A wealth of research documents the critical role of trust for social exchange and cooperative behavior. The ability to inspire trust in others can often be elusive, and distrust can have adverse interpersonal and ethical consequences. Drawing from the literature on social hierarchy and interpersonal judgments, the current research explores the predictive role of a structural paradox between high power and low status in identifying the actors most likely to be distrusted and monitored for ethical misconduct. Across four (...) studies and an internal meta-analysis, we found that the structural paradox was associated with distrust-related judgments and behaviors. In Study 1, high power-low status actors were judged as less trustworthy. In Studies 2 and 3, high power-low status actors were sent less money in a trust game, an effect fully mediated by feelings of dislike. Study 4 revealed that high power-low status actors were more likely to be monitored for cheating, an effect partially mediated by trust judgments. These findings contribute to business ethics research by identifying the structural paradox of high power-low status as a salient contextual influence impacting observers’ distrust and monitoring dynamics. Implications for reducing observers’ level of distrust of high power-low status actors are discussed. (shrink)

Rejecting structural contraction has been proposed as a strategy for escaping semantic paradoxes. The challenge for its advocates has been to make intuitive sense of how contraction might fail. I offer a way of doing so, based on a “naive” interpretation of the relation between structure and logical vocabulary in a sequent proof system. The naive interpretation of structure motivates the most common way of blaming Curry-style paradoxes on illicit contraction. By contrast, the naive interpretation will not as easily (...) motivate one recent noncontractive approach to the Liar paradox. (shrink)

Recently, several authors have pointed out that substructural logics are adequate for developing naive theories that represent semantic concepts such as truth. Among them, three proposals have been explored: dropping cut, dropping contraction and dropping reflexivity. However, nowhere in the substructural literature has anyone proposed rejecting the structural rule of weakening, while accepting the other rules. Some theorists have even argued that this task was not possible, since weakening plays no role in the derivation of semantic paradoxes. In this (...) article, I introduce a theory for naive truth based on the logic resulting from dropping the rule of weakening from classical logic, and maintaining the other structural rules. (shrink)

This article focuses on the link between borders and creativity that has come to light over the last two decades thanks to new interdisciplinary theoretical approaches proposing a systemic-processual shift within border studies. Following this, it is worth considering the creative interplay caused by the triad, bordering-ordering- othering, that conceives borders not only as demarcation lines, but also as dynamic, processual social practices. Borders are paradoxical structures that, created in order to separate and distinguish, signify created and creative spaces for (...) studying the contemporary world-system by adopting a pluri-versal perspective and moving toward a new border epistemology. (shrink)

Graham Priest argued that all the paradoxes of set theory and logic fall under one schema; and hence they should be solved by one kind of solution. This reply addresses both claims, and counters that in fact at least one paradox escapes the schema, and also some apparently "safe" theorems fall within it; and even for the range of paradoxes so captured by the schema, the assumption of a common solution is not obvious; each paradox surely depends upon (...) the theory and context in which it arises. Details of Priest's proposed solution are also sought. (shrink)

Anti-realist epistemic conceptions of truth imply what is called the knowability principle: All truths are possibly known. The principle can be formalized in a bimodal propositional logic, with an alethic modality ${\diamondsuit}$ and an epistemic modality ${\mathcal{K}}$, by the axiom scheme ${A \supset \diamondsuit \mathcal{K} A}$. The use of classical logic and minimal assumptions about the two modalities lead to the paradoxical conclusion that all truths are known, ${A \supset \mathcal{K} A}$. A Gentzen-style reconstruction of the Church–Fitch paradox is (...) presented following a labelled approach to sequent calculi. First, a cut-free system for classical bimodal logic is introduced as the logical basis for the Church–Fitch paradox and the relationships between ${\mathcal {K}}$ and ${\diamondsuit}$ are taken into account. Afterwards, by exploiting the structural properties of the system, in particular cut elimination, the semantic frame conditions that correspond to KP are determined and added in the form of a block of nonlogical inference rules. Within this new system for classical and intuitionistic “knowability logic”, it is possible to give a satisfactory cut-free reconstruction of the Church–Fitch derivation and to confirm that OP is only classically derivable, but neither intuitionistically derivable nor intuitionistically admissible. Finally, it is shown that in classical knowability logic, the Church–Fitch derivation is nothing else but a fallacy and does not represent a real threat for anti-realism. (shrink)

