Like all discourses on the ‘other’, Bataille’s heterology is faced with the problem of conceptualizing the heterogeneous (the other of thought, reason and language), while preserving its alterity, its fundamental resistance to conceptual thought. This paper interrogates the potential parallels between this aspect of Bataille’s notion and some of the prevalent concerns of contemporary and traditional aesthetics. The argument is based on the idea that theories of the aesthetic, akin to Bataille’s heterology, are always inevitably confronted with the paradoxical task (...) of conceptually framing an experience that, per definition, resists philosophical or political appropriation. In relation to this my paper traces a development in Bataille’s thinking from an initial rejection of art and the aesthetic to their later reconfiguration as manifestations of sovereignty. Here I show how Bataille’s notion of sovereign art presents an implicit attempt to overcome some of the aporias to have surfaced in his earlier account of heterology. This development in Bataille’s thought is analysed in the context of his changing relationship with Surrealism. (shrink)

The concept of hypodox is dual to the concept of paradox. Whereas a paradox is incompatibly overdetermined, a hypodox is underdetermined. Indeed, many particular paradoxes have dual hypodoxes. So, naively the dual of Russell’s Paradox is whether the set of all sets that are members of themselves is self-membered. The dual of the Liar Paradox is the Truth-teller, and a hypodoxical dual of the Heterological paradox is whether ‘autological’ is autological. I provide some analysis (...) of the duality and I search for modal hypodoxes as duals to known paradoxes. I also try to continue this search further by mapping the relations between some paradoxes and hypodoxes in duality squares. This investigation increases the known extension of the concept of hypodox, and the duality relation between paradoxes and hypodoxes assists in finding some of these. (shrink)

Graham Priest (1994) has argued that the following paradoxes all have the same structure: Russell’s Paradox, Burali-Forti’s Paradox, Mirimanoff’s Paradox, König’s Paradox, Berry’s Paradox, Richard’s Paradox, the Liar and Liar Chain Paradoxes, the Knower and Knower Chain Paradoxes, and the Heterological Paradox. Their common structure is given by Russell’s Schema: there is a property φ and function δ such that..

‘Definition of Heterology’ illuminates sacred, heterogeneous experiences Bataille never stopped interrogating, in their throbbing movement of emergence. Furthering orthodox disciplines in the sciences of man, Bataille accounts for the ambivalent feelings of ‘attraction and repulsion’ at the heart of inner experiences that constitute the heart of his thought. In this paper, I further a mimetic line of inquiry in Bataille studies and argue that the laws of attraction and repulsion that animate heterology find their polarized foundations in the laws of (...) the socius, which are also the laws of imitation understood in its heterogeneous – anthropological, ontological and psychological – manifestations. Paradoxically, heterology, while being the ‘science’ (logos) of the ‘totally other’ (hetero), may point toward an abyssal experience of a communicative homology that has the power to transform impure matters into pure spirits, angelic souls into material bodies. (shrink)

In line with the Principle of Uniform Solution, Graham Priest has challenged advocates like myself of the “multiple-meanings” solution to the paradoxes of truth and knowledge, due to the medieval logician Thomas Bradwardine, to extend this account to a similar solution to the paradoxes of denotation, such as Berry’s, König’s and Richard’s. I here rise to this challenge by showing how to adapt Bradwardine’s principles of truth and signification for propositions to corresponding principles of denotation and signification for descriptive phrases, (...) applying them to give a “multiple-meanings” solution to the denotational paradoxes. (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)

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 work is, in large part, a series of refutations; it is also the author's Ph.D. thesis. First to be refuted is Russell's vicious circle principle as a general remedy for the solution of the paradoxes. The author rejects the classification of paradoxes into syntactic and semantic, since in his view there are no purely syntactic paradoxes. The distinction in logic between the uninterpreted syntactical aspect of a system and the system when given a determinate interpretation is held to be (...) untenable. Tarski's distinction between object-language and meta-language and his concept of semantically closed language are considered irrelevant for the solution of the Liar paradox. The author claims that the usual versions of the Liar paradox have the same structure as the Barber paradox, viz., [S ↔ ~S]. The author solves the Liar paradox by pointing out that it does not have a proper reference. Cantor's diagonal argument for the indenumerability [[sic]] of the real numbers is labeled as unsatisfactory. Since the diagonal number is dependent upon the real numbers in the constructed list, the author claims that this makes the diagonal number to be of a different nature and status than the real numbers in the list; thus we have what the author calls the dependence fallacy. The author also refuses to accept Cantor's nested interval proof of the indenumerability [[sic]] of the real numbers. Within the proof, two infinite sequences are constructed, each of which converges to a limit. Because the proof does not give a "definite rule of convergence," the author is not satisfied that the infinite sequences converge. Also rejected is Cantor's theorem. Other paradoxes analyzed are the Berry, Richard, heterological, "Richardian", Russell, Cantor, and Burali-Forti paradoxes.--T. G. N. (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.

