Consequence is at the heart of logic; an account of consequence, of what follows from what, offers a vital tool in the evaluation of arguments. Since philosophy itself proceeds by way of argument and inference, a clear view of what logical consequence amounts to is of central importance to the whole discipline. In this book JC Beall and Greg Restall present and defend what thay call logical pluralism, the view that there is more than one genuine deductive consequence relation, a (...) position which has profound implications for many linguists as well as for philosophers. We should not search for one true logic, since there are many. (shrink)

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

Tarski and Mautner proposed to characterize the "logical" operations on a given domain as those invariant under arbitrary permutations. These operations are the ones that can be obtained as combinations of the operations on the following list: identity; substitution of variables; negation; finite or infinite disjunction; and existential quantification with respect to a finite or infinite block of variables. Inasmuch as every operation on this list is intuitively "logical", this lends support to the Tarski-Mautner proposal.

Logic is usually thought to concern itself only with features that sentences and arguments possess in virtue of their logical structures or forms. The logical form of a sentence or argument is determined by its syntactic or semantic structure and by the placement of certain expressions called “logical constants.”[1] Thus, for example, the sentences Every boy loves some girl. and Some boy loves every girl. are thought to differ in logical form, even though they share a common syntactic and semantic (...) structure, because they differ in the placement of the logical constants “every” and “some”. By contrast, the sentences Every girl loves some boy. and Every boy loves some girl. are thought to have the same logical form, because “girl” and “boy” are not logical constants. Thus, in order to settle questions about logical form, and ultimately about which arguments are logically valid and which sentences logically true, we must distinguish the “logical constants” of a language from its nonlogical expressions. (shrink)

This study looks to the work of Tarski's mentors Stanislaw Lesniewski and Tadeusz Kotarbinski, and reconsiders all of the major issues in Tarski scholarship in light of the conception of Intuitionistic Formalism developed: semantics, truth, paradox, logical consequence.

Before the law sits a gatekeeper. To this gatekeeper comes a man from the country who asks to gain entry into the law. But the gatekeeper says that he cannot grant him entry at the moment. The man thinks about it and then asks if he will be allowed to come in sometime later on. “It is possible,” says the gatekeeper, “but not now.”—Franz Kafka..

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)

There are two dominant approaches to quantification: the Fregean and the Tarskian. While the Tarskian approach is standard and familiar, deep conceptual objections have been pressed against its employment of variables as genuine syntactic and semantic units. Because they do not explicitly rely on variables, Fregean approaches are held to avoid these worries. The apparent result is that the Fregean can deliver something that the Tarskian is unable to, namely a compositional semantic treatment of quantification centered on truth and reference. (...) We argue that the Fregean approach faces the same choice: abandon compositionality or abandon the centrality of truth and reference to semantic theory. Indeed, we argue that developing a fully compositional semantics in the tradition of Frege leads to a typographic variant of the most radical of Tarskian views: variabilism, the view that names should be modeled as Tarskian variables. We conclude with the consequences of this result for Frege's distinction between sense and reference. (shrink)

The period from 1900 to 1935 was particularly fruitful and important for the development of logic and logical metatheory. This survey is organized along eight "itineraries" concentrating on historically and conceptually linked strands in this development. Itinerary I deals with the evolution of conceptions of axiomatics. Itinerary II centers on the logical work of Bertrand Russell. Itinerary III presents the development of set theory from Zermelo onward. Itinerary IV discusses the contributions of the algebra of logic tradition, in particular, Löwenheim (...) and Skolem. Itinerary V surveys the work in logic connected to the Hilbert school, and itinerary V deals specifically with consistency proofs and metamathematics, including the incompleteness theorems. Itinerary VII traces the development of intuitionistic and many-valued logics. Itinerary VIII surveys the development of semantical notions from the early work on axiomatics up to Tarski's work on truth. (shrink)