In recent years, substructural approaches to paradoxes have become quite popular. But whatever restrictions on structural rules we may want to enforce, it is highly desirable that such restrictions be accompanied by independent philosophical motivation, not directly related to paradoxes. Indeed, while these recent developments have shed new light on a number of issues pertaining to paradoxes, it seems that we now have even more open questions than before, in particular two very pressing ones: what (independent) motivations do we (...) have (if any) for restrictions on structural rules, and what to make of the plurality of new logics emerging from these restrictions, i.e. how to ‘choose’ among the different options. In this paper, we address these two questions from the perspective of a dialogical conception of logic that we've been advocating in recent years. We will argue that dialogical interpretations of structural rules, that is, as rules determining specific properties of the dialogues in question, provide a conveniently neutral framework to adjudicate between the different substructural proposals that have been made in the literature on paradoxes. (shrink)

For metaphysicians who have imbibed the sober and inebriating teachings of Thomas Aquinas, existence is an act, the act which makes all things actually to be. As the act of existence makes things to be, essence makes them to be what they are. Essence and the act of existence, in other words, are really distinct yet together they compose each of the things that are. Such an understanding involves a number of paradoxes, and Frederick D. Wilhelmsen's articulation of them reveals (...) his philosophical genius. These paradoxes include the fact that the act of existence does not exist, that it can be thought but not conceived by the mind, and that truths about God can be known while He himself remains absolutely unknown. Wilhelmsen argues the notion that the Christian faith and philosophical reason harmonize while remaining completely distinct from each other. Writing in a captivating style, Wilhelmsen begins with a discussion of the development, strengths, and limitations of the ancient Greek philosophical accounts of being. Following that, he develops such key topics as the problem of existence, St. Thomas Aquinas' understanding of being, critical analyses of Hegel's and Heidegger's doctrines of being, existence as "towards God," and a metaphysical approach to the human person. The final two chapters develop the sense in which metaphysical thinking is and is not shaped by historical and social factors. (shrink)

Propositions such as are paradoxical, in that even though they can be true, they cannot be truly asserted or believed. This is Moore’s paradox. Sydney Shoemaker has recently ar- gued that the paradox arises from a constitutive relation that holds between first- and second-order beliefs. This paper explores this approach to the paradox. Although Shoemaker’s own account of the paradox is rejected, a different account along similar lines is endorsed. At the core of the endorsed account (...) is the claim that conscious beliefs are always partly about themselves; it will be shown to follow from this that conscious beliefs in Moorean propositions are self-contradictory. (shrink)

This paper presents a model for the structure of universal frameworks in logic, mathematics, and physics that are closed to logical conclusion by the mechanism of paradox across a dualism of elements. The prohibition takes different forms defined by the framework of observation inherent to the structure. Forms include either prohibition to conclusion on the logical relationship of internal elements or prohibition to conclusion based on the existence of an element not included in the framework of a first element. (...) The model is applied to logical arguments in philosophy, mathematics, and physics and is initially a geometrical analysis of quantum theory and its application in experiment. Conclusion from the analysis is extended to give insight into the complexity of infinities above the two-dimensional boundary of the model. (shrink)

The way in which much of the conventional interpretation has tried to describe the structure of Hegel’s civil society is inaccurate and one-dimensional. To Hegel civil society is not just the economic marketplace, where every individual tries to maximize his or her enlightened self-interest: side by side with the elements of universal strife and unending clash which are of the nature of civil society, there is another element which strongly limits and inhibits self-interest and transcendswhat would otherwise be a universal (...) atomism into a sphere of solidarity and mutuality. The principle of civil society itself is dual. Hegel’s communitas grows organically within civil society itself, and is not imposed on it from outside by the state. (shrink)

We group the existing variants of the familiar set-theoretical and truth-theoretical paradoxes into two classes: connective paradoxes, which can in principle be ascribed to the presence of a contracting connective of some sort, and structural paradoxes, where at most the faulty use of a structural inference rule can possibly be blamed. We impute the former to an equivocation over the meaning of logical constants, and the latter to an equivocation over the notion of consequence. Both equivocation sources are (...) tightly related, and can be cleared up by adopting a particular substructural logic in place of classical logic. We then argue that our perspective can be justified via an informational semantics of contraction-free substructural logics. (shrink)

