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)

These preprints were automatically compiled into a PDF from the collection of papers deposited in PhilSci-Archive in conjunction with the PSA 2018.

This paper presents a new approach to the class-theoretic paradoxes. In the first part of the paper, I will distinguish classes from sets, describe the function of class talk, and present several reasons for postulating type-free classes. This involves applications to the problem of unrestricted quantification, reduction of properties, natural language semantics, and the epistemology of mathematics. In the second part of the paper, I will present some axioms for type-free classes. My approach is loosely based on the Gödel–Russell idea (...) of limited ranges of significance. It is shown how to derive the second-order Dedekind–Peano axioms within that theory. I conclude by discussing whether the theory can be used as a solution to the problem of unrestricted quantification. In an appendix, I prove the consistency of the class theory relative to Zermelo–Fraenkel set theory. (shrink)

I argue that absolutism, the view that absolutely unrestricted quantification is possible, is to blame for both the paradoxes that arise in naive set theory and variants of these paradoxes that arise in plural logic and in semantics. The solution is restrictivism, the view that absolutely unrestricted quantification is not possible. -/- It is generally thought that absolutism is true and that restrictivism is not only false, but inexpressible. As a result, the paradoxes are blamed, not on illicit quantification, but (...) on the logical conception of set which motivates naive set theory. The accepted solution is to replace this with the iterative conception of set. -/- I show that this picture is doubly mistaken. After a close examination of the paradoxes in chapters 2--3, I argue in chapters 4 and 5 that it is possible to rescue naive set theory by restricting quantification over sets and that the resulting restrictivist set theory is expressible. In chapters 6 and 7, I argue that it is the iterative conception of set and the thesis of absolutism that should be rejected. (shrink)

K. R. Popper distinguished between two main uses of logic, the demonstrational one, in mathematical proofs, and the derivational one, in the empirical sciences. These two uses are governed by the following methodological constraints: in mathematical proofs one ought to use minimal logical means (logical minimalism), while in the empirical sciences one ought to use the strongest available logic (logical maximalism). In this paper I discuss whether Popper’s critical rationalism is compatible with a revision of logic in the empirical sciences, (...) given the condition of logical maximalism. Apparently, if one ought to use the strongest logic in the empirical sciences, logic would remain immune to criticism and, thus, non-revisable. I will show that critical rationalism is theoretically compatible with a revision of logic in the empirical sciences. However, a question that remains to be clarified by the critical rationalists is what kind of evidence would lead them to revise the system of logic that underlies a physical theory, such as quantum mechanics? Popper’s falsificationist methodology will be compared with the recently advocated extension of the abductive methodology from the empirical sciences to logic by T. Williamson, since both of them arrive at the same conclusion concerning the status of classical logic. (shrink)

What requirements must deflationary formal theories of truth satisfy? This chapter argues against the widely accepted view that compositional and Tarskian theories of truth are substantial or otherwise unacceptable to deflationists. First, two purposes that a formal truth theory can serve are distinguished: one descriptive, the other logical (i.e., to characterise the correctness of inferences involving ‘true’). The chapter argues that the most compelling arguments for the incompatibility of compositional and Tarskian theories concern descriptive theories only. -/- Second, two requirements (...) that any deflationist truth theory intended to serve a logical purpose must satisfy are put forward. These requirements, it is argued, suggest that (i) many well-known compositional and Tarskian theories are acceptable from a deflationist standpoint (including CT); (ii) certain other popular theories of truth (including KF and FS) are not similarly acceptable; (iii) there are no conclusive reasons to impose a conservativeness requirement on deflationary theories of truth. (shrink)

In two recent papers, Bob Hale has attempted to free second-order logic of the 'staggering existential assumptions' with which Quine famously attempted to saddle it. I argue, first, that the ontological issue is at best secondary: the crucial issue about second-order logic, at least for a neo-logicist, is epistemological. I then argue that neither Crispin Wright's attempt to characterize a `neutralist' conception of quantification that is wholly independent of existential commitment, nor Hale's attempt to characterize the second-order domain in terms (...) of definability, can serve a neo-logicist's purposes. The problem, in both cases, is similar: neither Wright nor Hale is sufficiently sensitive to the demands that impredicativity imposes. Finally, I defend my own earlier attempt to finesse this issue, in "A Logic for Frege's Theorem", from Hale's criticisms. (shrink)

