Adding a transparent truth predicate to a language completely governed by classical logic is not possible. The trouble, as is well-known, comes from paradoxes such as the Liar and Curry. Recently, Cobreros, Egré, Ripley and van Rooij have put forward an approach based on a non-transitive notion of consequence which is suitable to deal with semantic paradoxes while having a transparent truth predicate together with classical logic. Nevertheless, there are some interesting issues concerning the set of metainferences validated (...) by this logic. In this paper, we show that this logic, once it is adequately understood, is weaker than classical logic. Moreover, the logic is in a way similar to the paraconsistent logic LP. (shrink)

A nonempty sequence T1,...,Tn of theories is tolerant, if there are consistent theories T 1 + ,..., T n + such that for each 1 i n, T i + is an extension of Ti in the same language and, if i n, T i + interprets T i+1 + . We consider a propositional language with the modality , the arity of which is not fixed, and axiomatically define in this language the decidable logics TOL and TOL. It is (...) shown that TOL (resp. TOL) yields exactly the schemata of PA-provable (resp. true) arithmetical sentences, if (A1,..., An) is understood as (a formalization of) PA+A1, ..., PA+An is tolerant. (shrink)

In this paper, the connection between logicism and the principle of tolerance in Carnap’s philosophy of logic and mathematics is to be presented in terms of the history of its development. Such development is conditioned by two lines of criticism to Carnap’s attempt to combine Logicism and Conventionalism, the first of which comes from Gödel, the second from Alfred Tarski. The presentation will take place in three steps. First, the Logicism of Carnap before the publication of The Logical Syntax (...) of Language will be analyzed in its main features. Second, the relationship between Logicism and the Principle of Tolerance at the time of the publication of Logical Syntax, and thirdly, in the so-called semantical phase of Carnap’s thought will be examined. On the basis of the two preceding points, we will then critically analyze two interpretations of the possibility to maintain a philosophical position like that of Carnap nowadays. (shrink)

This dissertation makes two primary contributions. The first three chapters develop an interpretation of Carnap's Meta-Philosophical Program which places stress upon his methodological analysis of the sciences over and above the Principle of Tolerance. Most importantly, I suggest, is that Carnap sees philosophy as contiguous with science—as a part of the scientific enterprise—so utilizing the very same methods and subject to the same limitations. I argue that the methodological reforms he suggests for philosophy amount to philosophy as the explication of (...) the concepts of science through the construction and use of suitably robust meta-logical languages. My primary interpretive claim is that Carnap's understanding of logic and mathematics as a set of formal auxiliaries is premised upon this prior analysis of the character of logico-mathematical knowledge, his understanding of its role in the language of science, and the methods used by practicing mathematicians. Thus the Principle of Tolerance, and so Carnap's logical pluralism, is licensed and justified by these methodological insights. This interpretation of Carnap's program contrasts with the popular Deflationary reading as proposed in Goldfarb & Ricketts. The leading idea they attribute to Carnap is a Logocentrism: That philosophical assertions are always made relative to some particular language, and that our choice of syntactical rules for a language are constitutive of its inferential structure and methods of possible justification. Consequently Tolerance is considered the foundation of Carnap's entire program. My third chapter argues that this reading makes Carnap's program philosophically inert, and I present significant evidence that such a reading is misguided. The final chapter attempts to extend the methodological ideals of Carnap's program to the analysis of the ongoing debate between category- and set-theoretic foundations for mathematics. Recent criticism of category theory as a foundation charges that it is neither autonomous from set theory, nor offers a suitable ontological grounding for mathematics. I argue that an analysis of concepts can be foundationally informative without requiring the construction of those concepts from first principles, and that ontological worries can be seen as methodologically unfruitful. (shrink)

I argue that a general logic of definitions must tolerate ω‐inconsistency. I present a semantical scheme, S, under which some definitions imply ω‐inconsistent sets of sentences. I draw attention to attractive features of this scheme, and I argue that S yields the minimal general logic of definitions. I conclude that any acceptable general logic should permit definitions that generate ω‐inconsistency. This conclusion gains support from the application of S to the theory of truth.

