Logical pluralism has been in vogue since JC Beall and Greg Restall 2006 articulated and defended a new pluralist thesis. Recent criticisms such as Priest 2006a and Field 2009 have suggested that there is a relationship between their type of logical pluralism and the meaning-variance thesis for logic. This is the claim, often associated with Quine 1970, that a change of logic entails a change of meaning. Here we explore the connection between logical pluralism and meaning-variance, both in general and (...) for Beall and Restall's theory specifically. We argue that contrary to what Beall and Restall claim, their type of pluralism is wedded to meaning-variance. We then develop an alternative form of logical pluralism that circumvents at least some forms of meaning-variance. (shrink)

It is a consequence of Quine’s confirmation holism that the logical laws are in principle revisable. Some have worried this is at odds with another dictum in Quine, viz., that any translation which construes speakers as systematically illogical is ipso facto inadequate. In this paper, I try to formulate exactly what the problem is here, and offer a solution to it by (1) disambiguating the term ‘logic,’ and (2) appealing to a Quinean understanding of ‘necessity.’ The result is that the (...) different theses in Quine’s philosophy of logic are to be situated within different contexts of inquiry. (shrink)

Infectious logics are systems that have a truth-value that is assigned to a compound formula whenever it is assigned to one of its components. This paper studies four-valued infectious logics as the basis of transparent theories of truth. This take is motivated as a way to treat different pathological sentences differently, namely, by allowing some of them to be truth-value gluts and some others to be truth-value gaps and as a way to treat the semantic pathology suffered by at least (...) some of these sentences as infectious. This leads us to consider four distinct four-valued logics: one where truth-value gaps are infectious, but gluts are not; one where truth-value gluts are infectious, but gaps are not; and two logics where both gluts and gaps are infectious, in some sense. Additionally, we focus on the proof theory of these systems, by offering a discussion of two related topics. On the one hand, we prove some limitations regarding the possibility of providing standard Gentzen sequent calculi for these systems, by dualizing and extending some recent results for infectious logics. On the other hand, we provide sound and complete four-sided sequent calculi, arguing that the most important technical and philosophical features taken into account to usually prefer standard calculi are, indeed, enjoyed by the four-sided systems. (shrink)

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)

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)

The problematic features of Quine's set theories NF and ML are a result of his replacing the higher-order predicate logic of type theory by a first-order logic of membership, and can be resolved by returning to a second-order logic of predication with nominalized predicates as abstract singular terms. We adopt a modified Fregean position called conceptual realism in which the concepts (unsaturated cognitive structures) that predicates stand for are distinguished from the extensions (or intensions) that their nominalizations denote as singular (...) terms. We argue against Quine's view that predicate quantifiers can be given a referential interpretation only if the entities predicates stand for on such an interpretation are the same as the classes (assuming extensionality) that nominalized predicates denote as singular terms. Quine's alternative of giving predicate quantifiers only a substitutional interpretation is compared with a constructive version of conceptual realism, which with a logic of nominalized predicates is compared with Quine's description of conceptualism as a ramified theory of classes. We argue against Quine's implicit assumption that conceptualism cannot account for impredicative concept-formation and compare holistic conceptual realism with Quine's class Platonism. (shrink)

I examine various claims to the effect that Cantor's Continuum Hypothesis and other problems of higher set theory are ill-posed questions. The analysis takes into account the viability of the underlying philosophical views and recent mathematical developments.

Richard Nisbett's The Geography of Thought is one of several recent works that have highlighted purported differences in thinking patterns between East Asians and Westerners on the basis of empirical research. This has implications for teaching and for other issues such as cultural integration. Based on a framework consisting of three distinct notions of rationality, this paper argues that some of the differences alleged by Nisbett are either not real or exaggerated, and that his geography of thought fails to provide (...) an adequate account of thinking styles across cultures. The paper concludes with a discussion of the implications for teaching and learning critical thinking that can be drawn from the framework developed. (shrink)

In a growing number of papers, one encounters arguments to the effect that certain philosophical views are objectionable because they would imply that there are necessary truths for whose necessity there is no explanation. That is, they imply that there are propositions p such that (a) it is necessary that p, but (b) there is no explanation why it is necessary that p. For short, they imply that there are “brute necessities.” Therefore, the arguments conclude, the views in question should (...) be rejected in favor of rival views under which the necessities would be explained. This style of argument raises a number of important and difficult questions. Do necessary truths really require explanation? Are they not paradigms of truths that either need no explanation or automatically have one, being in some sense self‐explanatory? If some necessary truths do require or admit of explanation, what types of explanation, are available? Are some necessary truths explained by other necessary truths? Are some necessary truths self‐explanatory? Are all necessary truths either self‐explanatory or explained by others? Or are there some necessary truths that are truly brute? This article surveys several representative arguments from brute necessity as well as a variety of answers to the questions above, noting their bearing on arguments from bruteness. (shrink)