It has been known for a few years that no more than Pi-1-1 comprehension is needed for the proof of "Frege's Theorem". One can at least imagine a view that would regard Pi-1-1 comprehension axioms as logical truths but deny that status to any that are more complex—a view that would, in particular, deny that full second-order logic deserves the name. Such a view would serve the purposes of neo-logicists. It is, in fact, no part of my view that, say, (...) Delta-3-1 comprehension axioms are not logical truths. What I am going to suggest, however, is that there is a special case to be made on behalf of Pi-1-1 comprehension. Making the case involves investigating extensions of first-order logic that do not rely upon the presence of second-order quantifiers. A formal system for so-called "ancestral logic" is developed, and it is then extended to yield what I call "Arché logic". (shrink)

The paper provides an alternative interpretation of ‘pair points’, discussed in Beall et al., "On the ternary relation and conditionality", J. of Philosophical Logic 41(3), 595-612. Pair points are seen as points viewed from two different ‘perspectives’ and the latter are explicated in terms of two independent valuations. The interpretation is developed into a semantics using pairs of Kripke models (‘pair models’). It is demonstrated that, if certain conditions are fulfilled, pair models are validity-preserving copies of positive substructural models. This (...) yields a general soundness and completeness result for a variety of (positive) substructural logics with respect to multimodal Kripke frames with binary accessibility relations. In addition, an epistemic interpretation of pair models is provided. (shrink)

The historical consensus is that logical evidence is special. Whereas empirical evidence is used to support theories within both the natural and social sciences, logic answers solely to a priori evidence. Further, unlike other areas of research that rely upon a priori evidence, such as mathematics, logical evidence is basic. While we can assume the validity of certain inferences in order to establish truths within mathematics and test scientifi c theories, logicians cannot use results from mathematics or the empirical sciences (...) without seemingly begging the question. Appeals to rational intuition and analyticity in order to account for logical knowledge are symptomatic of these commitments to the apriority and basicness of logical evidence. This chapter argues that these historically prevalent accounts of logical evidence are mistaken, and that if we take logical practice seriously we fi nd that logical evidence is rather unexceptional, sharing many similarities to the types of evidence appealed to within other research areas. (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)

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)

This paper is a critical evaluation of Kuenne's attempt to define truth via quantification into the position of a sentence.

This article discusses two coextensive concepts of logical consequence that are implicit in the two fundamental logical practices of establishing validity and invalidity for premise-conclusion arguments. The premises and conclusion of an argument have information content (they ?say? something), and they have subject matter (they are ?about? something). The asymmetry between establishing validity and establishing invalidity has long been noted: validity is established through an information-processing procedure exhibiting a step-by-step deduction of the conclusion from the premise-set. Invalidity is established by (...) exhibiting a countermodel satisfying the premises but not the conclusion. The process of establishing validity focuses on information content; the process of establishing invalidity focuses on subject matter. Corcoran's information-theoretic concept of logical consequence corresponds to the former. Tarski's model-theoretic concept of logical consequence formulated in his famous 1936 no-countermodels definition corresponds to the latter. Both are found to be indispensable for understanding the rationale of the deductive method and each complements the other. This study discusses the ontic question of the nature of logical consequence and the epistemic question of the human capabilities presupposed by practical applications of these two concepts as they make validity and invalidity accessible to human knowledge. (shrink)

This collection of papers, celebrating the contributions of Swedish logician Dag Prawitz to Proof Theory, has been assembled from those presented at the Natural Deduction conference organized in Rio de Janeiro to honour his seminal research. Dag Prawitz’s work forms the basis of intuitionistic type theory and his inversion principle constitutes the foundation of most modern accounts of proof-theoretic semantics in Logic, Linguistics and Theoretical Computer Science. The range of contributions includes material on the extension of natural deduction with higher-order (...) rules, as opposed to higher-order connectives, and a paper discussing the application of natural deduction rules to dealing with equality in predicate calculus. The volume continues with a key chapter summarizing work on the extension of the Curry-Howard isomorphism, via methods of category theory that have been successfully applied to linear logic, as well as many other contributions from highly regarded authorities. With an illustrious group of contributors addressing a wealth of topics and applications, this volume is a valuable addition to the libraries of academics in the multiple disciplines whose development has been given added scope by the methodologies supplied by natural deduction. The volume is representative of the rich and varied directions that Prawitz work has inspired in the area of natural deduction. (shrink)