According to the naive theory of vagueness, the vagueness of an expression consists in the existence of both positive and negative cases of application of the expression and in the non- existence of a sharp cut-off point between them. The sorites paradox shows the naive theory to be inconsistent in most logics proposed for a vague language. The paper explores the prospects of saving the naive theory by revising the logic in a novel way, placing principled restrictions on the (...) transitivity of the consequence relation. A lattice-theoretical framework for a whole family of “tolerant logics” is proposed and developed. Particular care is devoted to the relation between the salient features of the formal apparatus and the informal logical and semantic notions they are supposed to model. A suitable non-transitive counterpart to classical logic is defined. Some of its properties are studied, and it is eventually shown how an appropriate regimentation of the naive theory of vagueness is consistent in such a logic. (shrink)

We discuss in this paper the question of the scope of the principle of tolerance about languages promoted in Carnap's The Logical Syntax of Language and the nature of the analogy between it and the rudimentary conventionalism purportedly exhibited in the work of Poincaré and Hilbert. We take it more or less for granted that Poincaré and Hilbert do argue for conventionalism. We begin by sketching Coffa's historical account, which suggests that tolerance be interpreted as a conventionalism that allows us (...) complete freedom to select whatever language we wish—an interpretation that generalizes the conventionalism promoted by Poincaré and Hilbert which allows us complete freedom to select whatever axiom system we wish for geometry. We argue that such an interpretation saddles Carnap with a theory of meaning that has unhappy consequences, a theory we believe he did not hold. We suggest that the principle of linguistic tolerance in fact has a more limited scope; but within that scope the analogy between tolerance and geometric conventionalism is quite tight. (shrink)

Moral conflicts are the situations which emerge as a response to deal with conflicting obligations or duties. An interesting case arises when an agent thinks that two obligations A and B are equally important, but yet fails to choose one obligation over the other. Despite the fact that the systematic study and the resolution of moral conflicts finds prominence in our linguistic discourse, standard deontic logic when used to represent moral conflicts, implies the impossibility of moral conflicts. This presents (...) a conundrum for appropriate logic to address these moral conflicts. We frequently believe that there is a close connection between tolerating inconsistencies and conflicting moral obligations. In paraconsistent logics, we tolerate inconsistencies by treating them to be both true and false. In this paper, we analyze Graham Priest’s paraconsistent logic LP, and extend our examination to the deontic extension of LP known as DLP. We illustrate our work, with a classic example from the famous Indian epic Mahabharata, where the protagonist Arjuna faces a moral conflict in the battlefield of Kurukshetra. The paper aims to avoid deontic explosion and allows to accommodate Arjuna’s moral conflict in paraconsistent deontic logics. Our analysis is expected to provide novel tools towards the logical representation of moral conflicts and to shed some light on the context-sensitive paraconsistent deontic logic. (shrink)

Rudolf Carnap’s principle of tolerance states that there is no need to justify the adoption of a logic by philosophical means. Carnap uses the freedom provided by this principle in his philosophy of mathematics: he wants to capture the idea that mathematical truth is a matter of linguistic rules by relying on a strong metalanguage with infinitary inference rules. In this paper, I give a new interpretation of an argument by E. W. Beth, which shows that the principle of (...) tolerance does not suffice to remove all obstacles to the employment of infinitary rules. (shrink)

I see the perspective of Tolerance as enshrining an attitude toward philosophical work that stresses its continuity with the procedures of conceptual clarification through mathematisation found in the sciences. What I have tried to show is that Carnap's understanding of the philosophical foundations of mathematics is inseparable from his understanding of the business of philosophy of empirical science.

Originally published in 1966. Professor Rescher's aim is to develop a "logic of commands" in exactly the same general way which standard logic has already developed a "logic of truth-functional statement compounds" or a "logic of quantifiers". The object is to present a tolerably accurate and precise account of the logically relevant facets of a command, to study the nature of "inference" in reasonings involving commands, and above all to establish a viable concept of validity in (...) command inference, so that the logical relationships among commands can be studied with something of the rigour to which one is accustomed in other branches of logic. (shrink)

The formal logical characteristics of the categories of "tolerance" and "intolerance" are emphasized, as well as empirical-pragmatic advantages of a declaration and realization of tolerant positions in modern international life. It is mentioned that the limits of intolerant actions are set either by external resistance, or by intolerant subjects' potential for exhaustion. The historical and ideological prerequisites for political tolerance, as well as the principle of "resistance to evil by force" advocated by Russian philosopher Ivan lliyn, are reviewed. The basis (...) of socio-ontological tolerance in the modern life of the world community, its reinforcement by tendencies in scientific and technical development and in international law, and the role of comprehensive objective interpretations of the function of international tolerance by mass media systems are analyzed. The meaning of an axiological foundation for tolerance in international policy and the objective difficulty of consolidating it in the social life of the early decades of the 21st century are revealed. (shrink)

We present two defeasible logics of norm-propositions (statements about norms) that (i) consistently allow for the possibility of normative gaps and normative conflicts, and (ii) map each premise set to a sufficiently rich consequence set. In order to meet (i), we define the logic LNP, a conflict- and gap-tolerant logic of norm-propositions capable of formalizing both normative conflicts and normative gaps within the object language. Next, we strengthen LNP within the adaptive logic framework for non-monotonic reasoning in (...) order to meet (ii). This results in the adaptive logics LNPr and LNPm, which interpret a given set of premises in such a way that normative conflicts and normative gaps are avoided ‘whenever possible’. LNPr and LNPm are equipped with a preferential semantics and a dynamic proof theory. (shrink)

The logical empiricists often appear as a foil for feminist theories. Their emphasis on the individualistic nature of knowledge and on the value-neutrality of science seems directly opposed to most feminist concerns. However, several recent works have highlighted aspects of Carnap's views that make him seem like much less of a straightforwardly positivist thinker. Certain of these aspects lend themselves to feminist concerns much more than the stereotypical picture would imply.