This essay considers arguments for and against syntactical constraints on the proper formalization of definitions, originally owing to Alfred Tarski. It discusses and refutes an application of the constraints generalized to include a prohibition against not only object-place but also predicate-place variables in higher-order logic in a criticism of a recent effort to define the concept of heterologicality in a strengthened derivation of Grelling's paradox within type theory requirements. If the objections were correct, they would offer a more general (...) moral for the proper formal definition of terms in philosophical logic. The criticism nevertheless seems mistaken both in the substance and specific application with respect to legitimate synctactical constraints on definitions of key concepts in the case of Grelling's paradox. As such, the critique provides no justification for overturning previous conclusions concerning the possibility of resurrecting a type-observant version of Grelling's heterologicality paradox. (shrink)

The semantic paradoxes are a family of arguments – including the liar paradox, Curry’s paradox, Grelling’s paradox of heterologicality, Richard’s and Berry’s paradoxes of definability, and others – which have two things in common: first, they make an essential use of such semantic concepts as those of truth, satisfaction, reference, definition, etc.; second, they seem to be very good arguments until we see that their conclusions are contradictory or absurd. These arguments raise serious doubts concerning the coherence (...) of the concepts involved. This article will offer an introduction to some of the main theories that have been proposed to solve the paradoxes and avert those doubts. Included is also a brief history of the semantic paradoxes from Eubulides to Tarski and Curry. (shrink)

There is a little known paradox the solution to which is a guide to a much more thoroughgoing solution to a whole range of classic paradoxes. This is shown in this paper with respect to Berry's Paradox, Heterologicality, Russell's Paradox, and the Paradox of Predication, also the Liar and the Strengthened Liar, using primarily the epsilon calculus. The solutions, however, show not only that the first-order predicate calculus derived from Frege is inadequate as a basis for (...) a clear science, and should be replaced with Hilbert and Bernays' conservative extension. Standard second-order logic, and quantified propositional logic also must be substantially modified, to incorporate, in the first place, nominalizations of predicates, and whole sentences. And further modifications must be made, so as to insist that predicates are parts of sentences rather than forms of them, and that truth is a property of propositions rather than their sentential expressions. In all, a thorough reworking of what has been called 'logic' in recent years must be undertaken, to make it more fit for use. (shrink)

The paper defends the philosophical method of "regimentation" by example, especially in relation to the theory of mind. The starting point is the Place-Smart after-image argument: A green after-image will not be located outside the skull, but if we cracked open your skull, we won't find anything green in there either. (If we did, you'd have some disturbing medical news.) So the after-image seems not to be in physical space, suggesting that it is non-physical. In response, I argue that the (...) green blob is a fictional object, while assuming a weak sort of realism about fictional objects (where they exist as mind-dependent objects). This view can look like dualism, however, but I try to interpret it not as implying metaphysical dualism, but rather as reflecting a dualism of theory. Roughly, there can be a theory of mind-independent objects, and a theory of mind-dependent objects. Yet there are principled reasons why we cannot integrate the two into a consistent whole, for reasons related to Russell's vicious circle principle. Most of the paper motivates this by an analogy between the physicalist's theory of the world, and drawing a map with a complete representation of the map itself. Regimentation unearths the inconsistencies that arise, when trying to represent as part of a model the very representations used to define the model. (shrink)