This anthology of the very latest research on truth features the work of recognized luminaries in the field, put together following a rigorous refereeing process. Along with an introduction outlining the central issues in the field, it provides a unique and unrivaled view of contemporary work on the nature of truth, with papers selected from key conferences in 2011 such as Truth Be Told, Truth at Work, Paradoxes of Truth and Denotation and Axiomatic Theories of Truth. Studying the nature of (...) the concept of ‘truth’ has always been a core role of philosophy, but recent years have been a boom time in the topic. With a wealth of recent conferences examining the subject from various angles, this collection of essays recognizes the pressing need for a volume that brings scholars up to date on the arguments. Offering academics and graduate students alike a much-needed repository of today’s cutting-edge work in this vital topic of philosophy, the volume is required reading for anyone needing to keep abreast of developments, and is certain to act as a catalyst for further innovation and research. (shrink)

La teleosemántica es una teoría teleológica de las representaciones mentales, propugnada por David Papineau, que tiene como propósito ofrecer una explicación naturalista y evolucionista de dichas representaciones, en particular de las creencias. Mi objetivo será analizar las creencias y su relación con la verdad en la obra de Papineau. Según Papineau, los contenidos y las representaciones mentales, específicamente las creencias, cumplen funciones derivadas de la evolución biológica de la especie, y correlativamente, la finalidad de las creencias y los contenidos proviene (...) de las funciones biológicas que cada una de ellas tiene. De acuerdo a Papineau, para que las creencias cumplan sus funciones biológicas deben ser verdaderas, es decir, corresponder con la realidad. Defenderé la idea de que, a diferencia de lo que plantea la teleosemántica, la verdad y la falsedad, o más específicamente, los enunciados verdaderos y falsos son doxásticos, es decir, son enunciados que expresan creencias. Las creencias no tienen que ser verdaderas, sino más bien útiles, de manera que el que sean verdaderas o no es un producto secundario de la creencia. (shrink)

What is the source of logical and mathematical truth? This book revitalizes conventionalism as an answer to this question. Conventionalism takes logical and mathematical truth to have their source in linguistic conventions. This was an extremely popular view in the early 20th century, but it was never worked out in detail and is now almost universally rejected in mainstream philosophical circles. Shadows of Syntax is the first book-length treatment and defense of a combined conventionalist theory of logic and mathematics. It (...) argues that our conventions, in the form of syntactic rules of language use, are perfectly suited to explain the truth, necessity, and a priority of logical and mathematical claims, as well as our logical and mathematical knowledge. (shrink)

The book provides a historical and systematic exposition of the semantic theory of truth formulated by Alfred Tarski in the 1930s. This theory became famous very soon and inspired logicians and philosophers. It has two different, but interconnected aspects: formal-logical and philosophical. The book deals with both, but it is intended mostly as a philosophical monograph. It explains Tarski’s motivation and presents discussions about his ideas as well as points out various applications of the semantic theory of truth to philosophical (...) problems. (shrink)

The present contribution might be regarded as a kind of defense of the common sense in logic. It is demonstrated that if the classical negation is interpreted as the minimal negation with n = 2 truth values, then deviant logics can be conceived as extension of the classical bivalent frame. Such classical apprehension of negation is possible in non- classical logics as well, if truth value is internalized and bivalence is replaced by bipartition.

