This book presents the state of the art in the fields of formal logic pioneered by Graham Priest. It includes advanced technical work on the model and proof theories of paraconsistent logic, in contributions from top scholars in the field. Graham Priest’s research has had a considerable influence on the field of philosophical logic, especially with respect to the themes of dialetheism—the thesis that there exist true but inconsistent sentences—and paraconsistency—an account of deduction in which contradictory premises do not entail (...) the truth of arbitrary sentences. Priest’s work has regularly challenged researchers to reappraise many assumptions about rationality, ontology, and truth. This book collects original research by some of the most esteemed scholars working in philosophical logic, whose contributions explore and appraise Priest’s work on logical approaches to problems in philosophy, linguistics, computation, and mathematics. They provide fresh analyses, critiques, and applications of Priest’s work and attest to its continued relevance and topicality. The book also includes Priest’s responses to the contributors, providing a further layer to the development of these themes. (shrink)

In this article we revisit a number of disputes regarding significance logics---i.e., inferential frameworks capable of handling meaningless, although grammatical, sentences---that took place in a series of articles most of which appeared in the Australasian Journal of Philosophy between 1966 and 1978. These debates concern (i) the way in which logical consequence ought to be approached in the context of a significance logic, and (ii) the way in which the logical vocabulary has to be modified (either by restricting some notions, (...) or by adding some vocabulary) to keep as much of Classical Logic as possible. Our aim is to show that the divisions arising from these disputes can be dissolved in the context of a novel and intuitive proposal that we put forward. (shrink)

A wide family of many-valued logics—for instance, those based on the weak Kleene algebra—includes a non-classical truth-value that is ‘contaminating’ in the sense that whenever the value is assigned to a formula φ⁠, any complex formula in which φ appears is assigned that value as well. In such systems, the contaminating value enjoys a wide range of interpretations, suggesting scenarios in which more than one of these interpretations are called for. This calls for an evaluation of systems with multiple contaminating (...) values. In this paper, we consider the countably infinite family of multiple-conclusion consequence relations in which classical logic is enriched with one or more contaminating values whose behavior is determined by a linear ordering between them. We consider some motivations and applications for such systems and provide general characterizations for all consequence relations in this family. Finally, we provide sequent calculi for a pair of four-valued logics including two linearly ordered contaminating values before defining two-sided sequent calculi corresponding to each of the infinite family of many-valued logics studied in this paper. (shrink)

This article investigates some of the various ways in which theorists have used Machiavelli (and more specifically The Prince) in a business and management context and suggests that the two most common approaches, the use of metaphor and the use of analogy, are both flawed. Metaphor often relies on a reading of Machiavelli that cannot be sustained, whereas analogy takes Machiavelli too far out of historical context. This article discusses how business and management can more usefully incorporate Machiavelli’s ideas by (...) placing them within a tradition of discourse, along the lines of Lockyer’s historical method. We outline three potential discourses: those of humanism; of guides to leadership; and of power. In so doing the article suggests that historical texts (in particular Machiavelli) can prove useful to students and practitioners of business and management. (shrink)

What critical characteristics do firms have that determine the scale and scope of corporate social responsibility activities they undertake? This paper examines two disparate predictors of corporate social performance. First, using the lens of the resource-based view, we examine the role of alliance network centrality on corporate social performance. We find that centrality enhances corporate social performance. Second, we investigate how board composition affects corporate social performance. Specifically, drawing on stakeholder theory, we find that the percentage of female directors predicts (...) greater corporate social performance. In addition, we look at the influence of outside directors on this relationship. Our findings show that the presence of more outside directors positively moderates the relationship between female directors and corporate social performance. (shrink)

The placenta invades the adjacent uterus and controls the maternal immune system, like a cancer invades surrounding organs and suppresses the local immune response. Intriguingly, placental and cancer cells are globally hypomethylated and share an epigenetic phenomenon that is not well understood – they fail to silence repetitive DNA sequences that are silenced in healthy somatic cells. In the placenta, hypomethylation of retrotransposons has facilitated the evolution of new genes essential for placental function. In cancer, hypomethylation is thought to contribute (...) to activation of oncogenes, genomic instability, and retrotransposon unsilencing; the latter, we postulate, is possibly the most important consequence. Activation of placental retrotransposon-derived genes in cancer underpins our hypothesis that hypomethylation of these genes drives cancer cell invasion. This alludes to an interesting paradox, that while placental retrotransposon-derived genes are essential for promoting early hominid life, the same genes promote disease-susceptibility and death through cancer. Placental and cancer cells fail to silence retrotransposons that are normally silenced in healthy tissues. This has created new genes that are essential for placental function, yet they are also expressed in cancer. We hypothesize that active retrotransposons are a double-edged sword, contributing both adaptive and deleterious functions to biology. (shrink)