This paper deals with higher-order vagueness in Williamson's 'logic of clarity'. Its aim is to prove that for 'fixed margin models' (W,d,α ,[ ]) the notion of higher-order vagueness collapses to second-order vagueness. First, it is shown that fixed margin models can be reformulated in terms of similarity structures (W,~). The relation ~ is assumed to be reflexive and symmetric, but not necessarily transitive. Then, it is shown that the structures (W,~) come along with naturally defined maps h and (...) s that define a Galois connection on the power set PW of W. These maps can be used to define two distinct boundary operators bd and BD on W. The main theorem of the paper states that higher-order vagueness with respect to bd collapses to second-order vagueness. This does not hold for BD, the iterations of which behave in quite an erratic way. In contrast, the operator bd defines a variety of tolerance principles that do not fall prey to the sorites paradox and, moreover, do not always satisfy the principles of positive and negative introspection. (shrink)

This paper articulates an account of imperatives that sensibly supports the idea of a logic of imperative inferences. We rebuke common objections to the very possibility of such a logic, from a perspective based on recent linguistic work on the morphosyntax of imperatives. Specifically, we develop the notion that the content of an imperative sentence includes both a force operator alongside an imperational content to which the force applies. We further argue that this account of the content of (...) imperatives constitutes a plausible and flexible framework to develop a logic of imperative by examining a number of reconstructions of this idea using semantical analogs of widespread modal semantics. After studying the performance of those approaches, we conclude that progress in imperative logic has been hindered by the failure to adopt conflict-tolerant and resource-sensitive semantics, but suggest that such considerations can be incorporated in this flexible framework. Finally, we also propose a simple account of the difference between operators applying to the content of imperatives and imperative operators, in a way that sheds light on some of the issues underlying the usual antinomies. (shrink)

Strict/tolerant logic, ST, evaluates the premises and the consequences of its consequence relation differently, with the premises held to stricter standards while consequences are treated more tolerantly. More specifically, ST is a three-valued logic with left sides of sequents understood as if in Kleene’s Strong Three Valued Logic, and right sides as if in Priest’s Logic of Paradox. Surprisingly, this hybrid validates the same sequents that classical logic does. A version of this result has been (...) extended to meta, metameta, … consequence levels in Barrio et al.. In my earlier paper Fitting I showed that the original ideas behind ST are, in fact, much more general than first appeared, and an infinite family of many valued logics have Strict/Tolerant counterparts. This family includes both Kleene’s and Priest’s logic individually, as well as first degree entailment. For instance, for both the Kleene and the Priest logic, the corresponding strict/tolerant logic is six-valued, but with differing sets of strictly and tolerantly designated truth values. The present paper extends that generalization in two directions. We examine a reverse notion, of Tolerant/Strict logics, which exist for the same structures that were investigated in Fitting. And we show that the generalization extends through the meta, metameta, … consequence levels for the same infinite family of many valued logics. Finally we close with remarks on the status of cut and related rules, which can actually be rather nuanced. Throughout, the aim is not the philosophical applications of the Strict/Tolerant idea, but the determination of how general a phenomenon it is. (shrink)

Pierre Bayle’s theory of religious toleration has received much attention over the past three centuries, yet there is still little consensus surrounding the precise logic of Bayle’s argument, and even less consensus concerning whether that argument is successful or perhaps utterly inconsistent. One of the central themes in the literature concerns the role of skepticism in Bayle’s argument for toleration. Some argue that Baylean toleration is based entirely in a non-skeptical morality that is in turn based (...) in conscience, while others argue that Baylean toleration requires a foundation of skeptical doubt. In this paper I will offer an interpretation of Bayle’s argument for toleration as it is offered in the Ninth Letter of the Nouvelles lettres critiques (1685), and I will show that skepticism plays an essential role in the argument. (shrink)

The goal of this paper is a comprehensive analysis of basic reasoning patterns that are characteristic of vague predicates. The analysis leads to rigorous reconstructions of the phenomena within formal systems. Two basic features are dealt with. One is tolerance: the insensitivity of predicates to small changes in the objects of predication (a one-increment of a walking distance is a walking distance). The other is the existence of borderline cases. The paper shows why these should be treated as different, though (...) related phenomena. Tolerance is formally reconstructed within a proposed framework of contextual logic, leading to a solution of the Sorites paradox. Borderline-vagueness is reconstructed using certain modality operators; the set-up provides an analysis of higher order vagueness and a derivation of scales of degrees for the property in question. (shrink)

