Herein I investigate how four dogmas underpinning the traditional concepts of universality, the genus, class, and abstract universal, generate four paradoxes of self-reference. The four dogmas are the following: (1) that contradiction entails the total absence of determinacy, (2) the necessary finitude of the concept, (3) the separation of principles of universality and particularity, and (4) the necessity of appealing to foundations. In section III I show how these dogmas underpin the paradoxes of self-reference (...) and how one cannot make progress on these paradoxes as long as these four dogmas are in place. Corresponding to the abovementioned dogmas are the four paradoxes of self-reference: (1a) the problem of the .. (shrink)

The paradoxes of self reference have to be dealt with by anyone seeking to give a satisfactory account of the logic of truth, of properties, and even of sets of numbers. Unfortunately, there is no widespread agreement as to how to deal with these paradoxes. Some approaches block the paradoxical inferences by rejecting as invalid a move that classical logic counts as valid. In the recent literature, this deviant logic analysis of the paradoxes has been (...) called into question.This disagreement motivates a re-examination of the philosophy of formal logic and the status of logical truths and rules. In this paper I do some of this work, and I show that this gives us the means to defend the deviant approaches against such criticisms. As a result I hope to show that these analyses of the paradoxes are worthy of more serious consideration than they have so far received. (shrink)

All paradoxes of self-reference seem to share some structural features. Russell in 1908 and especially Priest nowadays have advanced structural descriptions that successfully identify necessary conditions for having a paradox of this kind. I examine in this paper Priest’s description of these paradoxes, the Inclosure Scheme (IS), and consider in what sense it may help us understand and solve the problems they pose. However, I also consider the limitations of this kind of structural descriptions and give (...) arguments against Priest’s use of IS in favour of dialetheism. IS fails to identify sufficient conditions for having a paradox of self-reference. That means that, even if we identified a problem common to any reasoning satisfying IS, that problem would not explain why some of those reasonings are paradoxical and some others are not. Therefore IS cannot justify by itself the claim that some particular theory offers the best solution to the paradoxes of self-reference. We still need to consider aspects concerning the content and context of occurrence of every paradox. (shrink)

The paradoxes of self-reference are genuinely paradoxical. The liar paradox, Russell’s paradox and their cousins pose enormous difficulties to anyone who seeks to give a comprehensive theory of semantics, or of sets, or of any other domain which allows a modicum of self-reference and a modest number of logical principles. One approach to the paradoxes of self-reference takes these paradoxes as motivating a non-classical theory of logical consequence. Similar logical principles are (...) used in each of the paradoxical inferences. If one or other of these problematic inferences are rejected, we may arrive at a consistent (or at least, a coherent) theory. In this paper I will show that such approaches come at a serious cost. The general approach of using the paradoxes to restrict the class of allowable inferences places severe constraints on the domain of possible propositional logics, and on the kind of metatheory that is appropriate in the study of logic itself. Proof-theoretic and model-theoretic analyses of logical consequence make provide different ways for non-classical responses to the paradoxes to be defeated by revenge problems: the redefinition of logical connectives thought to be ruled out on logical grounds. Non-classical solutions are not the “easy way out” of the paradoxes. (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..

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)

Central to the liar paradox is the phenomenon of 'self-reference'. The paradox typically begins with a sentence like: -/- (L): (L) is not true -/- Historically, doubts about the intelligibility of self-reference have been quite common. In some sense, though, these doubts were answered by Kurt Gödel's famous 'diagonal lemma'. This paper surveys some of the methods by which self-reference can be achieved, focusing first on purely syntactic methods before turning attention to the 'arithmetized' (...) methods introduced by Gödel. It's primary lesson is that we need to be more careful than we usually have been about self-reference. (shrink)