This paper examines from a historical perspective Tarski's 1936 essay, "On the concept of logical consequence." I focus on two main aims. The primary aim is to show how Tarski's definition of logical consequence satisfies two desiderata he himself sets forth for it: (1) it must declare logically correct certain formalizations of the -rule and (2) it must allow for variation of the individual domain in the test for logical consequence. My arguments provide a refutation of some interpreters of Tarski, (...) and notably John Etchemendy, who have claimed that his definition does not satisfy those desiderata. A secondary aim of the paper is to offer some basic elements for an understanding of Tarski's definition in the historical logico-philosophical context in which it was proposed. Such historical understanding provides useful insights on Tarski's informal ideas on logical consequence and their internal cohesion. (shrink)

Truth is one of the central subjects in philosophy. It is also one of the largest. Truth has been a topic of discussion in its own right for thousands of years. Moreover, a huge variety of issues in philosophy relate to truth, either by relying on theses about truth, or implying theses about truth.

In his classic 1936 essay "On the Concept of Logical Consequence", Alfred Tarski used the notion of satisfaction to give a semantic characterization of the logical properties. Tarski is generally credited with introducing the model-theoretic characterization of the logical properties familiar to us today. However, in his book, The Concept of Logical Consequence, Etchemendy argues that Tarski's account is inadequate for quite a number of reasons, and is actually incompatible with the standard model-theoretic account. Many of his criticisms are meant (...) to apply to the model-theoretic account as well. In this paper, I discuss the following four critical charges that Etchemendy makes against Tarski and his account of the logical properties: (1) (a) Tarski's account of logical consequence diverges from the standard model-theoretic account at points where the latter account gets it right. (b) Tarski's account cannot be brought into line with the model-theoretic account, because the two are fundamentally incompatible. (2) There are simple counterexamples (enumerated by Etchemendy) which show that Tarski's account is wrong. (3) Tarski committed a modal fallacy when arguing that his account captures our pre-theoretical concept of logical consequence, and so obscured an essential weakness of the account. (4) Tarski's account depends on there being a distinction between the "logical terms" and the "non-logical terms" of a language, but (according to Etchemendy) there are very simple (even first-order) languages for which no such distinction can be made. Etchemendy's critique raises historical and philosophical questions about important foundational work. However, Etchemendy is mistaken about each of these central criticisms. In the course of justifying that claim, I give a sustained explication and defense of Tarski's account. Moreover, since I will argue that Tarski's account and the model theoretic account really do come to the same thing, my subsequent defense of Tarski's account against Etchemendy's other attacks doubles as a defense against criticisms that would apply equally to the familiar model-theoretic account of the logical properties. (shrink)

I want to promote what I shall call ‘the identity theory of truth’. I suggest that other accounts put forward as theories of truth are genuine rivals to it, but are unacceptable. A certain conception of thinkables belongs with the identity theory’s conception of truth. I introduce these conceptions in Part I, by reference to John McDowell’s Mind and World; and I show why they have a place in an identity theory, which I introduce by reference to Frege. In Part (...) II, I elaborate on the conception of thinkables, with a view to demonstrating that the identity theory’s conception of truth is defensible. Part III is concerned with the theory’s relation to some recent work on the concept of truth: I hope to show that the identity theorist not only has a defensible conception of truth, but also, in the present state of play, has appropriate ambitions. (shrink)

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)

Doing Worlds with Words throws light on the problem of meaning as the meeting point of linguistics, logic and philosophy, and critically assesses the possibilities and limitations of elucidating the nature of meaning by means of formal logic, model theory and model-theoretical semantics. The main thrust of the book is to show that it is misguided to understand model theory metaphysically and so to try to base formal semantics on something like formal metaphysics; rather, the book states that model theory (...) and similar tools of the analysis of language should be understood as capturing the semantically relevant, especially inferential, structure of language. From this vantage point, the reader gains a new light on many of the traditional concepts and problems of logic and philosophy of language, such as meaning, reference, truth and the nature of formal logic. (shrink)