This paper is about the problem of explanation in anthropology. There are, broadly speaking, three theories of explanation, namely, the scientific theory, the historical theory, and finally what I have decided to call the phenomenological theory, after M. Natanson. The author argues that none of the three theories is adequate by itself to encompass the complex nature of anthropological science. The three theories correspond roughly to at least three different types of questions raised by anthropologists, and this being the case (...) the principle of methodological tolerance seems a natural and sensible principle to adopt. The paper also deals with the problem of reduction, i.e. the problem whether the three theories are different from and logically independent of one another. (shrink)

The purpose of this paper is to present a paraconsistent formal system and a corresponding intended interpretation according to which true contradictions are not tolerated. Contradictions are, instead, epistemically understood as conflicting evidence, where evidence for a proposition A is understood as reasons for believing that A is true. The paper defines a paraconsistent and paracomplete natural deduction system, called the Basic Logic of Evidence, and extends it to the Logic of Evidence and Truth. The latter is a (...) logic of formal inconsistency and undeterminedness that is able to express not only preservation of evidence but also preservation of truth. LETj is anti-dialetheist in the sense that, according to the intuitive interpretation proposed here, its consequence relation is trivial in the presence of any true contradiction. Adequate semantics and a decision method are presented for both BLE and LETj, as well as some technical results that fit the intended interpretation. (shrink)

The logical empiricists often appear as a foil for feminist theories. Their emphasis on the individualistic nature of knowledge and on the value-neutrality of science seems directly opposed to most feminist concerns. However, several recent works have highlighted aspects of Carnap's views that make him seem like much less of a straightforwardly positivist thinker. Certain of these aspects lend themselves to feminist concerns much more than the stereotypical picture would imply.

The paper discusses three aspects of belonging to religious systems of belief within a modern liberal society, namely (1) the sincerity and consistency of belief, (2) the possibility of exteriorization of belief through broader social interactions or transactions, and (3) the relationship between religious belief and the modern concept of affirmative tolerance, or affirmation of differences, which has become a pronounced public policy in multicultural liberal societies. The author argues that, while negative tolerance allows sincere religious belief to flourish in (...) the private sphere and for benevolence to be shown to those who are seen as mistaken in their beliefs, affirmative tolerance opens an array of logical issues. The demand to extend potential substantive validation to opposed beliefs produces the ricochet effect of de-validating one’s own beliefs. This creates difficulties for religious communities when issues at stake are beliefs that, in the respective belief-systems, are definitive of the moral goodness and moral badness. Upon a more careful examination of the logical relations between the soteriological promises characteristic of what is sometimes called the ‘substantive’ layer of religiousness, on the one hand, and the public expectation of a tolerant coexistence of religious communities on a social level, on the other hand, it becomes clear that the tolerance required can only be a negative tolerance. Any expectation of affirmative tolerance de-values the soteriological script of the respective system of religious belief, and is thus likely to lead to serious disturbances in a liberal context of multi-cultural coexistence. The author argues that the recent political announcements of a ‘failure of the multicultural experiment’ are caused by the aggressive pursuit of ‘affirmative tolerance’ rather than by any in-built intolerance of others in any of the large religious belief systems now prevalent in the liberal democratic world. (shrink)

Hans Hahn's long-neglected philosophy of mathematics is reconstructed here with an eye to his anticipation of the doctrine of logical pluralism. After establishing that Hahn pioneered a post-Tractarian conception of tautologies and attempted to overcome the traditional foundational dispute in mathematics, Hahn's and Carnap's work is briefly compared with Karl Menger's, and several significant agreements or differences between Hahn's and Carnap's work are specified and discussed.

In this paper, I distinguish different kinds of pluralism about logical consequence. In particular, I distinguish the pluralism about logic arising from Carnap’s Principle of Tolerance from a pluralism which maintains that there are different, equally “good” logical consequence relations on the one language. I will argue that this second form of pluralism does more justice to the contemporary state of logical theory and practice than does Carnap’s more moderate pluralism.

