributes the properties of logical truth or logical consequence to a schematic sentence or argument. This paper aims to (...) answer the question of how beliefs in such attributions are justified, on both its descriptive and normative interpretations; I aim to say when we generally take ourselves to be justified in forming such beliefs, and to make it plausible that beliefs formed this way really are justified.We can ask such questions about many domains but there are special difficulties for answering them in logic. Some of the difficulties stem from the fact that logic is thought t.. (shrink)

Languages involving modalities and languages involving vagueness have each been thoroughly studied. On the other hand, virtually nothing has been said about the interaction of modality and vagueness. This paper aims to start filling that gap. Section 1 is a discussion of various possible sources of vague modality. Section 2 puts forward a model theory for a quantified language with operators for modality and vagueness. The model theory is followed by a discussion of the resulting logic. In Section 3, the (...) framework will permit us to address a puzzle raised by Elizabeth Barnes and Robert Williams. (shrink)

In “Properties and the Interpretation of Second-Order Logic” Bob Hale develops and defends a deflationary conception of properties where a property with particular satisfaction conditions actually exists if and only if it is possible that a predicate with those same satisfaction conditions exists. He argues further that, since our languages are finitary, there are at most countably infinitely many properties and, as a result, the account fails to underwrite the standard semantics for second-order logic. Here a more lenient version of (...) the view is explored, which allows for the possibility of countably infinite predicates understood as the product of linguistic supertasks. This enriched deflationist account of properties—the Infinitary Deflationary Conception of Existence—supports the standard semantics for models with countable first-order domains, and allows one to prove the categoricity of the second-order Peano axioms. (shrink)

Truthmaker theorists hold that there is a metaphysically explanatory relation that holds between true claims and what exists. While some critics try to provide counterexamples to truthmaker theory, that response quickly leads to a dialectical standoff. The aim of this paper is to move beyond that standoff by attempting to undermine some standard arguments for truthmaker theory. Using realism about truth and a more pragmatic account of explanation, I show how some of those arguments can be undermined.