Grelling's Paradox is the paradox which results from considering whether heterologicality, the word-property which a designator has when and only when the designator does not bear the word-property it designates, is had by 'heterologicality'. Although there has been some philosophical debate over its solution, Grelling's Paradox is nearly uniformly treated as a variant of either the Liar Paradox or Russell's Paradox, a paradox which does not present any philosophical challenges not already presented by the (...) two better known paradoxes. The aims of this paper are, first, to offer a precise formulation of Grelling's Paradox which is clearly distinguished from both the Liar Paradox and Russell's Paradox; second, to offer a solution to Grelling's Paradox which both resolves the paradoxical reasoning and accounts for unproblematic predications of heterologicality; and, third, to argue that there are two lessons to be drawn from Grelling's Paradox which have not yet been drawn from the Liar or Russell's Paradox. The first lesson is that it is possible for the semantic content of a predicate to be sensitive to the semantic context; i.e., it is possible for a predicate to be an indexical expression. The second lesson is that the semantic content of an indexical predicate, though unproblematic for many cases, can nevertheless be problematic in some cases. In Section 1, Grelling's Paradox is presented informally. After making some refinements, Grelling's Paradox is then presented formally. In Section 2, the formal version of Grelling's Paradox is evaluated, and several previously proposed solutions are discussed and argued to be inadequate. In Section 3, it is argued that the heterologicality predicate is an indexical expression. A semantics for the heterologicality predicate is given, and it is shown how this semantics accounts for the unproblematic predications of heterologicality, as well as the problematic cases, and therefore constitutes a satisfactory and complete solution to Grelling's Paradox. Objections to this solution are addressed in Section 4. The conclusions of this paper are summarized in Section 5. (shrink)

Grelling’s Paradox is the paradox which results from considering whether heterologicality, the word-property which a designator has when and only when the designator does not bear the word-property it designates, is had by ‘ ȁ8heterologicality’. Although there has been some philosophical debate over its solution, Grelling’s Paradox is nearly uniformly treated as a variant of either the Liar Paradox or Russell’s Paradox, a paradox which does not present any philosophical challenges not already (...) presented by the two better known paradoxes. The aims of this paper are, first, to offer a precise formulation of Grelling’s Paradox which is clearly distinguished from both the Liar Paradox and Russell’s Paradox; second, to offer a solution to Grelling’s Paradox which both resolves the paradoxical reasoning and accounts for unproblematic predications of heterologicality; and, third, to argue that there are two lessons to be drawn from Grelling’s Paradox which have not yet been drawn from the Liar or Russell’s Paradox. The first lesson is that it is possible for the semantic content of a predicate to be sensitive to the semantic context; i.e., it is possible for a predicate to be an indexical expression. The second lesson is that the semantic content of an indexical predicate, though unproblematic for many cases, can nevertheless be problematic in some cases. (shrink)

This discusses a mistake (concerning what a definition is) in “Grelling’s revenge”, Analysis 64, 251-6 (2004), by Dale Jacquette, who claims that the simple theory of types is inconsistent.

In this paper three different solutions to Grelling’s paradox, also called the heterological paradox, are given. Firstly, after given the original formulation of the paradox by Grelling and Nelson in 1908, a solution to this paradox offered by Frank Plumpton Ramsey in 1925 is presented. His solution is based on the different meanings of the word “meaning.” Secondly, Grelling himself advocated the solution proposed by Uuno Saarnio in 1937. Saarnio’s solution is based on the exact (...) definitions of the concept of word, and the concept of denoting. Thirdly, a solution to this paradox was proposed also by Georg Henrik von Wright in 1960, but his solution consists of saying that the word “heterological” does not name a concept—or it names a concept only up to a singular point. (shrink)

The goal of this paper is to present Yabloesque versions of Grelling’s and Zwicker’s paradoxes concerning the notions of “heterological” and “hypergame” respectively. We will offer counterparts of these paradoxes that do not seem to involve self-reference or vicious circularity.El objetivo de este artículo es ofrecer versiones de las paradojas de Grelling y de Zwicker inspiradas en la paradoja de Yablo. Nuestras versiones de estas paradojas no parecen involucrar ni autorreferencia ni circularidad viciosa.