What José Luis Bermúdez calls the paradox of self-consciousness is essentially the conflict between two claims: (1) The capacity to use first-personal referential devices like “I” must be explained in terms of the capacity to think first-person thoughts. (2) The only way to explain the capacity for having a certain kind of thought is by explaining the capacity for the canonical linguistic expression of thoughts of that kind. (Bermúdez calls this the “Thought-Language Principle”.) The conflict between (1) and (2) (...) is obvious enough. However, if a paradox is an unacceptable conclusion drawn from apparently valid reasoning from apparently true premises, then Bermúdez’s conflict is no paradox. It is rather a conflict between the view that thought must be explained in terms of language, and the view that first person linguistic reference must be explained in terms of first-person thought. Neither view is immediately obvious, and nor is it obvious that the arguments for either are equally compelling. What we have here is a difference of philosophical opinion, not a paradox. (shrink)

emantic pathologies of self-reference include the Liar (‘this sentence is false’), the Truth-Teller (‘this sentence is true’) and the Open Pair (‘the neighbouring sentence is false’ ‘the neighbouring sentence is false’). Although they seem like perfectly meaningful declarative sentences, truth value assignment to their uses seems either inconsistent (the Liar) or arbitrary (the Truth-Teller and the Open-Pair). These pathologies thus call for a resolution. I propose such a resolution in terms of relative-truth: the truth value of a pathological (...) sentence use varies with the context of its assessment. It always has a determinate truth value, but this truth value is relative to the context of its assessment. I start by considering a fairly esoteric pathology: the Truth-Teller, that is, sentences which assert nothing but their own truth. I make the case that truth value of a given truth-teller use must in general depend on the context of its assessment, and that one can indeed change its truth value at will. I then show how the notion of assessment-sensitive truth can help us provide solutions to other semantic paradoxes such as the Liar and the Open Pair and that those solutions are immune to revenge problems. I conclude by situating my proposal among the main approaches to the semantic paradoxes, and by drawing a very broad moral about pathological self-reference and intentionality. (shrink)

Although it was traditionally thought that self-reference is a crucial ingredient of semantic paradoxes, Yablo (1993, 2004) showed that this was not so by displaying an infinite series of sentences none of which is self-referential but which, taken together, are paradoxical. Yablo's paradox consists of a countable series of linearly ordered sentences s(0), s(1), s(2),... , where each s(i) says: For each k > i, s(k) is false (or equivalently: For no k > i is s(k) (...) true). We generalize Yablo's results along two dimensions. First, we study the behavior of generalized Yablo-series in which each sentence s(i) has the form: For Q k > i, s(k) is true, where Q is a generalized quantifier (e.g., no, every, infinitely many, etc). We show that under broad conditions all the sentences in the series must have the same truth value, and we derive a characterization of those values of Q for which the series is paradoxical. Second, we show that in the Strong Kleene trivalent logic Yablo's results are a special case of a more general fact: under certain conditions, any semantic phenomenon that involves self-reference can be emulated without self-reference. Various translation procedures that eliminate self-reference from a non-quantificational language are defined and characterized. An Appendix sketches an extension to quantificational languages, as well as a new argument that Yablo's paradox and the translations we offer do not involve self-reference. (shrink)

A character in a novel pulls a book from a shelf and starts to read about himself in a novel. Puzzling, but what does it really mean? Does it force us to fundamentally reconsider the nature of fiction? Does it turn the novel into a kind of liar's paradox? And what exactly is a liar's paradox, anyway? Does the liar's paradox, despite its name, have anything to do with lying? What, if anything, does the liar's paradox have to tell us (...) about reality, beliefs, and fictional discourse? (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 (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 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.

A paradox, according to Wittgenstein, is something surprising that is taken out of its context. Thus, one way of dealing with paradoxical sentences is to imagine the missing context of use. Wittgenstein formulates what I call the paradigm paradox: ‘one sentence can never describe the paradigm in another, unless it ceases to be a paradigm.’ (PG, p.346) There are several instances of this paradox scattered throughout Wittgenstein’s writings. I argue that this paradox is structurally equivalent to Russell’s paradox. The above (...) quotation is Wittgenstein’s version of the vicious circle principle which counteracts the paradox. The prohibition Wittgenstein describes is, however, limited to a certain language-game. Finally, I argue that there is a structural analogy between a noun being employed as a self-membered set and a paradigmatic sample being included in or excluded from the set it generates. Paradoxical sentences are not prohibited forever; they can indicate a change in our praxis with a given paradigm. (shrink)