In lieu of an abstract, here is a brief excerpt of the content:Reviewed by:Critical Conditions: Postmodernity and the Question of FoundationsBruce KrajewskiCritical Conditions: Postmodernity and the Question of Foundations, by Horace L. Fairlamb; xii & 271 pp. New York: Cambridge University Press, 1994, $59.95 cloth, $17.95 paper.Some theories might be in critical condition, but others are terminal, run aground by their own illogic, according to Horace Fairlamb. Despite some theories’ terminal state, Fairlamb still senses dangers, for as he says in (...) his introduction: “If critical authority cannot turn to metaphysical permanence, transcendental subjectivity, scientific objectivity, formal systematicity, methodological closure, or any other transcending constraints for its authority, are we not left with nothing firmer than Nietzschean perspectivism and an anarchy of wills to power? Might not the respectable looking Trojan Horse of philosophical hermeneutics be filled with sophists, gamesters, and fascists?” Well, yes and no and maybe.Fairlamb explores the issue of foundationalism, later called foundationism, in eight chapters, an introduction, and a conclusion. Most of the eight chapters are labeled as devoted to single contemporary thinkers and theorists, all male: Stanley Fish, Jacques Derrida, Hans-Georg Gadamer, Michel Foucault, Jürgen Habermas. Fairlamb has problems with all these people, and he is very good at laying out objections, based in logic, that arise from the main positions of each. He wants to provide “an analysis of how certain strategies fail to address foundational problems” (p. xi).This analysis consists mainly of turning positions back on themselves, so that when Fish or Habermas or any one of the people addressed in the book makes a claim that indicates an anti-foundational position, Fairlamb jumps in to ask: where is the foundation for the anti-foundational positions? This tactic fills the book, and becomes the driving force of a number of questions and assertions that follow a similar pattern. For instance: “Fish’s radical hermeneutics condemns universalism, but constantly practices it” (p. 40), or “Gadamer’s vision of philosophical hermeneutics must have non-historical authority lest it reduce to his historically bound prejudices” (p. 127). At the end, Fairlamb feels he has demonstrated the logical paradoxes and argumentative blind spots of the various theorists and thinkers mentioned above, and he proposes instead what he calls “a heterological foundationism [that] is able to account for both what changes and what stays the same, and thereby account for the failure of both reductive foundationism and relativism” (p. 263).While I can applaud Fairlamb the logician, I cannot recommend the book. The deck is stacked from the beginning, as he admits early on: “I do not claim to represent the entire range of these authors’ works and thought, nor all their subsequent revisions and recantations” (p. xi). The game here is not to think about the thinkers at all, which is perhaps why Fairlamb rehearses some knee-jerk positions, such as an attack (p. 25) on Derrida’s too-famous statement “there is nothing outside the text.” While he cites (p. 266) Rodolphe Gasché’s [End Page 271] The Tain of the Mirror, Fairlamb apparently refuses Gasché’s reading of the sentence that “does not permit the conclusion that there is nothing else but texts, or for that matter, that all is language” (Tain, p. 281).By dealing only with the logic of some works, Fairlamb unburdens himself of the need, for instance, to attend to Gadamer’s Gesammelte Werke, or to any of the thinkers’ writings in their original languages, a task even some postmodernists agree is foundational for basic scholarship. One can only guess that the universal language of logic has no patience with foreign languages, except to lay bare the inconsistencies and paradoxes of selected bits of syntax.Bruce KrajewskiLaurentian UniversityCopyright © 1996 The Johns Hopkins University Press... (shrink)

To qualify as a fully rational agent, one must be able rationally to revise one’s beliefs in the light of new evidence. This requires, not only that one revise one’s beliefs in the right way, but also that one do so as a result of appreciating the evidence on the basis of which one is changing one’s mind. However, the very nature of belief seems to pose an obstacle to the possibility of satisfying this requirement – for, insofar as one (...) believes that p, any evidence that not-p will strike one as misleading and, on the face of it, believing that a certain piece of evidence is misleading is incompatible with appreciating the fact that such evidence should bear on the question at hand. Call this the ‘Paradox of Belief Revision’. This paper introduces the Paradox of Belief Revision, compares it with Kripke’s Dogmatism Paradox, and suggests that we may be able to see a way out of the former if we assume that rational agents are systematically aware of their own beliefs as beliefs they have. (shrink)