The goal of this paper is to present Yabloesque versions of Grelling’s and Zwicker’s paradoxes concerning the notions of “heterological” and “hypergame” respectively. We will offer counterparts of these paradoxes that do not seem to involve self-reference or vicious circularity.El objetivo de este artículo es ofrecer versiones de las paradojas de Grelling (sobre el predicado “heterológico”) y de Zwicker (sobre el hiperjuego) inspiradas en la paradoja de Yablo. Nuestras versiones de estas paradojas no parecen involucrar ni autorreferencia ni circularidad (...) viciosa. (shrink)

The paper discusses whether there are strictly inexpressible properties. Three main points are argued for: (i) Two different senses of ‘predicate t expresses property p ’ should be distinguished. (ii) The property of being a predicate that does not apply to itself is inexpressible in one of the senses of ‘express’, but not in the other. (iii) Since the said property is related to Grelling’s Antinomy, it is further argued that the antinomy does not imply the non-existence of that (...) property. (shrink)

This volume for the first time brings the scholarly discipline of comparative religious ethics into constructive collaboration with the community of interreligious dialogue. Its design is premised on two important insights. First, interreligious dialogue offers to comparative religious ethics a new, more persuasive rationale, agenda of issues, and practical orientation. Second, comparative religious ethics offers to interreligious dialogue an arsenal of critical tools and methods which will enhance the sophistication of its practical work. In this way, both theory (a dominant (...) concern and strength of comparative religious ethics) and praxis (a dominant concern and strength of interreligious moral dialogue) are joined together in mutual effort, each contributing to the benefit of the other.The volume’s contributors share this vision of collaboration, drawing explicitly from both communities of discourse in a manner that crosses disciplinary and professional boundaries to deal creatively and constructively with important methodological and global moral issue. Although theory and practice cannot easily be separated in such a collaborative project, for the purpose of clarity, the volume is divided into two main parts. The first specifically engages questions of method, theory, and the social role of the public intellectual; the second, on substantive moral themes and issues, many of which were raised at the 1993 Parliament. Taken together, the volume’s essays articulate and illustrate new ways of approaching contemporary moral concerns cross-culturally yet with a rigor appropriate to our complex and pluralistic world. (shrink)

Tarski's argumentative use of the liar paradox is well-known, but officially it is the Grelling paradox that has final pride of place in Tarski's argument, not the Liar at all. Tarski explicitly gives argumentation that adverts to the liar argument, but it is an alternative argument—one he only hints at and which adverts to the Grelling—which he says has the advantage of removing any empirical element. In this paper, we will examine how the Grelling might be used in (...) place of the Liar in Tarski's argument for his exact indefinability thesis, and assess in what way the difference might be significant. If successful, Tarski's use of the Grelling puts pressure on how Convention T can be justified. (shrink)

The Practices of Global Ethics takes a unique look at global ethics: not as mere written statements but as a set of practices undertaken by thousands of organisations and hundreds of thousands of people to shape the normative trajectory of human affairs. It looks at statements of global ethical principles including The Universal Declaration of Human Rights, the Earth Charter and the Rio Documents and positions them as the outcomes and expression of ongoing practices. Offering innovative, critical and thoughtful analyses (...) of ethical practices since World War II, the book examines efforts to promote human rights; foster ecological responsibility; end genocide; reduce global poverty; encourage responsible and sustainable international business practices; cultivate understanding and collaboration amongst the world's religions among other worldwide endeavours. (shrink)