In their recent article “A Hierarchy of Classical and Paraconsistent Logics”, Eduardo Barrio, Federico Pailos and Damien Szmuc present novel and striking results about meta-inferential validity in various three valued logics. In the process, they have thrown open the door to a hitherto unrecognized domain of non-classical logics with surprising intrinsic properties, as well as subtle and interesting relations to various familiar logics, including classical logic. One such result is that, for each natural number n, there is a (...) class='Hi'>logic which agrees with classical logic on tautologies, inferences, meta-inferences, meta-meta-inferences, meta-meta-...-meta-inferences, but that disagrees with classical logic on n + 1-meta-inferences. They suggest that this shows that classical logic can only be characterized by defining its valid inferences at all orders. In this article, I invoke some simple symmetric generalizations of BPS’s results to show that the problem is worse than they suggest, since in fact there are logics that agree with classical logic on inferential validity to all orders but still intuitively differ from it. I then discuss the relevance of these results for truth theory and the classification problem. (shrink)

This paper continues my work of [9], which showed there was a broad family of many valued logics that have a strict/tolerant counterpart. Here we consider a generalization of weak Kleene three valued logic, instead of the strong version that was background for that earlier work. We explain the intuition behind that generalization, then determine a subclass of strict/tolerant structures in which a generalization of weak Kleene logic produces the same results that the strong Kleene generalization did. This (...) paper provides much background, but is not self-contained. Some results from [9] are called on, and are not reproved here. [9] Melvin C. Fitting. “A Family of Strict/Tolerant Logics”. In: Journal of Philosophical Logic. Online. Print publication forthcoming. (shrink)

Liberals often assume that once people see the costs of intolerance that they will come to embrace toleration and that once they can accept toleration as a modus vivendi, they will soon be able to see it as a good in its own right. But, I argue, that the logic that make in tolerance difficult to break also compel people to resist any attempts to make toleration more than a modus vivendi. True toleration will not (...) be embraced unless the people undergo a kind of conversion experience. (shrink)

We expand first order models with a tolerance relation on thedomain. Intuitively, two elements stand in this relation if they arecognitively close for the agent who holds the model. This simplenotion turns out to be very powerful. It leads to a semanticcharacterization of the guarded fragment of Andréka, van Benthemand Németi, and highlights the strong analogies between modallogic and this fragment. Viewing the resulting logic – tolerance logic– dynamically it is a resource-conscious information processingalternative to classical first order (...) logic. The differences areindicated by several examples. (shrink)

In broadest terms, this thesis is concerned to answer the question of whether the view that arithmetic is analytic can be maintained consistently. Lest there be much suspense, I will conclude that it can. Those who disagree claim that accounts which defend the analyticity of arithmetic are either unable to give a satisfactory account of the foundations of mathematics due to the incompleteness theorems, or, if steps are taken to mitigate incompleteness, then the view loses the ability to account for (...) the applicability of mathematics in the sciences. I will show that this criticism is not successful against every view whereby arithmetic is analytic by showing that the brand of "conventionalism" about mathematics that Rudolf Carnap advocated in the 1930s, especially in Logical Syntax of Language, does not suffer from these difficulties. There, Carnap develops an account of logic and mathematics that ensures the analyticity of both. It is based on his famous "Principle of Tolerance", and so the major focus of this thesis will to defend this principle from certain criticisms that have arisen in the 80 years since the book was published. I claim that these criticisms all share certain misunderstandings of the principle, and, because my diagnosis of the critiques is that they misunderstand Carnap, the defense I will give is of a primarily historical and exegetical nature. Again speaking broadly, the defense will be split into two parts: one primarily historical and the other argumentative. The historical section concerns the development of Carnap's views on logic and mathematics, from their beginnings in Frege's lectures up through the publication of Logical Syntax. Though this material is well-trod ground, it is necessary background for the second part. In part two we shift gears, and leave aside the historical development of Carnap's views to examine a certain family of critiques of it. We focus on the version due to Kurt Gödel, but also explore four others found in the literature. In the final chapter, I develop a reading of Carnap's Principle - the `wide' reading. It is one whereby there are no antecedent constraints on the construction of linguistic frameworks. I argue that this reading of the principle resolves the purported problems. Though this thesis is not a vindication of Carnap's view of logic and mathematics tout court, it does show that the view has more plausibility than is commonly thought. (shrink)