“Dalla filosofia dell’azione alla filosofia della mente” è stato il percorso di alcuni filosofi di nazionalità varia degli anni 1980 – come Paul Churchland negli Stati Uniti o Ansgar Beckermann in Germania – che prima si sono interessati agli aspetti più teorici nella filosofia dell’azione, come il modo di funzionamento delle azioni e la loro spiegazione scientifica, e che poi, con l’arrivo e la diffusione dei personal computers e delle scienze cognitive, hanno ampliato e approfondito questo interesse di ricerca e (...) si sono dedicati alla filosofia della mente più in generale e in particolare alla spiegazione scientifica e filosofica del mentale. Sandro Nannini faceva parte di questo movimento ed è stato uno tra gli inizialmente pochi filosofi italiani che si sono occupati di questi argomenti; successivamente ne è diventato uno dei maggiori specialisti in Italia, proponendo una sua particolare versione di naturalizzazione del mentale. Subordinata agli interessi teorici è stata la sua iniziativa accademica di fondare e promuovere il primo dottorato italiano di ricerca in Scienze Cognitive. Il presente volume tratta dell’opera di Sandro Nannini in contributi che sono riflessioni più o meno specifiche sulle differenti tappe del suo percorso, affrontando temi come l’analisi dell'azione, il libero arbitrio, la discussione di Nannini di vari classici della filosofia, la tendenza del naturalismo a dissolvere la filosofia in un enciclopedismo empirico e la sfida dei qualia e della fenomenologia all’approccio naturalistico alla mente. Il volume contiene inoltre un saggio dello stesso Sandro Nannini, nel quale espone l’ultimo sviluppo della sua filosofia della mente nonché le risposte agli interventi degli altri autori: Mario De Caro, Sara Dellantonio, Rosaria Egidi, Roberta Lanfredini, Christoph Lumer, Paolo Parrini, Pietro Perconti, Claudio Pizzi, Emanuela Scribano e Giuseppe Varnier. (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)

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)

In contemporary North American contexts, to say that a claim is oracular is seriously to undermine its philosophical credibility. My thesis is that this negative judgement of oracularity is unwarranted and that it is rooted in an excessively narrow notion of what constitutes ‘good’ philosophy. More specifically, I argue that oracular utterance is appropriate to the expression of views that regard the phenomena towards which they are directed as radically, non‐systematically integrated wholes. Importantly, such views are falsifiable—or at least as (...) falsifiable as scientific paradigms, which, in one important respect, they resemble. However, I argue further that there is good reason to think that such views cannot, without distortion, be expressed using the systematic‐analytic forms of argumentation that are frequently regarded as essential to the pursuit of philosophy. Yet the questions that they compass, concerning the way in which parts are related to the wholes that they constitute, fall squarely within the purview of traditional metaphysics. Thus, in proscribing oracular utterance we divest ourselves of the opportunity to contemplate world orders of potential philosophical interest that systematic‐analytic argument is incapable of conveying to us. (shrink)

In this sequel to "The logic and meaning of plurals. Part I", I continue to present an account of logic and language that acknowledges limitations of singular constructions of natural languages and recognizes plural constructions as their peers. To this end, I present a non-reductive account of plural constructions that results from the conception of plurals as devices for talking about the many. In this paper, I give an informal semantics of plurals, formulate a formal characterization of truth for the (...) regimented languages that results from augmenting elementary languages with refinements of basic plural constructions of natural languages, and account for the logic of plural constructions by characterizing the logic of those regimented languages. (shrink)

Contemporary accounts of logic and language cannot give proper treatments of plural constructions of natural languages. They assume that plural constructions are redundant devices used to abbreviate singular constructions. This paper and its sequel, "The logic and meaning of plurals, II", aim to develop an account of logic and language that acknowledges limitations of singular constructions and recognizes plural constructions as their peers. To do so, the papers present natural accounts of the logic and meaning of plural constructions that result (...) from the view that plural constructions are, by and large, devices for talking about many things (as such). The account of logic presented in the papers surpasses contemporary Fregean accounts in its scope. This extension of the scope of logic results from extending the range of languages that logic can directly relate to. Underlying the view of language that makes room for this is a perspective on reality that locates in the world what plural constructions can relate to. The papers suggest that reflections on plural constructions point to a broader framework for understanding logic, language, and reality that can replace the contemporary Fregean framework as this has replaced its Aristotelian ancestor. (shrink)