Antonio Gramsci and the Question of Religionprovides a new introduction to the thought of Gramsci through the prisms of religious studies and comparative ethics. Bruce Grelle shows that Gramsci's key ideas - on hegemony, ideology, moral reformation, "traditional" and "organic" intellectuals - were formulated with simultaneous considerations of religion and politics. Identifying Gramsci's particular brand of Marxism, Grelle offers an overview of Gramsci's approach to religion and applies it to contemporary debates over the role of religion and morality in social (...) order and social change. This book is ideal for students and scholars interested in Gramsci, religion, and comparative ethics. (shrink)

La solution des antinomies s’accomplit en 3 étapes. 1° La théorie des types de Russell avec l’axiome de réductibilité. 2° Ramsey divise les antinomies en deux groupes. Le premier groupe reçoit sa solution de la simple théorie des types ; seul, le groupe élargi exige l’axiome de réductibilité. 3° Hilbert fonde la théorie métamathématique de la preuve, que les logiciens polonais élargissent en une métalogique. Gödel découvre l’arithmétisation et il prouve l’existence de propositions insolubles. Tarski montre que le concept de (...) vérité ne peut être défini sans contradiction que dans un métalangage. Carnap généralise ce résultat, ce qui fait que les antinomies syntactiques sont sans dommage pour la science. (shrink)

Cette réflexion s’articule en trois mouvements. Le premier aborde la question de l’évolution de la précarité comme objet d’expérience. Le deuxième tente de montrer l’évolution des processus de base auxquels se livrent les jeunes en situation de précarité lorsqu’ils veulent manifester leur sentiment d’existence et les opérations au moyen desquelles ils parviennent à construire ce qu’ils appellent une « petite vie ». Enfin, dans le troisième mouvement, se pose la question de l’originalité des relations symboliques qu’ils expriment, étant entendu que (...) cette réflexion se fonde sur l’expérience vécue d’une catégorie de jeunes dont les dispositifs situationnels de précarité portent à penser, au moins a priori, qu’ils se laisseraient plus facilement mener par les déterminations qui pèsent sur leur vie, qu’ils ne s’en écarteraient.This project is composed of three interrelated elements. The first deals with the problem of precariousness as a fact of experience. The second attempts to describe the evolution of the basic processes to which young people have recourse in a situation of precariousness when they wish to express their sense of existence, as well as the processes that allow them to succeed in constructing what they call a « day-to-day existence ». Thirdly and finally, we address the issue of the original aspect of symbolic relations expressed by young people. It is understood that the project situates itself upon the life experiences of a category of young people whose situational mechanisms of precariousness lead us to believe, at least a priori, that these young people would more easily let themselves be driven by social determinants that weigh them down than they would be to step away from them. (shrink)

This article is about the chief character of Sartre?s unfinished trilogy of novels known as Les chemins de la liberté—Daniel, Mathieu?s fellow-student at the École normale, Daniel the "archangel," Daniel the shamefaced pederast, Daniel the gaping wound, Daniel the strange hero, Daniel the recurrent figure in many of Sartre?s works. We do not intend to offer yet another explanation of this handsome young literature professor?s convoluted character to the explanations that already exist, nor to interpret yet again his detestation of (...) mankind and his prayers to God, which the author openly mocks. What we wish to do in these few pages is firstly to shed light on the procedures of Daniel?s imagination and evolution, and secondly to analyze how the author?s goals changed as, while writing the trilogy, he evolved from Gallimard?s up and coming star into the symbol of the search for freedom, the spokesman whom some disagreed with, criticised, despised, while others glorified him and praised him to the skies. We would like to try and elucidate the evolution of this character, steering between the free future of a literary work in progress and the ungraspable heart of darkness. (shrink)

Cover -- Title -- Copyright -- Contents -- List of figures -- Contributors -- Acknowledgements -- 1 Introduction -- 2 Philip Melanchthon and his significance for natural philosophy -- 3 Daniel Sennert and the chymico-atomical reform of medicine -- 4 The changing face of Lutheranism in post-Reformation Denmark -- 5 After Tycho: Philippist astronomy and cosmology in the work of Brahe's Scandinavian assistants -- 6 The Book of Nature and the Word of God: Lutheran natural philosophy and medicine in early-seventeenth-century (...) Denmark and Norway -- 7 Holger Rosenkrantz, 'the Learned' (1574-1642). (shrink)

Sumner B. (Barney) Twiss, who died in 2023, was for ten years a General Editor of the Journal of Religious Ethics (JRE). He was a frequent contributor of articles, a member of the JRE Editorial Board, and a member of the journal's Board of Trustees. In this article, colleagues and students reflect on some of his many contributions, not only to the JRE but to the broader discursive fields of comparative religious ethics and human rights.