The aim of this essay is to show that instances of valorising blackness have turned out to be harmful to African peoples. Whereas there have been several movements such as Black Power Movement, Black Consciousness Movement as well as individuals such as Steve Biko, Aime Cesaire, Leopold Sedar Senghor, William DuBois, Edward Blyden, Fela Anikulapo Kuti, it is the case that none of these minds made the conscious effort to interrogate the literal and symbolic use of black for Africans. Consequently, (...) this research limits its scope to Fela’s valorisation of blackness as enshrined in his blackism. Using the method of critical analysis, it argues that Fela’s “Blackism” takes the categorical and symbolic implications of blackness to an uncritical assimilation. The present study submits that until the ideological underpinning of the categorical and symbolic uses of blackness for Africans is engaged, all valorisation attempts will continue to yield meagre outputs. The first task is therefore to disclose the Eurocentric campaigns that mitigated the worth of the original or traditional people of Africa, south of the Sahara as well as the arrays of rejoinders which led to the valorisation of blackness. Afterward, Fela’s version of valorisation as encapsulated within the fold of his blackism will be disinterred. The rest of the paper shows not only that the valorisation agenda was a failed project but also that Fela’s “Blackism” is one of these failed projects. (shrink)

This paper examines two realisations of the television talk show in North America: The Oprah Winfrey Show and Dr. Phil, looking specifically at how they function within the sub-genre of ‘therapeutic talk show’ in keeping with Livingstone and Lunt’s (1994) classification of talk shows. Talk shows are defined by Ilie (2001) as “semi-institutional discourse” having features of a given setting (TV studio), topic- and goal-oriented talk, high degree of topic control, as well as restrictions on time and turn-taking. Theorists examining (...) this sub-genre of therapeutic talk show have argued that it provides a valuable means by which stories otherwise unrecognized have a forum, or that values of truth and honesty can be conveyed (Livingstone & Lunt 1994; Masciarotte 1991; Carbaugh 1988). However, theorists such as Abt and Seesholtz (1994) view therapeutic talk shows as potentially demeaning to guests who appear on them as well as a means by which suffering can be trivialized. Through an examination and analysis of requests for information, both direct and indirect, which are the principal features of all interviews, I look at how Oprah Winfrey and Dr. Phil problematize the narratives told by their guests. Both hosts rely heavily on one type of request, B-Event assertions functioning as indirect requests for information, to provoke specific response. My findings indicate that these talk shows do not in fact provide a forum for talk that would otherwise not be considered as suggested by Livingstone and Lunt (1994). Both Oprah Winfrey and Dr. Phil appropriate the stories provided by their guests; they also participate in their own overarching meta-narrative whereby as ‘heroes’ they solve their guests’ problems within a given time frame. Guests’ narrative responses share more with the speech act of confession than with free self-expression. The speech act of confession encouraged by these therapeutic talk shows serves in turn to reinforce conservatively-held values on the part of the at-home audience for whom such confession is also entertainment. (shrink)

Logics based on weak Kleene algebra (WKA) and related structures have been recently proposed as a tool for reasoning about flaws in computer programs. The key element of this proposal is the presence, in WKA and related structures, of a non-classical truth-value that is “contaminating” in the sense that whenever the value is assigned to a formula ϕ, any complex formula in which ϕ appears is assigned that value as well. Under such interpretations, the contaminating states represent occurrences of a (...) flaw. However, since different programs and machines can interact with (or be nested into) one another, we need to account for different kind of errors, and this calls for an evaluation of systems with multiple contaminating values. In this paper, we make steps toward these evaluation systems by considering two logics, HYB1 and HYB2, whose semantic interpretations account for two contaminating values beside classical values 0 and 1. In particular, we provide two main formal contributions. First, we give a characterization of their relations of (multiple-conclusion) logical consequence—that is, necessary and sufficient conditions for a set Δ of formulas to logically follow from a set Γ of formulas in HYB1 or HYB2 . Second, we provide sound and complete sequent calculi for the two logics. (shrink)