My aim in this paper is to gather some evident in favor of the view that a general purge of self-reference is possible. I do this by considering a modal-epistemic version of the Liar Paradox introduced by Roy Cook. Using yabloesque techniques, I show that it is possible to transform this circular paradoxical construction (and other constructions as well) into an infinitary construction lacking any sort of circularity. Moreover, contrary to Cook’s approach, I think that this can be (...) done without using any controversial multimodal rules, i.e., the usual rules from normal epistemic and modal logic are enough to show the paradoxicality of the infinitary construction. Mi objetivo en este trabajo es ofrecer cierta evidencia a favor de la tesis según la cual una purga general de la autorreferencia es posible. Hago esto considerando una versión modal-epistémica de la Paradoja del mentiroso introducida por Roy Cook. usando técnicas yablescas, muestro que es posible transformar esta construcción paradójica circular (y también otras construcciones) en una construcción infinitaria que carece de cualquier forma de circularidad. más aún, en contra de la propuesta de Cook, muestro que esto puede hacerse sin utilizar ninguna regla multimodal controversial, esto es, las reglas usuales de la lógica modal y la lógica epistémica son suficientes para mostrar la paradojicidad de la construcción infinitaria. (shrink)

A paradox, according to Wittgenstein, is something surprising that is taken out of its context. Thus, one way of dealing with paradoxical sentences is to imagine the missing context of use. Wittgenstein formulates what I call the paradigm paradox: ‘one sentence can never describe the paradigm in another, unless it ceases to be a paradigm.’ There are several instances of this paradox scattered throughout Wittgenstein’s writings. I argue that this paradox is structurally equivalent to Russell’s paradox. The above quotation is (...) Wittgenstein’s version of the vicious circle principle which counteracts the paradox. The prohibition Wittgenstein describes is, however, limited to a certain language-game. Finally, I argue that there is a structural analogy between a noun being employed as a self-membered set and a paradigmatic sample being included in or excluded from the set it generates. Paradoxical sentences are not prohibited forever; they can indicate a change in our praxis with a given paradigm. (shrink)

In this paper, I start by showing that sorites paradoxes are inclosure paradoxes. That is, they fit the Inclosure Scheme which characterizes the paradoxes of self-reference. Given that sorites and self-referential paradoxes are of the same kind, they should have the same kind of solution. The rest of the paper investigates what a dialetheic solution to sorites paradoxes is like, connections with a dialetheic solution to the self-referential paradoxes, and related (...) issues—especially so called "higher order" vagueness. (shrink)

Heinz Von Forester characterizes the objects “known” by an autopoietic system as eigen-solutions, that is, as discrete, separable, stable and composable states of the interaction of the system with its environment. Previous articles have presented the FBST, Full Bayesian Significance Test, as a mathematical formalism specifically designed to access the support for sharp statistical hypotheses, and have shown that these hypotheses correspond, from a constructivist perspective, to systemic eigen-solutions in the practice of science. In this article several issues related to (...) the role played by language in the emergence of eigen-solutions are analyzed. The last sections also explore possible connections with the semiotic theory of Charles Sanders Peirce. (shrink)

Self-reference in semantics, which leads to well-known paradoxes, is a thoroughly researched subject. The phenomenon can appear also in decision theoretic situations. There is a structural analogy between the two and, more interestingly, an analogy between principles concerning truth and those concerning rationality. The former can serve as a guide for clarifying the latter. Both the analogies and the disanalogies are illuminating.