Many books explain what is known about the universe. This book investigates what cannot be known. Rather than exploring the amazing facts that science, mathematics, and reason have revealed to us, this work studies what science, mathematics, and reason tell us cannot be revealed. In The Outer Limits of Reason, Noson Yanofsky considers what cannot be predicted, described, or known, and what will never be understood. He discusses the limitations of computers, physics, logic, and our own thought processes. Yanofsky describes (...) simple tasks that would take computers trillions of centuries to complete and other problems that computers can never solve; perfectly formed English sentences that make no sense; different levels of infinity; the bizarre world of the quantum; the relevance of relativity theory; the causes of chaos theory; math problems that cannot be solved by normal means; and statements that are true but cannot be proven. He explains the limitations of our intuitions about the world -- our ideas about space, time, and motion, and the complex relationship between the knower and the known. Moving from the concrete to the abstract, from problems of everyday language to straightforward philosophical questions to the formalities of physics and mathematics, Yanofsky demonstrates a myriad of unsolvable problems and paradoxes. Exploring the various limitations of our knowledge, he shows that many of these limitations have a similar pattern and that by investigating these patterns, we can better understand the structure and limitations of reason itself. Yanofsky even attempts to look beyond the borders of reason to see what, if anything, is out there. (shrink)

There are three questions associated with Simpson’s Paradox (SP): (i) Why is SP paradoxical? (ii) What conditions generate SP?, and (iii) What should be done about SP? By developing a logic-based account of SP, it is argued that (i) and (ii) must be divorced from (iii). This account shows that (i) and (ii) have nothing to do with causality, which plays a role only in addressing (iii). A counterexample is also presented against the causal account. Finally, the causal and (...) logic-based approaches are compared by means of an experiment to show that SP is not basically causal. (shrink)

Sensorimotor synchronization, the coordination of physical actions in time with a rhythmic sequence, is a skill that is necessary not only for keeping the beat when making music, but in a wide variety of interpersonal contexts. Being able to attend to temporal regularities in the environment is a prerequisite for event prediction, which lies at the heart of many cognitive and social operations. It is therefore of value to assess and potentially stimulate SMS abilities, particularly in aging and neurocognitive disorders, (...) to understand intra-individual communication in the later stages of life, and to devise effective music-based interventions. While a bulk of research exists about SMS and movement-based interventions in Parkinson’s disease, a lot less is known about other types of neurodegenerative disorders, such as Alzheimer’s disease, vascular dementia, or frontotemporal dementia. In this review, we outline the brain and cognitive mechanisms involved in SMS with auditory stimuli, and how they might be subject to change in healthy and pathological aging. Globally, SMS with isochronous sounds is a relatively well-preserved skill in old adulthood and in patients with NCDs. At the same time, natural tapping speed decreases with age. Furthermore, especially when synchronizing to sequences at slow tempi, regularity and precision might be lower in older adults, and even more so in people with NCDs, presumably due to the fact that this process relies on attention and working memory resources that depend on the prefrontal cortex and parietal areas. Finally, we point out that the effect of the severity and etiology of NCDs on sensorimotor abilities is still unclear: More research is needed with moderate and severe NCD, comparing different etiologies, and using complex auditory signals, such as music. (shrink)