Bertrand Russell, in the second of his 1914 Lowell lectures, Our Knowledge of the External World, asserted famously that ‘every philosophical problem, when it is subjected to the necessary analysis and purification, is found either to be not really philosophical at all, or else to be, in the sense in which we are using the word, logical’ (Russell 1993, p. 42). He went on to characterize that portion of logic that concerned the study of forms of propositions, or, as he (...) called them, ‘logical forms’. This portion of logic he called ‘philosophical logic’. Russell asserted that ... some kind of knowledge of logical forms, though with most people it is not explicit, is involved in all understanding of discourse. It is the business of philosophical logic to extract this knowledge from its concrete integuments, and to render it explicit and pure. (p. 53) Perhaps no one still endorses quite this grand a view of the role of logic and the investigation of logical form in philosophy. But talk of logical form retains a central role in analytic philosophy. Given its widespread use in philosophy and linguistics, it is rather surprising that the concept of logical form has not received more attention by philosophers than it has. The concern of this paper is to say something about what talk of logical form comes to, in a tradition that stretches back to (and arguably beyond) Russell’s use of that expression. This will not be exactly Russell’s conception. For we do not endorse Russell’s view that propositions are the bearers of logical form, or that appeal to propositions adds anything to our understanding of what talk of logical form comes to. But we will be concerned to provide an account responsive to the interests expressed by Russell in the above quotations, though one clarified of extraneous elements, and expressed precisely. For this purpose, it is important to note that the concern expressed by Russell in the above passages, as the surrounding text makes clear, is a concern not just with logic conceived narrowly as the study of logical terms, but with propositional form more generally, which includes, e.g., such features as those that correspond to the number of argument places in a propositional function, and the categories of objects which propositional.... (shrink)

It is shown that the logical truth of instances of the T-schema is incompatible with the formal nature of logical truth. In particular, since the formality of logical truth entails that the set of logical truths is closed under substitution, the logical truth of T-schema instances entails that all sentences are logical truths.

There is an incompatibility between the deflationist approach to truth, which makes truth transparent on the basis of an antecedent grasp of meaning, and the traditional endeavour, exemplified by Davidson, to explicate meaning through of truth. I suggest that both parties are in the explanatory red: deflationist lack a non-truth-involving theory of meaning and Davidsonians lack a non-deflationary account of truth. My focus is on the attempts of the latter party to resolve their problem. I look in detail at Davidson's (...) more recent work and suggest that it seeks to articulate a primitive notion of truth that may balance between a notion that collapses into deflationism and one that is wholly subsumed under a general theory of interpretation. I conclude that this tightrope walk is ultimately unsuccessful. Equally, however, some reasons are provided for thinking that deflationism might be equally unsuccessful with its problem. 'Truth or meaning?' remains an open question. (shrink)

We examine a contribution L. Susan Stebbing made to the understanding of critical thinking and its relation to formal logic. Stebbing took expertise in formal logic to authorise logical intervention in public debate, specifically in assessing of the validity of everyday reasoning. She held, however, that formal logic is purely the study of logical form. Given the problems of ascertaining logical form in any particular instance, and that logical form does not always track informal validity, it is difficult to see (...) how she could justify her belief in logical interventionism. Her answer to this problem is the contribution we explore here. It involves the view that although the logician’s expertise is not sufficient to assess arguments made in everyday contexts on its own, it nevertheless plays a unique role in giving systematicity and direction to the critique of such arguments, in particular, in public debate. (shrink)

Alfred Tarski’s refinement of an account of truth into a formal system that turns on the acceptance of Convention-T has had a lasting impact on philosophical logic, especially work concerning truth, meaning, and other semantic notions. In a series of studies completed from the 1930s to the 1960s, Arne Næss collected and analysed intuitive responses from non-philosophers to questions concerning truth, synonymy, certainty, and probability. Among the formulations of truth studied by Næss were practical variants of expressions of the form (...) “p’ is true if and only if p’. This paper calls attention to a series of experimental results Næss overlooked in his original study. These data collectively suggest that acceptance of expressions of the form “p’ is true if and only if p’ varies according to what kind of statement p is. (shrink)

John Etchemendy has argued that it is but "a fortuitous accident" that Tarski's work on truth has any signifance at all for semantics. I argue, in response, that Etchemendy and others, such as Scott Soames and Hilary Putnam, have been misled by Tarski's emphasis on definitions of truth rather than theories of truth and that, once we appreciate how Tarski understood the relation between these, we can answer Etchemendy's implicit and explicit criticisms of neo-Davidsonian semantics.