This book aids in the rehabilitation of the wrongfully deprecated work of William Parry, and is the only full-length investigation into Parry-type propositional logics. A central tenet of the monograph is that the sheer diversity of the contexts in which the mereological analogy emerges – its effervescence with respect to fields ranging from metaphysics to computer programming – provides compelling evidence that the study of logics of analytic implication can be instrumental in identifying connections between topics that would otherwise remain (...) hidden. More concretely, the book identifies and discusses a host of cases in which analytic implication can play an important role in revealing distinct problems to be facets of a larger, cross-disciplinary problem. It introduces an element of constancy and cohesion that has previously been absent in a regrettably fractured field, shoring up those who are sympathetic to the worth of mereological analogy. Moreover, it generates new interest in the field by illustrating a wide range of interesting features present in such logics – and highlighting these features to appeal to researchers in many fields. (shrink)

This is the first of two volumes announcing the emergence of the new legal realism as a field of study. At a time when the legal academy is turning to social science for new approaches, these volumes chart a new course for interdisciplinary research by synthesizing law on the ground, empirical research, and theory. Volume 1 lays the groundwork for this novel and comprehensive approach with an innovative mix of theoretical, historical, pedagogical, and empirical perspectives. Their empirical work covers such (...) wide-ranging topics as the financial crisis, intellectual property battles, the legal disenfranchisement of African-American landowners, and gender and racial prejudice on law school faculties. The methodological blueprint offered here will be essential for anyone interested in the future of law-and-society. (shrink)

In this paper, we examine a number of relevant logics’ variable sharing properties from the perspective of theories of topic or subject-matter. We take cues from Franz Berto’s recent work on topic to show an alignment between families of variable sharing properties and responses to the topic transparency of relevant implication and negation. We then introduce and defend novel variable sharing properties stronger than strong depth relevance—which we call cn-relevance and lossless cn-relevance—showing that the properties are satisfied by the weak (...) relevant logics and , respectively. We argue that such properties address a sort of semantic lossiness of strong depth relevance. (shrink)

Although logical settings are typically concerned with tracking alethic considerations, frameworks exist in which topic-theoretic considerations—e.g., tracking subject-matter or topic—are given equal importance. Intuitions about extending topic through a propositional language are generally straightforward for extensional cases. For a number of reasons, arriving at a compelling account of the subject-matter of intensional operators—such as intensional conditionals—is a more difficult task. In particular, the framework of topic-sensitive intentional modals (TSIMs) championed by Francesco Berto and his collaborators leave the topics of intensional (...) formulae undefined, which artificially constricts the expressivity of the theory. This paper proposes an approach to fill in this lacuna, emphasizing an analogous problem in Parry-style containment logics. In this setting, the approach receives a proof-of-concept through the introduction of a natural and general family of subsystems of Parry’s $${\textsf{PAI}}$$ PAI —with sound and complete axiomatizations—that allow a fine degree of control over the topics of intensional conditionals. (shrink)

The aim of this essay is to show that instances of valorising blackness have turned out to be harmful to African peoples. Whereas there have been several movements such as Black Power Movement, Black Consciousness Movement as well as individuals such as Steve Biko, Aime Cesaire, Leopold Sedar Senghor, William DuBois, Edward Blyden, Fela Anikulapo Kuti, it is the case that none of these minds made the conscious effort to interrogate the literal and symbolic use of black for Africans. Consequently, (...) this research limits its scope to Fela’s valorisation of blackness as enshrined in his blackism. Using the method of critical analysis, it argues that Fela’s “Blackism” takes the categorical and symbolic implications of blackness to an uncritical assimilation. The present study submits that until the ideological underpinning of the categorical and symbolic uses of blackness for Africans is engaged, all valorisation attempts will continue to yield meagre outputs. The first task is therefore to disclose the Eurocentric campaigns that mitigated the worth of the original or traditional people of Africa, south of the Sahara as well as the arrays of rejoinders which led to the valorisation of blackness. Afterward, Fela’s version of valorisation as encapsulated within the fold of his blackism will be disinterred. The rest of the paper shows not only that the valorisation agenda was a failed project but also that Fela’s “Blackism” is one of these failed projects. (shrink)

To gain an insight into how those entering the teaching profession regard cyberbullying, two focus groups were conducted with nine pre-service teachers. Thematic analytical approach revealed...