It is a fundamental intuition about truth that the conditions under which a sentence is true are given by what the sentence asserts. My aim in this paper is to show that this intuition captures the concept of truth completely and correctly. This is conceptual deflationism, for it does not go beyond what is asserted by a sentence in order to define the truth status of that sentence. This paper, hence, is a defense of deflationism as a conceptual account of (...) truth. This defense is developed in four stages. In the first stage I present a distinction between two types of deflationism, conceptual and metaphysical. This is the central stage of the argument and its main conclusion is that conceptual deflationism when joined with the principle of bivalence is inconsistent with metaphysical deflationism, that is, conceptual deflationism together with bivalence entails a non-deflationary metaphysical account of truth. In the second and third stages of the argument I argue that the totality of the Tarskian biconditionals, when interpreted as definitional biconditionals, offers a description of the nature of truth. In the fourth, and final, stage of the argument I advance a positive case for conceptual deflationism. I explain how the revision theory of truth provides this sort of deflationism with its best evidence: a clear demonstration of its consistency and a compelling argument for its material adequacy. (shrink)

ABSTRACT Four philosophical concerns about higher-order logic in general and the specific demands placed on it by the neo-logicist project are distinguished. The paper critically reviews recent responses to these concerns by, respectively, the late Bob Hale, Richard Kimberly Heck, and myself. It is argued that these score some successes. The main aim of the paper, however, is to argue that the most serious objection to the applications of higher-order logic required by the neo-logicist project has not been properly understood. (...) The paper concludes by outlining a strategy, prefigured in recent work of Øystein Linnebo, for meeting this objection. (shrink)

True to the spirit of Topoi’s Untimely Reviews section, the present essay is a work of the counterfactual imagination. Suppose that Quine’s “Two Dogmas” had been written and published in the late 1990s rather than the early 1950s. What, in those circumstances, would philosophical commentary look like, especially against the marked developments in Quine’s philosophy in that same period? In short, how would Quine’s “Two Dogmas” stand up as a late 1990s paper rather than an early 1950s paper? Answering that (...) question is my task here. (shrink)

Anthony Everett () argues that those who embrace the reality of fictional entities run into trouble when it comes to specifying criteria of character identity. More specifically, he argues that realists must reject natural principles governing the identity and distinctness of fictional characters due to the existence of fictions which leave it indeterminate whether certain characters are identical and the existence of fictions which say inconsistent things about the identities of their characters. Everett's critique has deservedly drawn much attention and (...) a number of defensive moves have been made by, or on the behalf of, fictional realists. My goal in this paper is to move this debate on a further step. I have three goals: to clarify the importance of Everett's discussion of identity criteria within the context of fictional realism, to reassess Everett's objections to realism in light of the resultant literature, and to develop a novel strategy for responding to Everett's concerns. On the approach to be developed, the problems emerge due to an indeterminacy inherent in the concept of a fictional character itself. (shrink)

I distinguish two ways of developing anti-exceptionalist approaches to logical revision. The first emphasizes comparing the theoretical virtuousness of developed bodies of logical theories, such as classical and intuitionistic logic. I'll call this whole theory comparison. The second attempts local repairs to problematic bits of our logical theories, such as dropping excluded middle to deal with intuitions about vagueness. I'll call this the piecemeal approach. I then briefly discuss a problem I've developed elsewhere for comparisons of logical theories. Essentially, the (...) problem is that a pair of logics may each evaluate the alternative as superior to themselves, resulting in oscillation between logical options. The piecemeal approach offers a way out of this problem andthereby might seem a preferable to whole theory comparisons. I go on to show that reflective equilibrium, the best known piecemeal method, has deep problems of its own when applied to logic. (shrink)

In this paper I argue that there can be genuine (as opposed to merely verbal) disputes about whether a sentence form is logically true or an argument form is valid. I call such disputes ?cases of deviance?, of which I distinguish a weak and a strong form. Weak deviance holds if one disputant is right and the other wrong, but the available evidence is insufficient to determine which is which. Strong deviance holds if there is no fact of the matter. (...) In section 2 I argue that weak deviance need not be trivial and may even be interesting. Section 3 considers what it could mean to say that logic is determined by a theory, especially a theory of meaning, an idea that arises in section 2. In section 4 I discuss the dispute between classical and relevance logicians over entailment and argue that it is a case of strong deviance. Finally, in section 5 I show that the result of the previous section is not absolute but relative to the background logic used in reaching it. (shrink)