This paper argues that the slogans “A Woman's Right to Choose” and “The Personal is the Political” typify different traditions within feminist thinking; one emphasizing rights and equality, the other the unconscious and the personal. The author responds to both traditions by bringing together mind and body, and reason and emotion, via the figure of the copula. The copula expresses an alternative model of identity which indicates that value can be produced only in relation.Let us say that the problem is (...) violence. At its most naive: how can the sexual relation, which is supposedly full of love, be violent?I mean the sexual relation in its resonances and ambiguity—to indicate the relation between the sexes, and the relation between lovers. In no way can the relation be confined to love, either heterosexual or homosexual, since it is often a contest. It cannot be reduced solely to a social relation, because in one of its aspects it addresses the most intimate subjectivity.In a certain feminist lifestyle advocacy, those women who are in same sex relations avoid sexual violence by avoiding men, and those who are in heterosexual relationships strive to find the “right kind”—that is, relationships of respectful and supportive love—rejecting all signs of aggression, from sexist disparagement and emotional cruelty to sexual humiliation and physical assault, as “abuse.”Strangely, this dichotomy does not explain the proximity of passion and aggression, whether in love between men and women or in same-sex relationships between feminist women. As rational counsel, it resists the important sense in which the erotic is, and is even valued as, the excess of the rational. And as an analysis of the oppression of women it defeats itself, for to insist on masculinity as violence itself, and/or on the sexual relation as properly governed by reason, seems to miss the point of both love and feminism.Stranger still, feminisms, which set out to address and redress the oppression of women, have become rivalrous themselves. Are these aggressions a legacy of the intellectual world they must take place in. Have we overlooked an aspect of the relation between sisters? Feminism has not addressed the question of aggression in feminism as anything more than contamination.Perhaps, after all, the thing that feminism has not yet successfully addressed is love. The “battle between the sexes” has not rendered the ambivalence of the heterosexual relation. As a species of theory, feminism has relished the rigor of distinction and has not found it easy to tolerate the proximity of opposites.And yet, in evoking the body, some feminisms approach closer to this difficulty. It remains to take up the relation between the body and the concept more thoroughly, in order to find out whether sexual difference could ever be philosophical. (shrink)

Available for the first time in 20 years, here is the Rudolf Carnap's famous principle of tolerance by which everyone is free to mix and match the rules of ...

This work introduces and defends a radically different type of liberal political theory by severing liberal thought from all underlying moral foundations. Its aim is to present a type of liberalism capable of accommodating the richly diverse differences of worldview and moral theory of the good present in today's pluralist societies. By constructing liberalism as a purely political doctrine, the author develops a theory of toleration, and civil association more generally, capable of meeting liberalism's historic commitment to diversity. While (...) the justification for such a liberalism must be made in prudential terms, rather than the more familiar moral terms used to support competing liberal theories, the liberalism developed here remains faithful to the liberal tradition by defending a theory of equal liberty as the primary political virtue of a just society. (shrink)

In this paper, I defend Rudolf Carnap's Principle of Tolerance from an accusation, due to Michael Friedman, that it is self-defeating by prejudicing any debate towards the logically stronger theory. In particular, Friedman attempts to show that Carnap's reconstruction of the debate between classicists and intuitionists over the foundations of mathematics in his book The Logical Syntax of Language, is biased towards the classical standpoint since the metalanguage he constructs to adjudicate between the rival positions is fully classical. I argue (...) that this criticism is mistaken on two counts: (1) it fails to fully appreciate the freedom with regard to the construction of linguistic frameworks that Carnap intended his Principle to embody, and (2) Friedman's objection underestimates the extent to which the evaluation of a framework is task-relative. I conclude that Tolerance is not self-undermining in the way that Friedman claims it is. While this is a restricted conclusion -- and is not a vindication of Carnap's views on logic and mathematics tout court -- it nonetheless suggests that his tolerant perspective has been dismissed too quickly, even by his supporters. (shrink)

This book examines philosophical approaches to linguistic vagueness, a puzzling feature of natural language that gives rise to the ancient Sorites paradox and challenges classical logic and semantics. -/- The Sorites, or Paradox of the Heap, consists in three claims: (1) One grain of sand does not make a heap. (2) One billion grains of sand do make a heap. (3) For any two amounts of sand differing by at most one grain: either both are heaps of sand, or (...) neither one is. The third claim is rendered plausible by an initial conviction that vague predicates like ‘heap’ tolerate small changes. However, the repeated application of a tolerance principle to the second claim yields the further proposition that one grain of sand does make a heap – which contradicts claim number one. Consequently, many philosophers reject or modify tolerance principles for vague predicates. -/- Inga Bones reassesses prominent responses to the Sorites and defends a Wittgensteinian dissolution of the paradox. She argues that vague predicates are, indeed, tolerant and discusses how this finding relates to the paradox itself, to the notion of validity and to the concept of a borderline case . (shrink)

Michael Friedman has recently argued that Carnap'sLogical Syntax of Language is fundamentally flawed in a way that reveals the ultimate failure of logical positivism. Friedman's argument depends crucially on two claims: (1) that Carnap was committed to the view that there is a universal metalanguage and (2) that given what Carnap wanted from a metalanguage, in particular given that he wanted a definition of analytic for an object language, he was in fact committed to a hierarchy of stronger and stronger (...) metalanguages. We argue that neither of these claims need be accepted. We show that there is no textual evidence for (1) and that if metalanguages are to be used for merely descriptive and not also justificatory purposes, Carnap does not need to define analyticity sufficiently for proving consistency, and so could have given a definition that does not entail a hierarchy of metalanguages. (shrink)