In this essay (for undergraduates) I introduce three of the famous semantic paradoxes: the Liar, Grelling’s, and the No-No. Collectively, they seem to show that the notion of truth is highly paradoxical, perhaps even contradictory. They seem to show that the concept of truth is a bit akin to the concept of a married bachelor—it just makes no sense at all. But in order to really understand those paradoxes one needs to be very comfortable thinking about how lots of (...) interesting sentences talk about not dogs or cats or elections or baseball but sentences. That is, we need to get familiar analyzing sentences that talk about sentences. (shrink)

G. E. Moore observed that to assert, 'I went to the pictures last Tuesday but I don't believe that I did' would be 'absurd'. Over half a century later, such sayings continue to perplex philosophers. In the definitive treatment of the famous paradox, Green and Williams explain its history and relevance and present new essays by leading thinkers in the area.

There are three distinct questions associated with Simpson's paradox, (i) Why or in what sense is Simpson's paradox a paradox? (ii) What is the proper analysis of the paradox? (iii) How one should proceed when confronted with a typical case of the paradox? We propose a "formar" answer to the first two questions which, among other things, includes deductive proofs for important theorems regarding Simpson's paradox. Our account contrasts sharply with Pearl's causal (and questionable) (...) account of the first two questions. We argue that the "how to proceed question?" does not have a unique response, and that it depends on the context of the problem. We evaluate an objection to our account by comparing ours with Blyth's account of the paradox. Our research on the paradox suggests that the "how to proceed question" needs to be divorced from what makes Simpson's paradox "paradoxical.". (shrink)

There are three distinct questions associated with Simpson’s paradox. Why or in what sense is Simpson’s paradox a paradox? What is the proper analysis of the paradox? How one should proceed when confronted with a typical case of the paradox? We propose a “formal” answer to the first two questions which, among other things, includes deductive proofs for important theorems regarding Simpson’s paradox. Our account contrasts sharply with Pearl’s causal account of the first two (...) questions. We argue that the “how to proceed question?” does not have a unique response, and that it depends on the context of the problem. We evaluate an objection to our account by comparing ours with Blyth’s account of the paradox. Our research on the paradox suggests that the “how to proceed question” needs to be divorced from what makes Simpson’s paradox “paradoxical.”. (shrink)

A version of nonstandard analysis, Internal Set Theory, has been used to provide a resolution of Zeno's paradoxes of motion. This resolution is inadequate because the application of Internal Set Theory to the paradoxes requires a model of the world that is not in accordance with either experience or intuition. A model of standard mathematics in which the ordinary real numbers are defined in terms of rational intervals does provide a formalism for understanding the paradoxes. This model suggests that in (...) discussing motion, only intervals, rather than instants, of time are meaningful. The approach presented here reconciles resolutions of the paradoxes based on considering a finite number of acts with those based on analysis of the full infinite set Zeno seems to require. The paper concludes with a brief discussion of the classical and quantum mechanics of performing an infinite number of acts in a finite time. (shrink)

There are three questions associated with Simpson’s paradox (SP): (i) Why is SP paradoxical? (ii) What conditions generate SP? and (iii) How to proceed when confronted with SP? An adequate analysis of the paradox starts by distinguishing these three questions. Then, by developing a formal account of SP, and substantiating it with a counterexample to causal accounts, we argue that there are no causal factors at play in answering questions (i) and (ii). Causality enters only in connection with (...) action. (shrink)

Hempel's paradox of the ravens has to do with the question of what constitutes confirmation from a logical point of view; Wason 's selection task has been used extensively to investigate how people go about attempting to confirm or disconfirm conditional claims. This paper presents an argument that the paradox is resolved, and that people's typical performance in the selection task can be explained, by consideration of what constitutes an effective strategy for seeking evidence of the tenability of (...) universal or conditional claims in everyday life. (shrink)