1. What are called ‘intuitions’ in philosophy are just applications of our ordinary capacities for judgement. We think of them as intuitions when a special kind of scepticism about those capacities is salient. 2. Like scepticism about perception, scepticism about judgement pressures us into conceiving our evidence as facts about our internal psychological states: here, facts about our conscious inclinations to make judgements about some topic rather than facts about the topic itself. But the pressure should be resisted, for it (...) rests on bad epistemology: specifically, on an impossible ideal of unproblematically identifiable evidence. 3. Our resistance to scepticism about judgement is not simply epistemic conservativism, for we resist it on behalf of others as well as ourselves. A reason is needed for thinking that beliefs tend to be true. 4. Evolutionary explanations of the tendency assume what they should explain. Explanations that appeal to constraints on the determination of reference are more promising. Davidson’s truth-maximizing principle of charity is examined but rejected. 5. An alternative principle is defended on which the nature of reference is to maximize knowledge rather than truth. It is related to an externalist conception of mind on which knowing is the central mental state. 6. The knowledge-maximizing principle of charity explains why scenarios for scepticism about judgement do not warrant such scepticism, although it does not explain how we know in any particular case. We should face the fact that evidence is always liable to be contested in philosophy, and stop using talk of intuition to disguise this unpleasant truth from ourselves. (shrink)

The paper is a critique of the widespread conception of logic as a neutral arbiter between metaphysical theories, one that makes no `substantive’ claims of its own (David Kaplan and John Etchemendy are two recent examples). A familiar observation is that virtually every putatively fundamental principle of logic has been challenged over the last century on broadly metaphysical grounds (however mistaken), with a consequent proliferation of alternative logics. However, this apparent contentiousness of logic is often treated as though it were (...) neutralized by the possibility of studying all these alternative logics within an agreed metalogical framework, typically that of first-order logic with set theory. In effect, metalogic is given the role of neutral arbiter. The paper will consider a variety of examples in which deep logical disputes re-emerge at the meta-level. One case is quantified modal logic, where some varieties of actualism require a modal meta-language (as opposed to the usual non-modal language of possible worlds model theory) in order not to make their denial of the Barcan formula self-defeating. Similarly, on some views the intended model theory for second-order logic can only be given in a second-order metalanguage—this may be needed to avoid versions of Russell’s paradox when the first-order quantifiers are read as absolutely unrestricted. It can be shown that the phenomenon of higher-order vagueness eventually forces fuzzy logical treatments of vagueness to use a fuzzy metalanguage, with consequent repercussions for what first-order principles are validated. The difficulty of proving the completeness of first-order intuitionistic logic on its intended interpretation by intuitionistically rather than just classically valid means is a more familiar example. These case studies will be discussed in some detail to reveal a variety of ways in which even metalogic is metaphysically contested, substantial and non-neutral. (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)

Several recent epistemologists have used understanding-assent links in theories of a priori knowledge and justification, but Williamson influentially argued against the existence of such links. Here I (1) clarify the nature of understanding-assent links and their role in epistemology; (2) clarify and clearly formulate Williamson’s arguments against their existence; (3) argue that Williamson has failed to successfully establish his conclusion; and (4) rebut Williamson’s claim that accepting understanding-assent links amounts to a form of dogmatism.