In this paper I examine a neglected question concerning the centerpiece of Carnap's philosophy: the principle of tolerance. The principle of tolerance states that we are free to devise and adopt any well-defined form of language or linguistic framework we please. A linguistic framework defines framework-internal standards of correct reasoning that guide us in our first-order scientific pursuits. The choice of a linguistic framework, on the other hand, is an ‘external’ question to be settled on pragmatic grounds and so not (...) itself constrained by these standards. However, even if choosing a framework is a practical matter, we would nevertheless expect the process of framework selection to be subject to rational norms. But which norms might those be? And where do they come from? I begin by showing that these questions are crucial to the success of Carnap's entire philosophical project. I then offer a response on behalf of the Carnapian which guarantees the rationality of the process of framework selection, while remaining true to Carnap's firm commitment to tolerance. (shrink)

meaning of a proper name is simply its referent.[1] This thesis, however, brings with it a whole host of problems. One particularly thorny difficulty is that of negative existentials, sentences of the form ‘N does not exist’ (where ‘N’ is a proper name). Intuitively, some such sentences are true, but the direct reference theory seems to imply that they must be either false or meaningless. After all, if the meaning of a name is just its referent, then a sentence such (...) as ‘Mary does not exist’ is meaningless unless there exists a person Mary who is the referent of the name ‘Mary’. But if such a person exists, then the sentence denying her existence must be false.            Now it might be suggested that negative existentials involve a rather rare and specialized use of names, for which an alternate analysis might well be appropriate. One might, for example, have independent reasons for thinking that existence is not a predicate. Even if this is right, however, the analysis of fictional discourse poses difficulties for the direct reference theory that cannot be so easily avoided. The trouble is that fictional names—‘Sherlock Holmes’ and ‘Bilbo Baggins’, for example—lack referents; fictional characters do not exist. As a result, a simple application of the direct reference view to fictional discourse is entirely untenable—this would entail that claims regarding fictional characters are not only never true, but always meaningless.            The tendency in the philosophy of language has been to treat fictional discourse as a peripheral case, posing little threat to the direct reference view. And, as such, the fact that the analysis of fiction seems to run into intractable difficulties has been downplayed, and the fact the analyses on offer tend to be ad hoc has been tolerated. Typical strategies include treating fictional names as abbreviations for definite descriptions, supposing that fictional names occur within the scope of tacit fictive operators of various sorts, or taking them to directly refer to non-existent objects.. (shrink)

Rudolf Carnap's 1930s philosophy of logic, including his adherence to the principle of tolerance, is discussed. What theses did Carnap commit himself to, exactly? I argue that while Carnap did commit himself to a certain multitude thesis—there are different logics of different languages, and the choice between these languages is merely a matter of expediency—there is no evidence that he rejected a language-transcendent notion of fact, contrary to what Warren Goldfarb and Thomas Ricketts have prominently argued. (In fact, it (...) is obscure just what Goldfarb and Ricketts claim about Carnap). Toward the end I critically discuss Michael Friedman's suggestion that Carnap believed in a relative a priori. (shrink)

In this paper we investigate a semantics for first-order logic originally proposed by R. van Rooij to account for the idea that vague predicates are tolerant, that is, for the principle that if x is P, then y should be P whenever y is similar enough to x. The semantics, which makes use of indifference relations to model similarity, rests on the interaction of three notions of truth: the classical notion, and two dual notions simultaneously defined in terms of (...) it, which we call tolerant truth and strict truth. We characterize the space of consequence relations definable in terms of those and discuss the kind of solution this gives to the sorites paradox. We discuss some applications of the framework to the pragmatics and psycholinguistics of vague predicates, in particular regarding judgments about borderline cases. (shrink)

Generally speaking, just war theory (JWT) holds that there are two just causes for war: self-defence and ‘other-defence’. The most common type of the latter is popularly known as ‘humanitarian intervention’. There is debate, however, as to whether these can serve as just causes for preventive war. Those who subscribe to JWT tend to be unified in treating so-called preventive war with a high degree of suspicion on the grounds that it fails to satisfy conventional criteria for jus ad bello; (...) – particularly the just cause and last resort criteria. Francisco di Vitoria held that the only just cause for war was ‘a wrong received’, which renders impossible any justification for preventive war. There are assumptions implicit in recent military practice, however – most notably, the US-led invasion of Iraq in 2003 – that challenge this ban on preventive war. Interestingly, both supporters and critics attempt to justify their views through the broader logic of JWT; viz., through a conception of what is good for both political communities and individuals, and through a legitimate defence of these goods. Supporters point to situations where so-called rogue states represent ‘grave and imminent risk’ of committing acts of aggression as grounds that justify preventive war; critics argue that to attack another political community on the basis of crimes not yet committed is a breach of the very rights JWT was created to defend. The advocate of preventive war does not appreciate important aspects concerning the morality of war. In the ongoing tension between Iran and The United States and her allies – if the rhetoric is to be believed – I am asked to tolerate a threat to my security and liberty, and to risk suffering aggression in defence of the rights of the antagonistic, but not yet aggressive, state. The crucial question is how such tolerance and risk fit in with the logic of just war: at what point, if any, does the risk of being attacked become great enough to justify declaring war in anticipation? In this paper I highlight some of the theoretical and practical difficulties in determining what counts as a grave and imminent threat, focusing especially on the complicated case of ‘imminence’ in the face of so-called ‘Weapons of Mass Destruction’. Secondly, I will argue that not only is the notion of preventive war inconsistent with the defence of the rights of political communities that JWT requires; it is also forbidden by the proportionality requirement of jus ad bellum. A risk of being subjected to aggression is the price for global peace. Whilst political communities can do much to prevent aggression and prepare themselves in case it occurs, the conditions for just war require that this prevention and preparation stop short of declaring war. We must live with a certain degree of risk in this area. (shrink)