In this article I describe and evaluate the debate that surrounds the proper interpretation of Tarski’s account of logical consequence given in his classic 1936 article ‘On the concept of logical consequence’. In the late 1980s Etchemendy argued that the familiar model theoretic account of logical consequence is not to be found in Tarski’s original article. Whereas the contemporary account of logical consequence is a variable‐domain conception – in that it calls for a reinterpretation of the domain of variation of (...) the quantifiers when evaluating logical consequence –, no such reinterpretation is found in Tarski’s original account, which was rather based on a ‘fixed‐domain’ conception. Etchemendy’s claims have sparked a debate on Tarski’s conception of logical consequence with important contributions by, among others, Bach, Bays, Corcoran, Gómez‐Torrente, Mancosu, Ray, Sagüillo, and Sher. (shrink)

It is often argued that the combination of deflationism about truth and the truth-conditional theory of meaning is impossible for reasons of circularity. I distinguish, and reject, two strains of circularity argument. Arguments of the first strain hold that the combination has a circular account of the order in which one comes to know the meaning of a sentence and comes to know its truth condition. I show that these arguments fail to identify any circularity. Arguments of the second strain (...) hold that the combination has a circular explanation of the ideas or concepts of meaning and truth. I show that these arguments identify a genuine, but acceptable, circularity. (shrink)

I argue that recent defenses of the view that in 1936 Tarski required all interpretations of a language to share one same domain of quantification are based on misinterpretations of Tarski’s texts. In particular, I rebut some criticisms of my earlier attack on the fixed-domain exegesis and I offer a more detailed report of the textual evidence on the issue than in my earlier work. I also offer new considerations on subsisting issues of interpretation concerning Tarski’s views on the logical (...) correctness of certain omega-arguments, on the Tarskian proof that Etchemendy took to be modal and fallacious, and on Tarski’s appeals to the “common concept of consequence”. (shrink)

This paper concerns Tarski’s use of the term “model” in his 1936 paper “On the Concept of Logical Consequence.” Against several of Tarski’s recent defenders, I argue that Tarski employed a non-standard conception of models in that paper. Against Tarski’s detractors, I argue that this non-standard conception is more philosophically plausible than it may appear. Finally, I make a few comments concerning the traditionally puzzling case of Tarski’s ω-rule example.

Hilary Putnam's famous arguments criticizing Tarski's theory of truth are evaluated. It is argued that they do not succeed to undermine Tarski's approach. One of the arguments is based on the problematic idea of a false instance of T-schema. The other ignores various issues essential for Tarski's setting such as language-relativity of truth definition.

P.F. Strawson contributed to many philosophical domains, including the philosophy of language, the history of philosophy, metaphysics, moral philosophy and philosophical methodology. Most of his contributions in these areas have influenced contemporary debates, either because his views are still defended or because they are still considered worthy of detailed responses. His views on the philosophy of logic have been only rarely discussed, however. My aim in this paper is threefold. First, I provide a systematic account of Strawson’s philosophy of logic. (...) I argue that Strawson is an important predecessor of logical expressivism, a contemporary position in the philosophy of logic most notably defended by Robert Brandom. My main focus is on Strawson’s largely-neglected 1982 paper ‘Logical Form and Logical Constants’, which contains his most mature ideas on the topic. Second, while Strawson’s position is of historical and independent philosophical interest, I argue that he leaves many points unclear. Finally, I propose several clarifications of Strawson’s position. (shrink)

Our standard model-theoretic definition of logical consequence is originally based on Alfred Tarski’s (1936) semantic definition, which, in turn, is based on Rudolf Carnap’s (1934) similar definition. In recent literature, Tarski’s definition is described as a conceptual analysis of the intuitive ‘everyday’ concept of consequence or as an explication of it, but the use of these terms is loose and largely unaccounted for. I argue that the definition is not an analysis but an explication, in the Carnapian sense: the replacement (...) of the inexact everyday concept with an exact one. Some everyday intuitions were thus brought into a precise form, others were ignored and forgotten. How exactly did the concept of logical consequence change in this process? I suggest that we could find some of the forgotten intuitions in Bernard Bolzano’s (1837) definition of ‘deducibility’, which is traditionally viewed as the main precursor of Tarski’s definition from a time before formalized languages. It turns out that Bolzano’s definition is subject to just the kind of natural features—paradoxicality of everyday language, Platonism about propositions, and dependence on the external world—that Tarski sought to tame by constructing an artificial concept for the special needs of mathematical logic. (shrink)