The axiom of reducibility plays an important role in the logic of Principia Mathematica, but has generally been condemned as an ad hoc non-logical axiom which was added simply because the ramified type theory without it would not yield all the required theorems. In this paper I examine the status of the axiom of reducibility. Whether the axiom can plausibly be included as a logical axiom will depend in no small part on the understanding of propositional functions. If we understand (...) propositional functions as constructions of the mind, it is clear that the axiom is clearly not a logical axiom and in fact makes an implausible claim. I look at two other ways of understanding propositional functions, a nominalist interpretation along the lines of Landini and a realist interpretation along the lines of Linsky and Mares. I argue that while on either of these interpretations it is not easy to see the axiom as a non-logical claim about the world, there are also appear to be difficulties in accepting it as a purely logical axiom. (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)

One of the standard views on plural quantification is that its use commits one to the existence of abstract objects–sets. On this view claims like ‘some logicians admire only each other’ involve ineliminable quantification over subsets of a salient domain. The main motivation for this view is that plural quantification has to be given some sort of semantics, and among the two main candidates—substitutional and set-theoretic—only the latter can provide the language of plurals with the desired expressive power (given that (...) the nominalist seems committed to the assumption that there can be at most countably many names). To counter this approach I develop a modal-substitutional semantics of plural quantification (on which plural variables, roughly speaking, range over ways names could be) and argue for its nominalistic acceptability. (shrink)

Michael Friedman’s Dynamics of Reason is a welcome contribution to the ongoing articulation of philosophical perspectives for understanding the sciences in the context of post-positivist philosophy of science. Two perspectives that have gained advocacy since the demise of the “received view” are Quinean naturalism and Kuhnian relativism. In his 1999 Stanford lectures, Friedman articulates and defends a neo-Kantian perspective for philosophy of science that opposes both of these perspectives. His proffered neo-Kantian perspective is presented within the context of the problem (...) of theory change or “scientific revolutions,” and its main feature is a conception of scientific knowledge that requires “relativized constitutive a priori principles.” The lectures make up the first part of the book; the second part of the book, “Fruits of Discussion,” is a further elaboration and defence of the ideas advanced in the lectures. The resulting book serves as a useful sequel to Friedman’s impressive historical studies in Foundations of Space-Time Theories, Kant and the Exact Sciences, and Reconsidering Logical Positivism. In the preface, Friedman tells us that this book represents the philosophical viewpoint that he has arrived at as a result of completing these works. As such, it is not surprising that the prominent themes of the book are ones that have occupied Friedman’s attention in the past, viz., the importance of a priori principles in the exact sciences, the conventionalism of the logical positivists, and, more generally, an articulation of what remains defensible in neo-Kantian philosophy of science. (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)

A neutralist framework is an account of the second-order quantifiers which does not by itself tell us what the ontological commitments of second-order quantification are, but which does tell us that those commitments cannot exceed those of predication. Recently, Wright has suggested that an inferentialist account of the second-order quantifiers is an adequate neutralist framework. I show that we do not have to become inferentialists in the pursuit of a neutralist framework: such a framework can be established within the semantic (...) tradition. (shrink)

In a recent article, Hofweber presents a new, and surprising, argument for idealism. His argument is surprising because it starts with an apparently innocent premiss from the philosophy of language: that ‘that’-clauses do not refer. I do not think that Hofweber's argument works, and my first aim in this paper is to explain why. However, I agree with Hofweber that what we say about ‘that’-clauses has important metaphysical consequences. My second aim is to argue that, far from leading us into (...) idealism, denying that ‘that’-clauses refer is the first step toward a kind of direct realism about belief. (shrink)

I articulate a Global Best-System Account (GBSA) of laws of nature along broadly Mill–Ramsey–Lewis lines. The guiding idea is that the job of laws is to capture real patterns across time—where a pattern is real if it allows to compress information about matters of particular fact. The GBSA’s key ingredient is a definition of ‘best system’ in terms of a ranking method that meets a number of desiderata: it is rigorously defined; it outputs the ranking based on the candidate systems’ (...) epistemic virtues; it is objective, in that the output does not depend on one’s choice of basic concepts; it avoids two trivialization results (by Lewis, and Arrow-Okasha); and it does not appeal to naturalness, or other metaphysical notions in that vicinity. Although the GBSA is independent of the controversial thesis of Humean Supervenience, it satisfies the weaker thesis that laws of nature supervene on the total physical state of the world. Moreover, the resulting notion of lawhood is hyperintensional, unlike the neighboring notion of nomological necessity. Finally, GBSA-laws do not track naturalness, contra the Lewisian orthodoxy. (shrink)