Paradox is a logical phenomenon. Usually, it is produced in type theory, on a type Ω of “truth values”. A formula Ψ (i.e., a term of type Ω) is presented, such that Ψ↔¬Ψ (with negation as a term¬∶Ω→Ω)-whereupon everything can be proved: In Sect. 1 we describe a general pattern which many constructions of the formula Ψ follow: for example, the well known arguments of Cantor, Russell, and Gödel. The structure uncovered behind these paradoxes is generalized in Sect. 2. (...) This allows us to show that Reynolds' [R] construction of a typeA ≃℘℘A in polymorphic λ-calculus cannot be extended, as conjectured, to give a fixed point ofevery variable type derived from the exponentiation: for some (contravariant) types, such a fixed point causes a paradox.Pursueing the idea that $$\frac{{{\text{type theory}}}}{{{\text{categorical interpretation}}}} = \frac{{{\text{(propositional) logic}}}}{{{\text{Lindebaum algebra}}}}$$ the language of categories appears here as a natural medium for logical structures. It allows us to abstract from the specific predicates that appear in particular paradoxes, and to display the underlying constructions in “pure state”. The essential role of cartesian closed categories in this context has been pointed out in [L]. The paradoxes studied here remain within the limits of the cartesian closed structure of types, as sketched in this Lawvere's seminal paper — and do not depend on any logical operations on the type Ω. Our results can be translated in simply typed λ-calculus in a straightforward way (although some of them do become a bit messy). (shrink)

Graham Priest 2002 argues that all logical paradoxes that include set-theoretic paradoxes and semantic paradoxes share a common structure, the Inclosure Schema, so they should be treated as one family. Through a discussion of Berry's Paradox and the semantic notion ?definable?, I argue that (i) the Inclosure Schema is not fine-grained enough to capture the essential features of semantic paradoxes, and (ii) the traditional separation of the two groups of logical paradoxes should be retained.

Gödel's conclusion that time-travel is possible in his models of Einstein's gravitational theory has been questioned by Chandrasekhar and Wright, and treated as doubtful in the recent philosophical literature. The present note is intended to remove this doubt: a review of Gödel's construction shows that his arguments are entirely correct; and the objection is seen to rest upon a misunderstanding. Computational points treated succinctly by Gödel are here presented in fuller detail. The philosophical significance of Gödel's results is briefly considered, (...) and a set of technical questions is posed whose answers would clarify this significance. (shrink)

Starting from the minimal principle of generative anthropology - that human culture originates as 'the deferral of violence through representation' - the author proposes a new understanding of the fundamental concepts of metaphysics and an explanation of the historical problematic that underlies the postmodern 'end of culture.' Part I discusses the nature of paradox and the related notion of irony, as well as the fundamental concepts of being, thinking, and signification, leading to an anthropological interpretation of the origin of (...) philosophy and semiotics in Plato's Ideas. Part II develops the idea that material exchange originates in the sparagmos or violent rendering of the sacrificial victim from which each participant obtains a roughly equal portion. Examining the holocaust, the author demonstrates how postmodern dialogue becomes dominated by the rhetoric of victimage, and the culture of centrality gives way to an aesthetic of the marginal. (shrink)

This short article aims to illustrate the mutually question-begging arguments that are often presented in debates between opponents and defenderss of McTaggart’s “proof” that A-properties (pastness, presentness and futurity) are logically incoherent. A sample of such arguments is taken from a recent debate between L. Nathan Oaklander (a defender of McTaggart) and myself (an opponent of McTaggart) and a method of escaping the impasse that is often reached in such debates is suggested.

This short article aims to illustrate the mutually question-begging arguments that are often presented in debates between opponents and defenderss of McTaggart’s “proof” that A-properties (pastness, presentness and futurity) are logically incoherent. A sample of such arguments is taken from a recent debate between L. Nathan Oaklander (a defender of McTaggart) and myself (an opponent of McTaggart) and a method of escaping the impasse that is often reached in such debates is suggested.