In this essay I focus on the idea of the univocity of being, championed by Duns Scotus and given prominence more recently by Deleuze. Although I am interested in how this idea can be established, my primary concern is with something more basic: how the idea can even be properly thought. In the course of exploring this issue, which I do partly by borrowing some ideas about logical syntax from Wittgenstein's Tractatus, I try to show how there can be dialogue (...) between analytic philosophers and those of other traditions. (shrink)

In recent discussions of the problem of truth, Austin's views have been largely overlooked. This is unfortunate, since many of his criticisms aimed at Strawson's redundancy theory carry over to more recent incarnations of deflationism. And unlike contemporary versions of the correspondence theory of truth, Austin's manages properly to situate truth in its conceptual neighbourhood wherein it belongs to “a whole dimension of different appraisals which have something or other to do with the relation between what we say and the (...) facts.” A proper analysis of truth cannot be given apart from a broader study of speech acts. (shrink)

In his 1936 paper,On the Concept of Logical Consequence, Tarski introduced the celebrated definition oflogical consequence: “The sentenceσfollows logicallyfrom the sentences of the class Γ if and only if every model of the class Γ is also a model of the sentenceσ.” [55, p. 417] This definition, Tarski said, is based on two very basic intuitions, “essential for the proper concept of consequence” [55, p. 415] and reflecting common linguistic usage: “Consider any class Γ of sentences and a sentence which (...) follows from the sentences of this class. From an intuitive standpoint it can never happen that both the class Γ consists only of true sentences and the sentenceσis false. Moreover, … we are concerned here with the concept of logical, i.e.,formal, consequence.” [55, p. 414] Tarski believed his definition of logical consequence captured the intuitive notion: “It seems to me that everyone who understands the content of the above definition must admit that it agrees quite well with common usage. … In particular, it can be proved, on the basis of this definition, that every consequence of true sentences must be true.” [55, p. 417] The formality of Tarskian consequences can also be proven. Tarski's definition of logical consequence had a key role in the development of the model-theoretic semantics of modern logic and has stayed at its center ever since. (shrink)

Neste artigo, discutimos em que sentido a verdade é considerada como um objeto matemático na lógica proposicional. Depois de esclarecer como este conceito é usado na lógica clássica, através das noções de tabela de verdade, de função de verdade, de bivaloração, examinamos algumas generalizações desse conceito nas lógicas não clássicas: semânticas matriciais multi-valoradas com três ou quatro valores, semântica bivalente não veritativa, semânticas dos mundos possiveis de Kripke. DOI:10.5007/1808-1711.2010v14n1p31.

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)

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)

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)

Thanks to the work of Kendall Walton, appeals to the notion of pretence (or make-believe) have become popular in philosophy. Now the notion has begun to appear in accounts of truth. My aim here is to assess one of these accounts, namely the ‘constructive methodological deflationism’ put forward by Jc Beall. After introducing the view, I argue that Beall does not manage to overcome the problem of psychological implausibility. Although Beall claims that constructive methodological deflationism supports dialetheism, I argue that (...) it does not, and I show that it in fact provides a classical response to the Liar paradox. (shrink)

Virtually all currently discussed accounts advert to a shift or replacement of a property or properties in describing what happens to the ordinary words in metaphors. And the mechanism of this shift tends to involve an overt or sometimes hidden appeal to similarity, or to some notion that is essentially connected to it. In the first part of the paper, I argue that this route is a dead end, and in the second part I offer my own preferred alternative. That (...) alternative is not argued for, or developed in detail – that is done in my book Objects of Metaphor – but my main aim in the paper is simply showing how radically it differs from the property route. (shrink)

I defend the Received View on scientific theories as developed by Carnap, Hempel, and Feigl against a number of criticisms based on misconceptions. First, I dispute the claim that the Received View demands axiomatizations in first order logic, and the further claim that these axiomatizations must include axioms for the mathematics used in the scientific theories. Next, I contend that models are important according to the Received View. Finally, I argue against the claim that the Received View is intended to (...) make the concept of a theory more precise. Rather, it is meant as a generalizable framework for explicating specific theories. (shrink)

Philosophers are very fond of making non-factualist claims—claims to the effect that there is no fact of the matter as to whether something is the case. But can these claims be coherently stated in the context of classical logic? Some care is needed here, we argue, otherwise one ends up denying a tautology or embracing a contradiction. In the end, we think there are only two strategies available to someone who wants to be a non-factualist about something, and remain within (...) the province of classical logic. But one of these strategies is rather controversial, and the other requires substantially more work than is often supposed. Being a non-factualist is no easy business, and it may not be the most philosophically perspicuous way to go. (shrink)