In a series of publications beginning in the 1980s, John Etchemendy has argued that the standard semantical account of logical consequence, due in its essentials to Alfred Tarski, is fundamentally mistaken. He argues that, while Tarski's definition requires us to classify the terms of a language as logical or non-logical, no such division is guaranteed to deliver the correct extension of our pre-theoretical or intuitive consequence relation. In addition, and perhaps more importantly, Tarski's account is claimed to be incapable of (...) explaining an essential modal/epistemological feature of consequence, namely, its necessity and apriority. Bernard Bolzano (1781-1848) is widely recognized as having anticipated Tarski's definition in his Wissenschaftslehre (or Theory of Science ) of 1837. Because of the similarities between his account and Tarski's, Etchemendy's arguments have also been extended to cover Bolzano. The purpose of this article is to consider Bolzano's theory in the light of these criticisms. We argue that, due to important differences between Bolzano's and Tarski's theories, Etchemendy's objections do not apply immediately to Bolzano's account of consequence. Moreover, Bolzano's writings contain the elements of a detailed philosophical response to Etchemendy. (shrink)

The paper discusses what kind of truth bearer, or truth-ascription, a deflationist should take as primary. I first present number of arguments against a sententialist view. I then present a deflationary theory which takes propositions as primary, and try to show that it deals neatly with a wide range of linguistic data. Next, I consider both the view that there is no primary truth bearer, and the most common account of sentence truth given by deflationists who take propositions as primary, (...) and argue that they both attribute an implausible type of ambiguity to “true”. This can be avoided, however, if truth-ascriptions to sentences are taken as a certain form of pragmatic ellipses. I end by showing how this hypothesis accommodates a number of intuitions involving truth-ascriptions to sentences. (shrink)

The paper presents an argument against a "metaphysical" conception of logic according to which logic spells out a specific kind of mathematical structure that is somehow inherently related to our factual reasoning. In contrast, it is argued that it is always an empirical question as to whether a given mathematical structure really does captures a principle of reasoning. (More generally, it is argued that it is not meaningful to replace an empirical investigation of a thing by an investigation of its (...) a priori analyzable structure without paying due attention to the question of whether it really is the structure of the thing in question.) It is proposed to elucidate the situation by distinguishing two essentially different realms with which our reason must deal: "the realm of the natural", constituted by the things of our empirical world, and "the realm of the formal", constituted by the structures that we use as "prisms" to view, to make sense of, and to reconstruct the world. It is suggested that this vantage point may throw light on many foundational problems of logic. (shrink)

The aim of this article is to show that, just as in recent years Cobreros, Egré, Ripley and van Rooij have provided a non-transitive counterpart of classical logic (i.e. one in which all classically acceptable inferences are valid but Cut and other metainferences are not), the same can be done for every Tarskian logic, with full generality. To establish this fact, a semantic approach is taken by showing that appropriate structures can be devised to characterize a non-transitive counterpart of every (...) Tarskian logic, starting from the logical matrices that are usually taken to render them. (shrink)

Many commentators on Alfred Tarski have, following Hartry Field, claimed that Tarski's truth-definition was motivated by physicalism—the doctrine that all facts, including semantic facts, must be reducible to physical facts. I claim, instead, that Tarski did not aim to reduce semantic facts to physical ones. Thus, Field's criticism that Tarski's truth-definition fails to fulfill physicalist ambitions does not reveal Tarski to be inconsistent, since Tarski's goal is not to vindicate physicalism. I argue that Tarski's only published remarks that speak approvingly (...) of physicalism were written in unusual circumstances: Tarski was likely attempting to appease an audience of physicalists that he viewed as hostile to his ideas. In later sections I develop positive accounts of: (1) Tarski's reduction of semantic concepts; (2) Tarski's motivation to develop formal semantics in the particular way he does; and (3) the role physicalism plays in Tarski's thought. (shrink)