The classical theory of semantic information (ESI), as formulated by Bar-Hillel and Carnap in 1952, does not give a satisfactory account of the problem of what information, if any, analytically and/or logically true sentences have to offer. According to ESI, analytically true sentences lack informational content, and any two analytically equivalent sentences convey the same piece of information. This problem is connected with Cohen and Nagel's paradox of inference: Since the conclusion of a valid argument is contained in the (...) premises, it fails to provide any novel information. Again, ESI does not give a satisfactory account of the paradox. In this paper I propose a solution based on the distinction between empirical information and analytic information. Declarative sentences are informative due to their meanings. I construe meanings as structured hyperintensions, modelled in Transparent Intensional Logic as so-called constructions. These are abstract, algorithmically structured procedures whose constituents are sub-procedures. My main thesis is that constructions are the vehicles of information. Hence, although analytically true sentences provide no empirical information about the state of the world, they convey analytic information, in the shape of constructions prescribing how to arrive at the truths in question. Moreover, even though analytically equivalent sentences have equal empirical content, their analytic content may be different. Finally, though the empirical content of the conclusion of a valid argument is contained in the premises, its analytic content may be different from the analytic content of the premises and thus convey a new piece of information. (shrink)

How social workers do construct what is ‘ethical’ in their work, especially when they are positioned at the intersection of multiple paradoxes, including that of two opposing responsibilities in society: namely, to care for others but also to prevent others from harm? Paradoxes in practice are especially complicated to manage in the neoliberalism of the Global North where the priority of efficiency has been heightened and the obligation towards the most vulnerable has been weakened. Taking data from a Canadian study, (...) this paper delineates the structural paradoxes of practice and elaborates on the concept of ethical trespass, especially in times of austerity. Ideas are illustrated with case material from participants who were practitioners working with a population of young single impoverished mothers. Impacts of the discourses on single mothers, resource inadequacies, and increased surveillance on clients are discussed, and the effects on workers such as individualization and burnout will be outlined. Despite the challenges, practitioners in the study found ways to minimize trespass and act ethically. The strategies employed included problematizing the helping relationship, being a responsible traitor, dissident speech, and the use of contextualized practice. (shrink)

This book will examine paradoxes in diverse areas of thought: philosophy, mathematics, physics, economics, political science, psychology, computer science, logic, statistics, linguistics, law, etc. Though the treatment of each paradox is rigorous, the book will be written accessibly with a lighthearted and humorous tone so as to keep the reader engaged. Each chapter will focus on a single paradox, structured roughly like so: 1. A question is asked in the context of a story. As an answer, the (...) class='Hi'>paradox is presented (which often results in an aha moment). The historical background of the paradox is recounted. 2. The dénouement explains how the paradox is resolved or why there is no resolution. 3. The chapter ends with further remarks, usually contemporary real-world examples or applications of said paradox. Some examples of the paradoxes covered are the Axiom of Choice (Mathematics), Monty Hall Problem (Statistics), Morgenbesser's Paradox (Linguistics), Tea Leaves Paradox (Physics), The Ultimatum Game (Economics), and The Chicken or Egg Question (Evolution). (shrink)

We introduce a variant of pointer structures with denotational semantics and show its equivalence to systems of boolean equations: both have the same solutions. Taking paradoxes to be statements represented by systems of equations (or pointer structures) having no solutions, we thus obtain two alternative means of deciding paradoxical character of statements, one of which is the standard theory of solving boolean equations. To analyze more adequately statements involving semantic predicates, we extend propositional logic with the assertion operator and give (...) its complete axiomatization. This logic is a sub-logic of statements in which the semantic predicates become internalized (for instance, counterparts of Tarski’s definitions and T-schemata become tautologies). Examples of analysis of self-referential paradoxes are given and the approach is compared to the alternative ones. (shrink)

This paper presents a structural-functionalist solution to a paradox that historian of anthropology George Stocking dug up: from the point of view of parts of the Victorian middle class, Victorian society was highly evolved yet also contained savage components.

“Weak relevant model structures” (wr-ms) are defined on “weak relevant matrices” by generalizing Brady’s model structure ${\mathcal{M}_{\rm CL}}$ built upon Meyer’s Crystal matrix CL. It is shown how to falsify in any wr-ms the Generalized Modus Ponens axiom and similar schemes used to derive Curry’s Paradox. In the last section of the paper we discuss how to extend this method of falsification to more general schemes that could also be used in deriving Curry’s Paradox.