The project of antirealism is to construct an assertibility semantics on which (1) the truth of statements obeys a recognition condition so that (2) counterexamples are forthcoming to the law of the excluded third and (3) intuitionistic formal predicate logic is provably sound and complete with respect to the associated notion of validity. Using principles of intuitionistic mathematics and employing only intuitionistically correct inferences, we show that prima facie reasonable formulations of (1), (2), and (3) are inconsistent. Therefore, it should (...) not be assumed that the project of anti-realism as it bears upon intuitionistic mathematics and logic can be accomplished. (shrink)

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.

In recent work on a priori justification, one thing about which there is considerable agreement is that the notion of truth in virtue of meaning is bankrupt and infertile. (For the sake of more readable prose, I will use ‘TVM’ as an abbreviation for ‘the notion of truth in virtue of meaning’.) Arguments against the worth of TVM can be found across the entire spectrum of views on the a priori, in the work of uncompromising rationalists (such as BonJour (1998)), (...) of centrist moderates (such as Boghossian (1997)), and of uncompromising empiricists (such as Devitt (2004)). My aim is to dispute this widespread opinion. The outline is as follows: First, §§2-3 consist of preliminary stage-setting. Then, in §4 I will argue that some of the most prevalent arguments against the worth of TVM – in particular, one which is given clear expression by Quine (1970), and is recently reinforced by Boghossian (1997) – do not engage with the core idea motivating TVM. After deflecting this charge of incoherence, the aim of §§5-8 is to work toward developing a useful conception of TVM. (shrink)

Notice that each of (1)–(4) is an instance of a more general pattern. For example, we could replace ‘black’ in (1) with any of a wide range of other adjectives such as ‘furry’ or ‘hungry’ or ‘three-legged’, without rendering the entailment invalid or any less obvious. Similarly, there are a number of verbs that occur in entailments parallel to (3): ‘Moe boiled the water; so the water boiled’; ‘Bart blew up the school; so the school blew up’; ‘Homer sank the (...) boat; so the boat sank’ and so on. (shrink)

Der Kern des Leib-Seele-Problems besteht darin, dass mentale Phänomene (Ereignisse, Eigenschaften, Zustände) Merkmale zu haben scheinen, die es auf den ersten Blick unmöglich machen, diese Phänomene in ein naturalisti- sches Weltbild zu integrieren – sie mit physikalischen Phänomenen zu identifizieren oder auf physikalische Phänomene zu reduzieren.2 Heute stehen hauptsächlich zwei von in diesem Sinne kritischen Merkmalen im Mit- telpunkt des Interesses.3 Das erste ist das Merkmal intentionaler Zustände, einen repräsentationalen oder semantischen Inhalt zu besitzen. Das Problem der Naturalisierung dieser Zustände (...) möchte ich das ‘Problem der Intentiona- lität’ nennen. Das zweite kritische Merkmal ist die Eigenschaft von Wahr- nehmungseindrücken und körperlichen Empfindungen, einen qualitativen Aspekt zu besitzen. Dieses Merkmal beruht auf der Tatsache, dass es auf eine bestimmte Weise ist oder sich auf eine bestimmte Weise anfühlt, in diesen Zuständen zu sein. Das Problem der Naturalisierung dieser Zustände wird gewöhnlich das ‘Qualia-Problem’ genannt. (shrink)

In the recent literature on all things metaontological, discussion of a notorious Meinongian doctrine—the thesis that some objects have no kind of being at all—has been conspicuous by its absence. And this is despite the fact that this thesis is the central element of the noneist metaphysics of Richard Routley (1980) and Graham Priest (2005). In this paper, we therefore examine the metaontological foundations of noneism, with a view to seeing exactly how the noneist's approach to ontological inquiry differs from (...) the orthodox Quinean one. We proceed by arguing that the core anti-Quinean element in noneism has routinely been misidentified: rather than concerning Quine's thesis that to be is to be the value of a variable, the real difference is that the noneist rejects what we identify as Quine's “translate-and-deflate” methodology. In rejecting this aspect of Quinean orthodoxy, the noneist is in good company: many of those who think that questions of fundamentality should be the proper focus of ontological inquiry can be read as rejecting it too. Accordingly, we then examine the differences between the noneist's conception of ontology and that offered by the fundamentalist. We argue that these two anti-Quinean approaches differ in terms of their respective conceptions of the theoretical role associated with the notion of being. And the contrast that emerges between them is, in the end, an explanatory one. (shrink)