Tarski’s pioneering work on truth has been thought by some to motivate a robust, correspondence-style theory of truth, and by others to motivate a deflationary attitude toward truth. I argue that Tarski’s work suggests neither; if it motivates any contemporary theory of truth, it motivates conceptual primitivism, the view that truth is a fundamental, indefinable concept. After outlining conceptual primitivism and Tarski’s theory of truth, I show how the two approaches to truth share much in common. While Tarski does not (...) explicitly accept primitivism, the view is open to him, and fits better with his formal work on truth than do correspondence or deflationary theories. Primitivists, in turn, may rely on Tarski’s insights in motivating their own perspective on truth. I conclude by showing how viewing Tarski through the primitivist lens provides a fresh response to some familiar charges from Putnam and Etchemendy. (shrink)

In the early 20th century, scepticism was common among philosophers about the very meaningfulness of the notion of truth – and of the related notions of denotation, definition etc. (i.e., what Tarski called semantical concepts). Awareness was growing of the various logical paradoxes and anomalies arising from these concepts. In addition, more philosophical reasons were being given for this aversion.1 The atmosphere changed dramatically with Alfred Tarski’s path-breaking contribution. What Tarski did was to show that, assuming that the syntax of (...) the object language is specified exactly enough, and that the metatheory has a certain amount of set theoretic power,2 one can explicitly define truth in the object language. And what can be explicitly defined can be eliminated. It follows that the defined concept cannot give rise to any inconsistencies (that is, paradoxes). This gave new respectability to the concept of truth and related notions. Nevertheless, philosophers’ judgements on the nature and philosophical relevance of Tarski’s work have varied. It is my aim here to review and evaluate some threads in this debate. (shrink)

The papers where Gerhard Gentzen introduced natural deduction and sequent calculi suggest that his conception of logic differs substantially from the now dominant views introduced by Hilbert, Gödel, Tarski, and others. Specifically, (1) the definitive features of natural deduction calculi allowed Gentzen to assert that his classical system nk is complete based purely on the sort of evidence that Hilbert called ?experimental?, and (2) the structure of the sequent calculi li and lk allowed Gentzen to conceptualize completeness as a question (...) about the relationships among a system's individual rules (as opposed to the relationship between a system as a whole and its ?semantics?). Gentzen's conception of logic is compelling in its own right. It is also of historical interest, because it allows for a better understanding of the invention of natural deduction and sequent calculi. (shrink)

This book is an inquiry into the philosophical concern with truth as one joint subject in philosophy of language and metaphysics and presents a theory of truth, substantive perspectivism (SP). Emphasizing our basic pre-theoretic understanding of truth (i.e., what is captured by the axiomatic thesis of truth that the nature of truth consists in capturing the way things are), and in the deflationism vs. substantivism debate background, SP argues for the substantive nature of non-linguistic truth and its notion’s indispensable substantive (...) explanatory role, both of which are not only intrinsically beyond what the linguistic function of the truth predicate can tell but are fundamentally related to the raison d’être of the truth predicate. Taking a holistic approach, SP endeavors to do justice to various reasonable perspectives, which are somehow contained in many competing accounts of truth, through a coordinate system: SP interprets such perspectives as distinct but related perspective-elaboration principles that distinctively (regarding distinct dimensions of the truth concern and/or for the sake of distinct purposes) elaborate, but are also unified by, the truth axiom thesis. To look at the issue from a broader vision, the book also takes a cross-tradition approach exploring the relationship between Daoist thinking of truth and thinking about truth in analytic philosophy.This book will enhance our systematic understanding of the issue through its holistic approach, broaden our vision on the issue via its cross-tradition approach, and enrich the conceptual and explanatory resources in treating the issue. (shrink)