Background In June 2016, the Parliament of Canada passed federal legislation allowing eligible adults to request Medical Assistance in Dying (MAID). Since its implementation, there likely exists a degree of hesitancy among some healthcare providers due to the law being inconsistent with personal beliefs and values. It is imperative to explore how nurses in Quebec experience the shift from accompanying palliative clients through “a natural death” to participating in “a premeditated death.” Research question/aim/objectives This study aims to explore how Quebec (...) nurses personally and professionally face the new practice of MAID and their role evolution. Research design A grounded theory design was used. Participants and research context We recruited 37 nurses who participated in or coordinated at least one MAID. Semi-structured interviews and focus groups were conducted and audiotaped. Data collection and analysis followed Strauss and Corbin steps. Ethical considerations Ethics approval was received from the investigator’s affiliated University. Participants were informed regarding the research goal, signed a written consent, and were assigned pseudonyms. Findings/results Results show that nurses experienced the wide range of paradoxe during MAID centering around the following eight elements: 1) confrontation abouth death, 2) choice, 3) time of death, 4) emotional load, 5) new Bill, 6) relationship with the person, 7) communication skills, and 8) healthcare setting. The shifting of views and values in this new role is presented by the contradiction of opposites. Conclusions A better understanding of the paradox experienced by nurses involved with MAID paves the way for the development of interventions. (shrink)

Late modern existence is built around ambivalences: subjects experience the structural paradoxes of global capitalism or information society as social suffering; yet they follow behaviour patterns reinforcing the unsustainable trajectories. The article explores the discourses justifying such structural paradoxes, while normalizing the related suffering. First, the pragmatic theory of justification (Boltanski, Thévenot) is reinterpreted from a modernization theoretical perspective: a distinction is drawn between traditional, classic and late modern ‘tests’, ‘critique’ and ‘cités’. In the second and third sections, (...) the gradual emptying of critique is analysed: as disillusionment reaches the sphere of subjective experiences, not even personal suffering can ground critique any more (Berlant), thus the impossibility of critique is demonstrated in a cynical manner (Sloterdijk). In the fourth section, the various cynical modalities of justification fitting the ambivalent contemporary existence are overviewed. Finally, a way out from the naturalized, quotidian cynicism is sketched: by turning cynicism’s logic against itself, the dialectics of justification can move forward. (shrink)

I will use paradox as a guide to metaphysical grounding, a kind of non-causal explanation that has recently shown itself to play a pivotal role in philosophical inquiry. Specifically, I will analyze the grounding structure of the Predestination paradox, the regresses of Carroll and Bradley, Russell's paradox and the Liar, Yablo's paradox, Zeno's paradoxes, and a novel omega plus one variant of Yablo's paradox, and thus find reason for the following: We should continue to characterize (...) grounding as asymmetrical and irreflexive. We should change our understanding of the transitivity of grounding in a certain sense. We should require foundationality in a new, generalized sense, that has well-foundedness as its limit case. Meta-grounding is important. The polarity of grounding can be crucial. Thus we will learn a lot about structural properties of grounding from considering the various paradoxes. On the way, grounding will also turn out to be relevant to the diagnosis (if not the solution) of paradox. All the paradoxes under consideration will turn out to be breaches of some standard requirement on grounding, which makes uniform solutions of large groups of these paradoxes more desirable. In sum, bringing together paradox and grounding will be shown to be of considerable value to philosophy.1. (shrink)

Within contemporary analytic philosophy, varieties of “naturalism” have recently attained an almost unchallenged methodological and thematic dominance. As David Papineau wrote in the introduction to his 1993 book Philosophical Naturalism, “nearly everybody nowadays wants to be a naturalist,” although as Papineau also notes, those who aspire to the term also continue to disagree widely about what specific methods or doctrines it implies. My purpose in this paper, however, is not to argue for or against philosophical naturalism on any of the (...) several conceptions current among analytic philosophers, but rather simply to suggest that a closer look at the history of the analytic tradition can offer helpful terms for rethinking what can be meant by applying the categories of “nature” and “culture” within philosophy’s ongoing reflection on the constitutive forms of human life and practice. For, as I shall argue, the central experience of this history – philosophy’s radical encounter with what it envisions as the logical or conceptual structure of everyday language – also repeatedly demonstrates the existence of a fundamental aporia or paradox of origin and practice at the center of the claim of language upon an ordinary human life. The appearance of this paradox has repeatedly determined the results and projects of the analytic tradition, even as analytic philosophers have also reacted to it, on the level of positive theory, in characteristic modes of dismissal, denial, or repression. Besides offering to elicit more clearly what analytic philosophy still offers to show us about our everyday relation to the language that we speak, I shall argue, documenting the existence and effects of this aporia can also yield a clarified sense of the relationship of the analytic tradition itself to the neighboring streams of “continental” philosophy that have also taken up the question of language during the twentieth century. (shrink)