In this paper I examine the question of logic’s normative status in the light of Carnap’s Principle of Tolerance. I begin by contrasting Carnap’s conception of the normativity of logic with that of his teacher, Frege. I identify two core features of Frege’s position: first, the normative force of the logical laws is grounded in their descriptive adequacy; second, norms implied by logic are constitutive for thinking as such. While Carnap breaks with Frege’s absolutism about logic (...) and hence with the notion that any system of logic should have a privileged claim to correctness, I argue that there is a sense in which Carnap’s framework-relative conception of logical norms has a constitutive role to play: though they are not constitutive for the conceptual activity for thinking, they do nevertheless set the ground rules that make certain forms of scientific inquiry possible in the first place. I conclude that Carnap’s principle of tolerance is tamer than one might have thought and that, despite remaining differences, Frege’s and Carnap’s conceptions of logic have more in common than one might have thought. (shrink)

Generally speaking, just war theory (JWT) holds that there are two just causes for war: self‐defence and ‘other‐defence’. The most common type of the latter is popularly known as ‘humanitarian intervention’. There is debate, however, as to whether these can serve as just causes for preventive war. Those who subscribe to JWT tend to be unified in treating so‐called preventive war with a high degree of suspicion on the grounds that it fails to satisfy conventional criteria for jus ad bello; (...) – particularly the just cause and last resort criteria. Francisco di Vitoria held that the only just cause for war was ‘a wrong received’, which renders impossible any justification for preventive war. There are assumptions implicit in recent military practice, however – most notably, the US‐led invasion of Iraq in 2003 – that challenge this ban on preventive war.Interestingly, both supporters and critics attempt to justify their views through the broader logic of JWT; viz., through a conception of what is good for both political communities and individuals, and through a legitimate defence of these goods. Supporters point to situations where so‐called rogue states represent ‘grave and imminent risk’ of committing acts of aggression as grounds that justify preventive war; critics argue that to attack another political community on the basis of crimes not yet committed is a breach of the very rights JWT was created to defend.The advocate of preventive war does not appreciate important aspects concerning the morality of war. In the ongoing tension between Iran and The United States and her allies – if the rhetoric is to be believed – I am asked to tolerate a threat to my security and liberty, and to risk suffering aggression in defence of the rights of the antagonistic, but not yet aggressive, state. The crucial question is how such tolerance and risk fit in with the logic of just war: at what point, if any, does the risk of being attacked become great enough to justify declaring war in anticipation?In this paper I highlight some of the theoretical and practical difficulties in determining what counts as a grave and imminent threat, focusing especially on the complicated case of ‘imminence’ in the face of so‐called ‘Weapons of Mass Destruction’. Secondly, I will argue that not only is the notion of preventive war inconsistent with the defence of the rights of political communities that JWT requires; it is also forbidden by the proportionality requirement of jus ad bellum. A risk of being subjected to aggression is the price for global peace. Whilst political communities can do much to prevent aggression and prepare themselves in case it occurs, the conditions for just war require that this prevention and preparation stop short of declaring war. We must live with a certain degree of risk in this area. (shrink)

The abstract status of Kant's account of his ‘general logic’ is explained in comparison with Gödel's general definition of a formal logical system and reflections on ‘abstract’ (‘absolute’) concepts. Thereafter, an informal reconstruction of Kant's general logic is given from the aspect of the principles of contradiction, of sufficient reason, and of excluded middle. It is shown that Kant's composition of logic consists in a gradual strengthening of logical principles, starting from a weak principle of contradiction that (...) tolerates a sort of contradictions in predication, and then proceeding to the (constructive) principle of sufficient reason, and to a classical-like logic, which includes the principle of excluded middle. A first-order formalisation is applied to this reconstruction, which reveals implicit modalities in Kant's account of logic, and confirms the implementability of Kant's logic into a sound and complete formal system. (shrink)