Demonstrates that slapstick film comedies display a canny and sometimes profound understanding of their medium. Slapstick film comedy may be grounded in idiocy and failure, but the genre is far more sophisticated than it initially appears. In this book, Burke Hilsabeck suggests that slapstick is often animated by a philosophical impulse to understand the cinema. He looks closely at movies and gags that represent the conditions and conventions of cinema production and demonstrates that film comedians display a canny and sometimes (...) profound understanding of their medium—from Buster Keaton’s encounter with the film screen in Sherlock Jr. (1924) to Harpo Marx’s lip-sync turn with a phonograph in Monkey Business (1931) to Jerry Lewis’s film-on-film performance in The Errand Boy (1961). The Slapstick Camera follows the observation of philosopher Stanley Cavell that self-reference is one way in which “film exists in a state of philosophy.” By moving historically across the studio era, the book looks at a series of comedies that play with the changing technologies and economic practices behind film production and describes how comedians offered their own understanding of the nature of film and filmmaking. Hilsabeck locates the hidden intricacies of Hollywood cinema in a place where one might least expect them—the clowns, idiots, and scoundrels of slapstick comedy. “From its analysis of the vaudevillian Victorian origins to early Hollywood expressions, and from defining classical performances by the likes of Keaton to recent postmodern recapitulations, Hilsabeck’s theoretically rigorous and wide-ranging study masterfully weaves a path through the historical, technical, and philosophical art of slapstick comedy. A must for scholars working in this field.” — Daniel Varndell, author ofHollywood Remakes, Deleuze and the Grandfather Paradox. (shrink)

In this paper, we examine a fundamental problem that appears in Greek philosophy: the paradoxes of self-reference of the type of “Third Man” that appears first in Plato’s 'Parmenides', and is further discussed in Aristotle and the Peripatetic commentators and Proclus. We show that the various versions are analysed using different language, reflecting different understandings by Plato and the Platonists, such as Proclus, on the one hand, and the Peripatetics (Aristotle, Alexander, Eudemus), on the other hand. We (...) show that the Peripatetic commentators do not focus on Plato’s solution but primarily on the formulation of the “Third Man” paradox. On the contrary, Proclus seems to be convinced that Plato suggests a sound solution to the paradox by defining the predicate of similarity (homogeneity) that demarcates two types of homogeneous entities – the eide and the participants in them in a way that their confusion would be inadmissible. We claim that Plato’s solution follows a sound line of reasoning that is formalisable in a language of Frege-Russell type; hence there exists a model in which Plato’s reasoning is valid. Furthermore, we notice that Plato’s definition of the second-order predicate of similarity is attained by resorting to first-order entities. In this sense, Plato’s definition is comparable to Eudoxus’ definition of ratio, which is also attained by resorting to first-order objects. Consequently, Plato seems to follow a logical practice established by the mathematicians of the 5th century, notably Eudoxus, in his solution to the paradox. (shrink)

An anthology of previously unpublished essays from some of the most outstanding scholars working in philosophy, mathematics, and computer science today, _Self-Reference_ reexamines the latest theories of self-reference, including those that attempt to explain and resolve the semantic and set-theoretic paradoxes. With a thorough introduction that contextualizes the subject for students, this book will be important reading for anyone interested in the general area of self-reference and philosophy.

John Buridan was a fourteenth-century philosopher who enjoyed an enormous reputation for about two hundred years, was then totally neglected, and is now being 'rediscovered' through his relevance to contemporary work in philosophical logic. The final chapter of Buridan's Sophismata deals with problems about self-reference, and in particular with the semantic paradoxes. He offers his own distinctive solution to the well-known 'Liar Paradox' and introduces a number of other paradoxes that will be unfamiliar to most logicians. (...) Buridan also moves on from these problems to more general questions about the nature of propositions, the criteria of their truth and falsity and the concepts of validity and knowledge. This edition of that chapter is intended to make Buridan's ideas and arguments accessible to a wider range of readers. The volume should interest many philosophers, linguists and logicians, who are increasingly finding in medieval work striking anticipations of their own concerns. (shrink)

An anthology of previously unpublished essays from some of the most outstanding scholars working in philosophy, mathematics, and computer science today, _Self-Reference_ reexamines the latest theories of self-reference, including those that attempt to explain and resolve the semantic and set-theoretic paradoxes. With a thorough introduction that contextualizes the subject for students, this book will be important reading for anyone interested in the general area of self-reference and philosophy.