In this thesis, I examine the metaphysical debate between the A-theory and the B-theory of time, first by elaborating upon its proper characterization, and then by examining the sorts of evidence that are often thought to be germane to it. This debate, as I see it, is about whether or not time passes in any objective sense: the A-theory holds that it does, while the B-theory holds that it does not. I identify two opposing conceptions of time—that of the “time (...) of ordinary experience” on one hand, and that of “scientific time” on the other—and argue that the tension between them is the driving force behind this debate. I then examine two aspects of “evidence” from the time of ordinary experience: the phenomenological experience of time and the linguistic experience of time. It is often supposed, by both A- and B-theorists alike, that these sorts of evidence lend credence to the A-theory of time, since ordinary experience suggests that time passes. I hope to discredit this presumption, and so challenge the very framework in which this debate is so often carried out. In particular, by closely examining both of these kinds of experience—phenomenological and linguistic—in turn, I hope to provide a partial argument to the effect that the ordinary experience of time as a whole does not favour the A-theory over the B-theory of time. In the case of the phenomenological evidence, this is because the A-theory is just as inconsistent with such evidence as is the B-theory of time; in the case of the linguistic evidence, this is because the B-theory is equally consistent with such evidence as is the A-theory of time, particularly once it is revealed that a certain key assumption is tacitly accepted by both sides of the debate. Because of the popularity of the claim that the ordinary experience of time favours the A-theory, I take this conclusion to be something of a modest defence for the B-theory of time. (shrink)

We examine the relationship between the logics of nonsense of Bochvar and Halldén and the containment logics in the neighborhood of William Parry’s A I. We detail two strategies for manufacturing containment logics from nonsense logics—taking either connexive and paraconsistent fragments of such systems—and show how systems determined by these techniques have appeared as Frederick Johnson’s R C and Carlos Oller’s A L. In particular, we prove that Johnson’s system is precisely the intersection of Bochvar’s B 3 and Graham Priest’s (...) non-symmetrized connexive logic and that Oller’s system lies just beneath the intersection of B 3 and Priest’s paraconsistent L P. We conclude by examining Oller’s system in more depth, giving it a characterization in terms of L P and showing that it plays the same role to Harry Deutsch’s paraconsistent containment logic S that Aleksandr Zinov'ev’s S 1 plays with respect to A I. (shrink)

In this article, we consider variations of Nuel Belnap’s ‘artificial reasoner’. In particular, we examine cases in which the artificial reasoner is faulty, e.g. situations in which the reasoner is unable to calculate the value of a formula due to an inability to retrieve the values of its atoms. In the first half of the article, we consider two ways of modelling such circumstances and prove the deductive systems arising from these two types of models to be equivalent to Graham (...) Priest’s first-degree entailment with an ‘emptiness’ value and Richard Angell’s analytic containment, making computational interpretations of these systems possible. The Belnap-type semantics for AC bring FDE φ and AC in line with other containment logics in their neighborhood. The second half of the article examines formal questions, such as whether AC admits an analysis along the lines of that given to the related system of William Parry’s system of analytic implication, as suggested by Kurt Gödel and confirmed by Kit Fine. Furthermore, a natural means of extending these systems to languages with an intensional implication connective is investigated. (shrink)

The hallmark of the deductive systems known as ‘conceptivist’ or ‘containment’ logics is that for all theorems of the form , all atomic formulae appearing in also appear in . Significantly, as a consequence, the principle of Addition fails. While often billed as a formalisation of Kantian analytic judgements, once semantics were discovered for these systems, the approach was largely discounted as merely the imposition of a syntactic filter on unrelated systems. In this paper, we examine a number of prima (...) facie unrelated deductive contexts in which Addition fails and attempt to harmonise them by developing a computational interpretation of conceptivist logics. (shrink)