A hallmark of correspondence theories of truth is the principle that sentences are made true by some truth-makers. A well-known objection to treating Tarski’s definition of truth as a correspondence theory has been put forward by Donald Davidson. He argued that Tarski’s approach does not relate sentences to any entities (like facts) to which true sentences might correspond. From the historical viewpoint, it is interesting to observe that Tarski’s philosophical teacher Tadeusz Kotarbinski advocated an ontological doctrine of reism which accepted (...) only concrete individuals and rejected all such abstract entities as facts, states of affairs, properties, and sets. Kotarbinski’s physicalism influenced Tarski who also avoided concepts like “fact” and “property” in his theory of truth, but—unlike Kotarbinski—he used freely set-theoretical terminology. In his mature work in model theory in the 1950s, Tarski used systematically the notion of a relational system (i.e., a domain of objects with designated elements, subsets, and relations). Wilfrid Hodges has argued that the notions of “structure” and “truth in a structure” appeared in Tarski’s work only in 1950. In my view, one can find the main ingredients of the model-theoretic account of truth already in the 1930s. These considerations suggest, against Davidson, that Tarski’s definition presupposes that material truth is always related to some kind of truth-maker. Further, facts as truth-makers can be reconstructed by employing the resources of model theory. (shrink)

Philosopher’s judgements on the philosophical value of Tarski’s contributions to the theory of truth have varied. For example Karl Popper, Rudolf Carnap, and Donald Davidson have, in their different ways, celebrated Tarski’s achievements and have been enthusiastic about their philosophical relevance. Hilary Putnam, on the other hand, pronounces that “[a]s a philosophical account of truth, Tarski’s theory fails as badly as it is possible for an account to fail.” Putnam has several alleged reasons for his dissatisfaction,1 but one of them, (...) the one I call the modal objection (cf. Raatikainen 2003), has been particularly influential. In fact, very similar objections have been presented over and over again in the literature. Already in 1954, Arthur Pap had criticized Tarski’s account with a similar argument (Pap 1954). Moreover, both Scott Soames (1984) and John Etchemendy (1988) use, with an explicit reference to Putnam, similar modal arguments in relation to Tarski. Richard Heck (1997), too, shows some sympathy for such considerations. Simon Blackburn (1984, Ch. 8) has put forward a related argument against Tarski. Recently, Marian David has criticized Tarski’s truth definition with an analogous argument as well (David 2004, p. 389-390).2 This line of argument is thus apparently one of the most influential critiques of Tarski. It is certainly worthy of serious attention. Nevertheless, I shall argue that, given closer scrutiny, it does not present such an acute problem for the Tarskian approach to truth as many philosophers think. But I also believe that it is important to understand clearly why this is so. Moreover, I think that a careful consideration of the issue illuminates certain important but somewhat neglected aspects of the Tarskian approach. (shrink)

We shift attention from the development of model theory for demarcated languages to the development of this theory for fragments of a language. Although it is often assumed that model theory for demarcated languages is not compatible with a universalist conception of logic, no one has denied that model theory for fragments of a language can be compatible with that conception. It thus seems unwarranted to ignore the universalist tradition in the search for the origins and development of model theory. (...) This point is illustrated by Carnap’s early semantics and model theory, which he developed within a type theoretical framework and which stand out both for their universalistic treatment and for certain idiosyncratic technicalities by which the construction is supported. One special property is that individuals are context relative in Carnap’s system. This leads to a model theory in which the model domains are more flexible than has been suggested in the literature. (shrink)

In "Logical consequence: A defense of Tarski" (Journal of Philosophical Logic, vol. 25, 1996, pp. 617-677), Greg Ray defends Tarski's account of logical consequence against the criticisms of John Etchemendy. While Ray's defense of Tarski is largely successful, his attempt to give a general proof that Tarskian consequence preserves truth fails. Analysis of this failure shows that de facto truth preservation is a very weak criterion of adequacy for a theory of logical consequence and should be replaced by a stronger (...) absence-of-counterexamples criterion. It is argued that the latter criterion reflects the modal character of our intuitive concept of logical consequence, and it is shown that Tarskian consequence can be proved to satisfy this criterion for certain choices of logical constants. Finally, an apparent inconsistency in Ray's interpretation of Tarski's position on the modal status of the consequence relation is noted. (shrink)