We address the need for a model by considering two competing theories regarding the origin of life: (i) the Metabolism First theory, and (ii) the RNA World theory. We discuss two interrelated points, namely: (i) Models are valuable tools for understanding both the processes and intricacies of origin-of-life issues, and (ii) Insights from models also help us to evaluate the core objection to origin-of-life theories, called “the inefficiency objection”, which is commonly raised by proponents of both the Metabolism First theory (...) and the RNA World theory against each other. We use Simpson’s Paradox (SP) as a tool for challenging this objection. We will use models in various senses, ranging from taking them as representations of reality to treating them as theories/accounts that provide heuristics for probing reality. In this paper, we will frequently use models and theories interchangeably. Additionally, we investigate Conway’s Game of Life and contrast it with our SP-based approach to emergence-of-life issues. Finally, we discuss some of the consequences of our view. A scientific model is testable in three senses: (i) a logical sense, (ii) a nomological sense, and (iii) a current technological sense. The SP-based model is testable in the first two senses but it is not feasible to test it using current technology. (shrink)

There are two paradoxes of satisfaction, and they are of different kinds. The classic satisfaction paradox is a version of Grelling’s: does ‘does not satisfy itself’ satisfy itself? The Unsatisfied paradox finds a predicate, P, such that Px if and only if x does not satisfy that predicate: paradox results for any x. The two are intuitively different as their predicates have different paradoxical extensions. Analysis reduces each paradoxical argument to differing rule sets, wherein their respective (...) pathologies lie. Having different pathologies, they are paradoxes of different kinds. Furthermore, each of these satisfaction paradoxes has an analogue with the same pathology in set theory. Therefore, these analogues are respectively of the same two kinds. This level of abstraction is significant in that it tracks two related but different pathologies. Thus, not all paradoxes of semantics and set theory share the same pathology: there are at least two kinds of paradox cutting across the semantic and set-theoretic distinction. (shrink)

The aim of this paper is to distinguish between, and examine, three issues surrounding Humphreys's paradox and interpretation of conditional propensities. The first issue involves the controversy over the interpretation of inverse conditional propensities — conditional propensities in which the conditioned event occurs before the conditioning event. The second issue is the consistency of the dispositional nature of the propensity interpretation and the inversion theorems of the probability calculus, where an inversion theorem is any theorem of probability that makes (...) explicit (or implicit) appeal to a conditional probability and its corresponding inverse conditional probability. The third issue concerns the relationship between the notion of stochastic independence which is supported by the propensity interpretation, and various notions of causal independence. In examining each of these issues, it is argued that the dispositional character of the propensity interpretation provides a consistent and useful interpretation of the probability calculus. (shrink)

Paradoxes and their Resolutions is a ‘thematic compilation’ by Avi Sion. It collects in one volume the essays that he has written in the past (over a period of some 27 years) on this subject. It comprises expositions and resolutions of many (though not all) ancient and modern paradoxes, including: the Protagoras-Euathlus paradox (Athens, 5th Cent. BCE), the Liar paradox and the Sorites paradox (both attributed to Eubulides of Miletus, 4th Cent. BCE), Russell’s paradox (UK, 1901) (...) and its derivatives the Barber paradox and the Master Catalogue paradox (also by Russell), Grelling’s paradox (Germany, 1908), Hempel's paradox of confirmation (USA, 1940s), and Goodman’s paradox of prediction (USA, 1955). This volume also presents and comments on some of the antinomic discourse found in some Buddhist texts (namely, in Nagarjuna, India, 2nd Cent. CE; and in the Diamond Sutra, date unknown, but probably in an early century CE). (shrink)

Moore's paradox pits our intuitions about semantic oddnessagainst the concept of truth-functional consistency. Most solutions tothe problem proceed by explaining away our intuitions. But``consistency'' is a theory-laden concept, having different contours indifferent semantic theories. Truth-functional consistency is appropriateonly if the semantic theory we are using identifies meaning withtruth-conditions. I argue that such a framework is not appropriate whenit comes to analzying epistemic modality. I show that a theory whichaccounts for a wide variety of semantic data about epistemic modals(Update Semantics) (...) buys us a solution to Moore's paradox as a corollary.It turns out that Moorean propositions, when looked at through the lenseof an appropriate semantic theory, are inconsistent after all. (shrink)