In frameworks in which _topic-__theoretic_ considerations—_e.g._, tracking _subject-matter_ or _topic_—are given equal importance with _veridical_ considerations, assigning topics to formulae in a satisfactory way is of critical importance. While intuitions are more-or-less solid for _extensional_ formulae in a propositional language, arriving at a compelling account of the subject-matter of _intensional_ formulae, _i.e._, formulae including intensional operators, is more challenging. This paper continues previous work on modeling topics of intensional formulae in William Parry’s logic of analytic implication, adapting the general techniques (...) to the framework of _topic-sensitive intentional modals_ (TSIMs) championed by Francesco Berto and his collaborators. As illustrations, we introduce variations on Berto and Peter Hawke’s logic of knowability relative to information ( \(\pmb {\textsf{KRI}}\) ), including a refinement sensitive to topic-theoretic distinctions between knowledge and belief and a refinement capable of internalizing its own properties. Finally, subsystems of Aybüke Ozgun and Berto’s logic of plain hyperintensional belief ( \(\pmb {\textsf{PHB}}\) ) are introduced in which fine-grained distinctions in subject-matter are possible. (shrink)

Logical frameworks that are sensitive to features of sentences’ subject-matter—like Berto’s topic-sensitive intentional modals (TSIMs)—demand a maximally faithful model of the topics of sentences. This is an especially difficult task in the case in which topics are assigned to intensional formulae. In two previous papers, a framework was developed whose model of intensional subject-matter could accommodate a wider range of intuitions about particular intensional conditionals. Although resolving a number of counterintuitive features, the work made an implicit assumption that the subject-matter (...) of an intensional conditional is a function of the subject-matters of its subformulae. This assumption—which I will call a principle of topic sufficiency—runs counter to some natural intuitions concerning topic. In this paper, we will investigate topic sufficiency and offer a semantic account that is state-sensitive, providing an implementation through the introduction of topic-sensitive logics related to William Parry’s prototypical $\mathsf {PAI}$. (shrink)

Scientists and clinicians are starting to translate genomic discoveries from research labs to the clinical setting. In the process, big data genomic technologies are both a risk to individual privacy and a benefit to personalized medicine. There is an opportunity to address the social and ethical demands of various stakeholders and shape the adoption of diagnostic genome technologies. We discuss ethical and practical issues associated with the networking of genomics by comparing how the European Union and North America understand and (...) practice notions of privacy and consent in research. An overview of international policy suggests the embedding of genomics within digital networks and the Internet creates conditions that challenge the management of privacy and consent in the age of big data. The risks of re-identification, informational harms, and data security vulnerabilities are issues that need to be better addressed in the clinical setting to reconcile the unpredictable pathway of research and practice in the networked information society. (shrink)

In this paper, we look at applying the techniques from analyzing superintuitionistic logics to extensions of the cointuitionistic Priest-da Costa logic daC (introduced by Graham Priest as “da Costa logic”). The relationship between the superintuitionistic axioms- definable in daC- and extensions of Priest-da Costa logic (sdc-logics) is analyzed and applied to exploring the gap between the maximal si-logic SmL and classical logic in the class of sdc-logics. A sequence of strengthenings of Priest-da Costa logic is examined and employed to pinpoint (...) the maximal non-classical extension of both daC and Heyting-Brouwer logic HB . Finally, the relationship between daC and Logics of Formal Inconsistency is examined. (shrink)

A key facet of Valerie Plumwood’s feminist critique of logic is her analysis of classical negation. On Plumwood’s reading, the exclusionary features of classical negation generate hierarchical dualisms, i.e., dichotomies in which dominant groups’ primacy is reinforced while underprivileged groups are oppressed. For example, Plumwood identifies the system collapse following from ex contradictione quodlibet—that a theory including both φ and ∼φ trivializes—as a primary source of many of these features. Although Plumwood considers the principle of excluded middle to be compatible (...) with her goals, that she identifies relevant logics as systems lacking a hierarchical negation—whose first-degree fragments are both paraconsistent and paracomplete—suggests that excluded middle plays some role in hierarchical dualisms as well. In these notes, I examine the role of excluded middle in generating oppressive homogenization and try to clarify the relationship between Plumwood’s critique and this principle from several contemporary perspectives. Finally, I examine the matter of whether Plumwood’s critique requires relevance or whether a non-relevant logic could satisfy her criteria and serve as a liberatory logic of difference. (shrink)

While participating in a symposium on Dave Ripley’s forthcoming book Uncut, I had proposed that employing a strict-tolerant interpretation of the weak Kleene matrices provided a content-theoretical conception of the bounds of conversational norms that enjoyed advantages over Ripley’s use of the strong Kleene matrices. During discussion, I used the case of sentences that are taken to be out-of-bounds for being secrets as an example of a case in which the setting of conversational bounds in practice diverged from the account (...) championed by Ripley. In this paper, I consider an objection that my treatment of quantifiers was mistaken insofar as the confidentiality of a sentence ϕ may not lift to the sentence ∃xϕ and draw from this objection that neither the strong nor the weak Kleene interpretation of quantifiers suffices, but that a novel interpretation may do so. (shrink)