Most discussions frame the Liar Paradox as a formal logical-linguistic puzzle. Attempts to resolve the paradox have focused very little so far on aspects of cognitive psychology and processing, because semantic and cognitive-psychological issues are generally assumed to be disjunct. I provide a motivation and carry out a cognitive-computational treatment of the liar paradox based on a cognitive-computational model of language and conceptual knowledge within the Predictive Processing framework. I suggest that the paradox arises as a (...) failure of synchronization between two ways of generating the liar situation in two different PP sub-models, one corresponding to language processing and the other to the processing of meaning and world-knowledge. In this way, I put forward the claim that the liar sentence is meaningless but has an air of meaningfulness. I address the possible objection that the proposal violates the Principle of Unrestricted Compositionality, which purportedly regulates the conceptual competence of thinkers. (shrink)

This study investigated faculty attitudes towards student violations of academic integrity in Canada using a qualitative review of 17 universities’ academic integrity/dishonesty policies combined with a quantitative survey of faculty members’ (N = 412) attitudes and behaviours around academic integrity and dishonesty. Results showed that 53.1% of survey respondents see academic dishonesty as a worsening problem at their institutions. Generally, they believe their respective institutional policies are sound in principle but fail in application. Two of the major factors identified by (...) faculty as contributing to academic dishonesty are administrative. Many faculty members feel unsupported by their administration and are reluctant to formally report academic dishonesty due to the excessive burdens of dealing with paperwork and providing proof. Faculty members also cite unprepared students and international students who struggle with language issues and the Canadian academic context as major contributors to academic dishonesty. This study concludes with recommendations for educators and recommendations for future research. (shrink)

In this discussion note we argue, contrary to the thrust of a recent article by Jenann Ismael, that resolving the paradox of predictability does not require denying the possibility of a natural oracle, and thus stands in no need of the response that she proposes.

You are presented with a choice between two envelopes. You know one envelope contains twice as much money as the other, but you don't know which contains more. You arbitrarily choose one envelope -- call it Envelope A -- but don't open it. Call the amount of money in that envelope X. Since your choice was arbitrary, the other envelope (Envelope B) is 50% likely to be the envelope with more and 50% likely to be the envelope with less. But, (...) strangely, that very fact might make Envelope B seem attractive: Wouldn't switching to Envelope B give you a 50% chance of doubling your money and a 50% chance of halving it? Since double or nothing is a fair bet, double or half is more than fair. Applying the standard expectation formula, you might calculate the expected value of switching to Envelope B as (.50)½X [50% chance it has less] + (.50)2X [50% chance it has more] = (1.25)X. So, it seems, you ought to switch to Envelope B: Your expected return -- your return on average, over the long run, if you did this many times -- would seem to be 25% more. But obviously that's absurd: A symmetrical calculation could persuade you to switch back to Envelope A. Hence the paradox. (shrink)

The Knower Paradox is an element of the class of paradoxes of self-reference. It demonstrates that any theory Ó which (1) extends Robinson arithmetic Q, (2) includes a unary knowledge predicate K, and (3) contains certain elementary epistemic principles involving K is inconsistent. In this paper I present different versions of the Knower Paradox (both in the framework of the first-order arithmetic and in the modal logic). There are several solutions of the paradox. Some of them I (...) discuss in detail, namely solution developed within modal logic, solution proposed by C. A. Anderson and solution proposed by P. Égré. The common defect of these proposals is that they developed a connection between the concepts of knowledge and provability. Finally, I suggest a solution using the basic ideas of the revision theory of definitions. (shrink)

According to a widely held view epistemic justification is a normative notion. According to another widely held assumption, epistemic justification comes in degrees. Given that gradability requires a context-sensitivity that normativity seems to lack, these two assumptions stand in tension. Giving up the assumption of gradability of justification represents a lesser theoretical cost.

We begin by showing that every theory of the value of uncertain prospects must have one of three unpalatable properties. _Reckless_ theories recommend giving up a sure thing, no matter how good, for an arbitrarily tiny chance of enormous gain; _timid_ theories permit passing up an arbitrarily large potential gain to prevent a tiny increase in risk; _non-transitive_ theories deny the principle that, if A is better than B and B is better than C, then A must be better than (...) C. Having set up this trilemma, we study its horns. Non-transitivity has been much discussed; we focus on drawing out the costs and benefits of recklessness and timidity when it comes to axiology, decision theory, and normative uncertainty. (shrink)