Écrire un livre sur les fondements empiriques de la signification qui reprenne la question tant débattue de la critique de l'analycité, de la traduction radicale et de l'indétermination de la traduction, d'un point de vue éclairant, précis, et renouvelé à bien des égards, est la gageure que relève Martin Montminy avec son excellent livre Les fondements empiriques de la signification. La thèse simple mais convaincante de l'auteur est que la critique de l'analycité et de la distinction entre analytique et synthétique, (...) comme critique de toute approche normative de la signification, est la voie d'entrée, le fil directeur et l'argument central des différentes thèses de Quine sur l'épistémologie naturalisée, le holisme épistémologique et l'indétermination de la traduction. C'est par ce biais qu'il défend une approche empirique de la signification liant toute théorie sémantique à des données empiriques en principe accessibles à un observateur. Par ce fil directeur, Montminy, dans une argumentation toujours claire et explicite, offre à la fois une introduction pédagogique au. (shrink)

It is a standard feature of the BSA and its variants that systematizations of the world competing to be the best must be expressed in the same language. This paper argues that such single language privileging is problematic because it enhances the objection that the BSA is insufficiently objective, and it breaks the parallel between the BSA and scientific practice by not letting laws and basic kinds be identified/discovered together. A solution to these problems and the ones that prompt single (...) language privileging is proposed in the form of privileging the best system competition. (shrink)

Ascriptions of truth give rise to an explanatory asymmetry. For instance, we accept ‘ is true because Rex is barking’ but reject ‘Rex is barking because is true’. Benjamin Schnieder and other philosophers have recently proposed a fresh explanation of this asymmetry : they have suggested that the asymmetry has a conceptual rather than a metaphysical source. The main business of this paper is to assess this proposal, both on its own terms and as an option for deflationists. I offer (...) a pair of objections to the proposal and defend them from counter-objections. To conclude, I discuss how else to explain the asymmetry, and set out the implications for deflationism and correspondence theories of truth. (shrink)

We construct an extension P of the standard language of classical propositional logic by adjoining to the alphabet of a new category of logical-pragmatic signs. The well formed formulas of are calledradical formulas (rfs) of P;rfs preceded by theassertion sign constituteelementary assertive formulas of P, which can be connected together by means of thepragmatic connectives N, K, A, C, E, so as to obtain the set of all theassertive formulas (afs). Everyrf of P is endowed with atruth value defined classically, (...) and everyaf is endowed with ajustification value, defined in terms of the intuitive notion of proof and depending on the truth values of its radical subformulas. In this framework, we define the notion ofpragmatic validity in P and yield a list of criteria of pragmatic validity which hold under the assumption that only classical metalinguistic procedures of proof be accepted. We translate the classical propositional calculus (CPC) and the intuitionistic propositional calculus (IPC) into the assertive part of P and show that this translation allows us to interpret Intuitionistic Logic as an axiomatic theory of the constructive proof concept rather than an alternative to Classical Logic. Finally, we show that our framework provides a suitable background for discussing classical problems in the philosophy of logic. (shrink)

A common objection against deflationist theories of truth is that they cannot do justice to the correspondence intuition, i.e. the intuition that there is an explanatory relationship between, for instance, the truth of ‘Snow is white’ and snow's being white. We scrutinize two attempts to meet this objection and argue that both fail. We then propose a new response to the objection which, first, sheds doubt on the correctness of the correspondence intuition and, second, seeks to explain how we may (...) nonetheless have come to have that intuition. (shrink)

Quine’s notion of fact of the matter has received very little attention, although a good grasp of it is crucial to an understanding of some of Quine’s famous formulations of the indeterminacy of translation thesis. The notion is used and cited by many but has to my knowledge never been thoroughly analysed. In the present article, I attempt to analyse and clarify it. In the first section, my exposition focuses on the relations Quine has developed between his notion of fact (...) of the matter and his views on physicalism and ontology. The main conclusion of this section is that Quine’s notion of fact of the matter is ontological. That is to say, for Quine, the notion concerns extralinguistic reality, which is ultimately described by physics. In the second section, I try to show what relations Quine sees between facts of the matter and truth. The main conclusion of this section is that, for Quine, facts of the matter determine truth. This determination is to be understood in the context of Quine’s genetic approach to evidence, which reveals that it is through the mechanism of conditioned response that facts of the matter determine truth. It is hoped that the present analyses will shed new light on Quine’s controversial indeterminacy of translation thesis as well as on the asymmetry that Quine sees between that thesis and underdetermination of theory. (shrink)

The aim of this paper is show a global strategy for defining and connecting logical criteria. Three partial criteria are distinguished: transparency for expressions, topic neutrality for consequence relation, and universality for theories. A global criterion is suggested, and proved to be fulfilled by classical and intuionistic logic.