We here make preliminary investigations into the model theory of DeMorgan logics. We demonstrate that Łoś's Theorem holds with respect to these logics and make some remarks about standard model-theoretic properties in such contexts. More concretely, as a case study we examine the fate of Cantor's Theorem that the classical theory of dense linear orderings without endpoints is $\aleph_{0}$-categorical, and we show that the taking of ultraproducts commutes with respect to previously established methods of constructing nonclassical structures, namely, Priest's Collapsing (...) Lemma and Dunn's Theorem in 3-Valued Logic. (shrink)

In this paper, we consider some contributions to the model theory of the logic of formal inconsistency $\mathsf{QmbC}$ as a reply to Walter Carnielli, Marcelo Coniglio, Rodrigo Podiacki and Tarcísio Rodrigues’ call for a ‘wider model theory.’ This call demands that we align the practices and techniques of model theory for logics of formal inconsistency as closely as possible with those employed in classical model theory. The key result is a proof that the Keisler–Shelah isomorphism theorem holds for $\mathsf{QmbC}$, i.e. (...) that the strong elementary equivalence of two $\mathsf{QmbC}$ models $\mathfrak{A}$ and $\mathfrak{B}$ is equivalent to them having strongly isomorphic ultrapowers. As intermediate steps, we introduce some notions of model-theoretic equivalence between $\mathsf{QmbC}$ models, explicitly prove Łoś’ theorem and introduce a useful technique of model-theoretic ‘atomization’ in which the satisfaction sets of non-deterministically evaluated formulae are associated with new predicates. Finally, we consider some of the extensions of $\mathsf{QmbC}$, explicitly showing that Keisler–Shelah holds for $\mathsf{QCi}$ and suggesting that it holds of extensions like $\mathsf{QCila}$ and $\mathsf{QCia}$ as well. (shrink)

This is the introduction to the special issue on Robert K. Meyer and the philosophy of arithmetic.

The mathematician G.F.C. Griss is known for his program of negationless intuitionistic mathematics. Although Griss’s rejection of negation is regarded as characteristic of his philosophy, this is a consequence of an executability requirement that mental constructions presuppose agents’ executing corresponding mental activity. Restoring Griss’s executability requirement to a central role permits a more subtle characterization of the rejection of negation, according to which D. Nelson’s strong constructible negation is compatible with Griss’s principles. This exposes a ‘holographic’ theory of negation in (...) negationless mathematics, in which a full theory of negation is ‘flattened’ in a putatively negationless setting. (shrink)

Bounds consequence provides an interpretation of a multiple-conclusion consequence relation in which the derivability of a sequent is understood as the claim that it is conversationally out-of-bounds to take a position in which each member of Γ is asserted while each member of Δ is denied. Two of the foremost champions of bounds consequence—Greg Restall and David Ripley—have independently indicated that the shape of the bounds in question is determined by conversational practice. In this paper, I suggest that the standard (...) treatments of bounds consequence have focused heavily on the matter of veridicality at the expense of ignoring other features by which conversational bounds are set, prime among them being the matter of content or subject-matter. Furthermore, I argue that the semantic behavior of propositions containing “monstrous” content—content whose introduction is inappropriate to a context independently of veridical considerations—leads to a weak Kleene account of bounds consequence. (shrink)

Yehoshua Bar-Hillel and Rudolph Carnap’s classical theory of semantic information entails the counterintuitive feature that inconsistent statements convey maximal information. Theories preserving Bar-Hillel and Carnap’s modal intuitions while imposing a veridicality requirement on which statements convey information—such as the theories of Fred Dretske or Luciano Floridi—avoid this commitment, as inconsistent statements are deemed not information-conveying by fiat. This paper produces a pair of paradoxical statements that such “veridical-modal” theories must evaluate as both conveying and not conveying information, although Bar-Hillel and (...) Carnap’s theory accommodates these statements without inconsistency. Moreover, the paradoxes are independently interesting as the mode in which they self-refer bears on their evaluation. (shrink)