In approaching Ch. 4 of Saving Truth from Paradox, it might be helpful first to revisit Curry’s original paper, and to revisit Lukasiewicz too, to provide more of the scenesetting that Field doesn’t himself fill in. So in §1 I’ll say something about Curry, in §2 we’ll look at what Lukasiewicz was up to in his original three-valued logic, and in §3 we’ll look at the move from a three-valued to a many-valued Lukasiewicz logic. In §4, I move on (...) to announce a theorem by H´. (shrink)

Whether we're buying a pair of jeans, ordering a cup of coffee, selecting a long-distance carrier, applying to college, choosing a doctor, or setting up a 401(k), everyday decisions ; both big and small ; have become increasingly complex due to the overwhelming abundance of choice with which we are presented. As Americans, we assume that more choice means better options and greater satisfaction. But beware of excessive choice: choice overload can make you question the decisions you make before you (...) even make them, it can set you up for unrealistically high expectations, and it can make you blame yourself for any and all failures. In the long run, this can lead to decision-making paralysis, anxiety, and perpetual stress. And, in a culture that tells us that there is no excuse for falling short of perfection when your options are limitless, too much choice can lead to clinical depression. In The Paradox of Choice, Barry Schwartz explains at what point choice ; the hallmark of individual freedom and self-determination that we so cherish ; becomes detrimental to our psychological and emotional well-being. In accessible, engaging, and anecdotal prose, Schwartz shows how the dramatic explosion in choice ; from the mundane to the profound challenges of balancing career, family, and individual needs ; has paradoxically become a problem instead of a solution. Schwartz also shows how our obsession with choice encourages us to seek that which makes us feel worse. By synthesizing current research in the social sciences, Schwartz makes the counter intuitive case that eliminating choices can greatly reduce the stress, anxiety, and busyness of our lives. He offers eleven practical steps on how to limit choices to a manageable number, have the discipline to focus on those that are important and ignore the rest, and ultimately derive greater satisfaction from the choices you have to make."--provided by publisher. (shrink)

Standpoint epistemologies are based on two central theses: the situated knowledge thesis and the thesis of epistemic privilege. The bias paradox suggests that there is a tension between these two notions, in the sense that they are self-contradictory. In this paper, I aim to defend standpoint epistemologies from this challenge. This defense is based on a distinction between subjective and objective justifications. According to the former, a subject S is subjectively justified in believing a proposition P iff S's belief (...) in P coheres with S's pre-existing beliefs. According to the latter, a subject S is objectively justified in believing a proposition P iff S's subjective justification is truth-conducive. I argue that, if the situated knowledge thesis is spelled out in terms of subjective justification, and if the thesis of epistemic privilege is spelled out in terms of objective justification, then there is no contradiction. If this line of thought is correct, then the bias paradox does not show that standpoint epistemologies are self-contradictory. (shrink)

McTaggart’s argument for the unreality of time, first published in 1908, set the agenda for 20th-century philosophy of time. Yet there is very little agreement on what it actually says—nobody agrees with the conclusion, but still everybody finds something important in it. This book presents the first critical overview of the last century of debate on what is popularly called "McTaggart’s Paradox". Scholars have long assumed that McTaggart’s argument stands alone and does not rely on any contentious ontological principles. (...) The author demonstrates that these assumptions are incorrect—McTaggart himself explicitly claimed his argument to be dependent on the ontological principles that form the basis of his idealist metaphysics. The result is that scholars have proceeded to understand the argument on the basis of their own metaphysical assumptions, duly arriving at very different interpretations. This book offers an alternative reading of McTaggart’s argument, and at the same time explains why other commentators arrive at their mutually incompatible interpretations. It will be of interest to students and scholars with an interest in the philosophy of time and other areas of contemporary metaphysics. (shrink)

A notable feature of paradox is recognition that seemingly contradictory terms are inextricably intertwined and interrelated—holding out the hope that something new can be learned from the cognitive tension contained within. Aram has characterized the central concern of the business and society field as the paradox of interdependent relations. Our study argues that this and related paradoxes can be addressed by engaging with others and trying to gain shared insight via an interactive, developmental, exploratory sensemaking process that can (...) inform the governance of stakeholder networks. We advocate multistakeholder learning dialogues (MSLDs) as a means for both scholars and practitioners to construct meanings that can guide joint efforts to cope with messy problems that help shape complex, paradoxical relationships within stakeholder networks. (shrink)

water paradox has long served as an argument against the Principle of Indifference. A solution to the paradox is proposed, with a view toward resolving general difficulties in applying the principle.