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)

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.

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.

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)

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 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.

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)

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)

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)

This paper explores the relationship borne by the traditional paradoxes of set theory and semantics to formal incompleteness phenomena. A central tool is the application of the Arithmetized Completeness Theorem to systems of second-order arithmetic and set theory in which various “paradoxical notions” for first-order languages can be formalized. I will first discuss the setting in which this result was originally presented by Hilbert & Bernays (1939) and also how it was later adapted by Kreisel (1950) and Wang (1955) in (...) order to obtain formal undecidability results. A generalization of this method will then be presented whereby Russell’s paradox, a variant of Mirimanoff’s paradox, the Liar, and the Grelling–Nelson paradox may be uniformly transformed into incompleteness theorems. Some additional observations are then framed relating these results to the unification of the set theoretic and semantic paradoxes, the intensionality of arithmetization (in the sense of Feferman, 1960), and axiomatic theories of truth. (shrink)

The liar paradox in its simplest form is the following argument. Consider the sentence 'this sentence is false'; call that the "liar sentence". Suppose the liar sentence is true. Then, since it says it is false, the liar sentence is false. So our supposition that it is true was mistaken, and the liar sentence must be false. But that's precisely what the liar sentence says, so it is true after all. The liar sentence is, therefore, both true and false---an (...) absurd result. ;Hans Herzberger has argued that several solutions to the Grelling paradox exhibit a common pattern: the very devices we introduce in order to avoid one version of the paradox are integral components of new versions of the paradox. Herzberger suggests that this is typical of semantic paradox in general. Chapters 1, 2, and 3 of this dissertation examine several possible solutions to the liar---especially appeals to language levels and to contexts---and attempt to locate these possible solutions in Herzberger's pattern. ;There is some reason to think that this pattern is inescapable---that is, that the liar paradox is ultimately unsolvable---so the remaining two chapters of this dissertation explore what follows from the claim that it is unsolvable. Chapter 4 develops an argument from the claim that the liar is unsolvable to the claim that we cannot understand ourselves. Chapter 5, then, attempts to make sense of this circumstance by invoking a Nietzschean view of thinking and truth---perspectivalism, which holds that all thinking concerns interpretation and that there are no uninterpreted facts. Given some perspectivalist assumptions, we can see how it is inevitable that we will be unable to understand ourselves---and how we can nevetherless attain a certain limited kind of understanding. Perspectivalism also recommends a certain intellectual humility: if everything is interpretation, then no view of mine can be a comprehensive and accurate view of the way the world really is. This by itself is not a surprising claim; the surprising claim is that the liar paradox is the basis of it. (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)

A three-valued propositional logic is presented, within which the three values are read as ?true?, ?false? and ?nonsense?. A three-valued extended functional calculus, unrestricted by the theory of types, is then developed. Within the latter system, Bochvar analyzes the Russell paradox and the Grelling-Weyl paradox, formally demonstrating the meaninglessness of both.

1. t. Wirklichkeit und logik.--2. t. Die grundbegriffe der wissenschaft.

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)

Was charakterisiert den Geist im Gegensatz zur Materie? Wodurch unterscheidet sich die Psychologie von der Physik? Der Stoff, aus dem die Welt unserer Erfahrung besteht, ist nach Russell weder Geist noch Materie, sondern etwas Ursprünglicheres. In den Vorlesungen über Die Analyse des Geistes versucht er so genau wie möglich zu beschreiben, was in Wirklichkeit stattfindet, wenn wir z.B. etwas glauben oder begehren. Die Einfachheit und zugleich Präzision der Russellschen Beschreibungen machen die Lektüre zu einem außerordentlichen Genuß.

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)