The article deals with the problematic aspects of the concept of identity, the analysis of which helps to point out and to overcome the paradoxes of the “diachronic identity”, the identity of the human person (as identity of its inner cell) and “plural, flexible identity”, and also to clarify the conditions of the legitimate use of these concepts in contemporary philosophy and social science. The article examines two paradigms of identity: the substantive, when the identity of a thing is sought (...) in an invariable property, which provides its synchronous identity, and the formal, when the identity is sought in a form, a structure of the language, which provides its duration in time and helps to understand the diachronic identity. The article shows the importance of the use of “criteria of identity”, introduced by analytical philosophers to find out the way of duration in time of beings which they try to identify, from the material objects to the collective beings, including the identity of the human person. The problem of subjective identity is pointed out as a separate problem. Two main approaches to it are differentiated: mentalist and expressivist. The first is focused on the inner world of the human being, its memories and feelings, creating paradoxes of the «identity for itself» which is not the «identity for the others», whereas the second lets include the social world in the definition of the subjective identity and facilitates the reconsideration of the boundaries of the internal and the external in determining the human self. The article analyses contemporary use of the concept of identity in social science and public discourses and demonstrates the contradiction of the concept of “plural, heterogeneous identity”, which formulates but doesn’t solve the problem of the subjective identity as the identification of an individual with different social groups. (shrink)

The author believes that large‐scale rationality on the part of the interpretant is essential to his interpretability, and therefore, in his view, to her having a mind. How, then are cases of irrationality, such as akrasia or self‐deception, judged by the interpretant's own standards, possible? He proposes that, in order to resolve the apparent paradoxes, one must distinguish between accepting a contradictory proposition and accepting separately each of two contradictory propositions, which are held apart, which in turn requires to conceive (...) of the mind as containing a number of semi‐independent structures of interlocking beliefs, desires, emotions, memories, and other mental states. (shrink)

According to the revision theory of truth, the paradoxical sentences have certain revision periods in their valuations with respect to the stages of revision sequences. We find that the revision periods play a key role in characterizing the degrees of paradoxicality for Boolean paradoxes. We prove that a Boolean paradox is paradoxical in a digraph, iff this digraph contains a closed walk whose height is not any revision period of this paradox. And for any finitely many numbers greater (...) than 1, if any of them is not divisible by any other, we can construct a Boolean paradox whose primary revision periods are just these numbers. Consequently, the degrees of Boolean paradoxes form an unbounded dense lattice. The area of Boolean paradoxes is proved to be rich in mathematical structures and properties. (shrink)

This paper is concerned with the paradox of decrease. Its aim is to defend the answer to this puzzle that was propounded by its originator, namely, the Stoic philosopher Chrysippus. The main trouble with this answer to the paradox is that it has the seemingly problematic implication that a material thing could perish due merely to extrinsic change. It follows that in order to defend Chrysippus’ answer to the paradox, one has to explain how it could be (...) that Theon is destroyed by the amputation without changing intrinsically. In this paper, I shall answer this challenge by appealing to the broadly Aristotelian idea that at least some of the proper parts of a material substance are ontologically dependent on that substance. I will also appeal to this idea in order to offer a new solution to the structurally similar paradox of increase. In this way, we will end up with a unified solution to two structurally similar paradoxes. (shrink)

This paper argues that the theory of structured propositions is not undermined by the Russell-Myhill paradox. I develop a theory of structured propositions in which the Russell-Myhill paradox doesn't arise: the theory does not involve ramification or compromises to the underlying logic, but rather rejects common assumptions, encoded in the notation of the $\lambda$-calculus, about what properties and relations can be built. I argue that the structuralist had independent reasons to reject these underlying assumptions. The theory is given (...) both a diagrammatic representation, and a logical representation in a novel language. In the latter half of the paper I turn to some technical questions concerning the treatment of quantification, and demonstrate various equivalences between the diagrammatic and logical representations, and a fragment of the $\lambda$-calculus. (shrink)

Any theory of truth must find a way around Curry’s paradox, and there are well-known ways to do so. This paper concerns an apparently analogous paradox, about validity rather than truth, which JC Beall and Julien Murzi call the v-Curry. They argue that there are reasons to want a common solution to it and the standard Curry paradox, and that this rules out the solutions to the latter offered by most “naive truth theorists.” To this end they (...) recommend a radical solution to both paradoxes, involving a substructural logic, in particular, one without structural contraction. In this paper I argue that substructuralism is unnecessary. Diagnosing the “v-Curry” is complicated because of a multiplicity of readings of the principles it relies on. But these principles are not analogous to the principles of naive truth, and taken together, there is no reading of them that should have much appeal to anyone who has absorbed the morals of both the ordinary Curry paradox and the second incompleteness theorem. (shrink)

When we evaluate moral agents, we consider many factors, including whether the agent acted freely, or under duress or coercion. In turn, moral evaluations have been shown to influence our (non-moral) evaluations of these same factors. For example, when we judge an agent to have acted immorally, we are subsequently more likely to judge the agent to have acted freely, not under force. Here, we investigate the cognitive signatures of this effect in interpersonal situations, in which one agent (“forcer”) forces (...) another agent (“forcee”) to act either immorally or morally. The structure of this relationship allowed us to ask questions about both the “forcer” and the “forcee.” Paradoxically, participants judged that the “forcer” forced the “forcee” to act immorally (i.e. X forced Y), but that the “forcee” was not forced to act immorally (i.e. Y was not forced by X). This pattern obtained only for human agents who acted intentionally. Directly changing participants’ focus from one agent to another (forcer vs. forcee) also changed the target of moral evaluation and therefore force attributions. The full pattern of judgments may provide a window into motivated moral reasoning and focusing bias more generally; participants may have been motivated to attribute greater force to the immoral forcer and greater freedom to the immoral forcee. (shrink)

The semantic paradoxes are associated with self-reference or referential circularity. However, there are infinitary versions of the paradoxes, such as Yablo's paradox, that do not involve this form of circularity. It remains an open question what relations of reference between collections of sentences afford the structure necessary for paradoxicality -- these are the so-called "dangerous" directed graphs. Building on Rabern, et. al (2013) we reformulate this problem in terms of fixed points of certain functions, thereby boiling it down to (...) get a purely mathematical problem. (shrink)

The semantic paradoxes are often associated with self-reference or referential circularity. Yablo (Analysis 53(4):251–252, 1993), however, has shown that there are infinitary versions of the paradoxes that do not involve this form of circularity. It remains an open question what relations of reference between collections of sentences afford the structure necessary for paradoxicality. In this essay, we lay the groundwork for a general investigation into the nature of reference structures that support the semantic paradoxes and the semantic hypodoxes. We develop (...) a functionally complete infinitary propositional language endowed with a denotation assignment and extract the reference structural information in terms of graph-theoretic properties. We introduce the new concepts of dangerous and precarious reference graphs, which allows us to rigorously define the task: classify the dangerous and precarious directed graphs purely in terms of their graph-theoretic properties. Ungroundedness will be shown to fully characterize the precarious reference graphs and fully characterize the dangerous finite graphs. We prove that an undirected graph has a dangerous orientation if and only if it contains a cycle, providing some support for the traditional idea that cyclic structure is required for paradoxicality. This leaves the task of classifying danger for infinite acyclic reference graphs. We provide some compactness results, which give further necessary conditions on danger in infinite graphs, which in conjunction with a notion of self-containment allows us to prove that dangerous acyclic graphs must have infinitely many vertices with infinite out-degree. But a full characterization of danger remains an open question. In the appendices we relate our results to the results given in Cook (J Symb Log 69(3):767–774, 2004) and Yablo (2006) with respect to more restricted sentences systems, which we call $\mathcal{F}$ -systems. (shrink)

The structure of Yablo’s paradox is analysed and generalised in order to show that beginningless step-by-step determination processes can be used to provoke antinomies, more concretely, to make our logical and our on-tological intuitions clash. The flow of time and the flow of causality are usually conceived of as intimately intertwined, so that temporal causation is the very paradigm of a step-by-step determination process. As a conse-quence, the paradoxical nature of beginningless step-by-step determina-tion processes concerns time and causality as (...) usually conceived. (shrink)