John Buridan was a fourteenth-century philosopher who enjoyed an enormous reputation for about two hundred years, was then totally neglected, and is now being 'rediscovered' through his relevance to contemporary work in philosophical logic. The final chapter of Buridan's Sophismata deals with problems about self-reference, and in particular with the semantic paradoxes. He offers his own distinctive solution to the well-known 'Liar Paradox' and introduces a number of other paradoxes that will be unfamiliar to most logicians. (...) Buridan also moves on from these problems to more general questions about the nature of propositions, the criteria of their truth and falsity and the concepts of validity and knowledge. This edition of that chapter is intended to make Buridan's ideas and arguments accessible to a wider range of readers. The volume should interest many philosophers, linguists and logicians, who are increasingly finding in medieval work striking anticipations of their own concerns. (shrink)

This paper provides a procedure which, from any Boolean system of sentences, outputs another Boolean system called the ‘_m_-cycle unwinding’ of the original Boolean system for any positive integer _m_. We prove that for all \(m>1\), this procedure eliminates the direct self-reference in that the _m_-cycle unwinding of any Boolean system must be indirectly self-referential. More importantly, this procedure can preserve the primary periods of Boolean paradoxes: whenever _m_ is relatively prime to all primary periods of (...) a Boolean paradox, this paradox and its _m_-cycle unwinding have the same primary periods. In this way, we can produce an indirectly self-referential Boolean paradox with the same periodic characteristics as a known Boolean paradox. (shrink)

The Paradox of the Knower was originally presented by Kaplan and Montague [26] as a puzzle about the everyday notion of knowledge in the face of self-reference. The paradox shows that any theory extending Robinson arithmetic with a predicate K satisfying the factivity axiom K → A as well as a few other epistemically plausible principles is inconsistent. After surveying the background of the paradox, we will focus on a recent debate about the role of epistemic closure principles (...) in the Knower. We will suggest this debate sheds new light on the concept of knowledge which is at issue in the paradox – i.e. is it a “thin” notion divorced from concepts such as evidence or justification, or is it a “thick” notion more closely resembling mathematical provability? We will argue that a number of features of the paradox suggest that the latter option is more plausible. Along the way, we will provide a reconstruction of the paradox using a quantified extension of Artemovʼs [2] Logic of Proofs, as well as a series of results linking the original formulation of the paradox to reflection principles for formal arithmetic. On this basis, we will argue that while the Knower can be understood to motivate a distinction between levels of knowledge, it does not provide a rationale for recognizing a uniform hierarchy of knowledge predicates in the manner suggested by Anderson. (shrink)

A dialogue among statements that try to explain to each other the mechanisms and peculiarities of self-referential assertions and, particularly, of their context-dependence.

This is a book that every logician will want to read. The well-worn topics of self-reference and the paradoxes have been given new life in these papers by a distinguished group of logicians.

[[[ (Here only the chapters 3 – 8, see *** ) First I argue that the prohibition of linguistic self-reference as a solution to the antinomy problem contains a pragmatic contradiction and is thus not only too restrictive, but just inconsistent (chap.1). Furthermore, the possibilities of non-restrictive strategies for antinomy avoidance are discussed, whereby the explicit inclusion of the – pragmatically presuposed – consistency requirement proves to be the optimal strategy (chap.2). ]]] The central question here is that (...) about the actual reason for antinomic structures. It turns out to be a form of negative self-conditioning (chap.3). This makes it necessary to clarify the status of negative concepts (chap.4). The generalization of these considerations (chap.5) leads to the actual analysis of the antinomic basic structure (chap.6): Decisively for the pragmatics of the concept is that it positively owns a meaning, so that positivity is always constituted by the concept qua concept. Thus a negative concept is characterized by a fundamental ambivalence: From a semantic point of view it has negative character, in its pragmatic status as a concept, however, it has positive character. If the meaning is especially that of a negative self-reference, the ambivalence leads to the antinomic constellation of a negative self-condition – that is the crux of the matter here! The concept thus possesses the property defined by it exactly when it does not possess it and vice versa. A closer analysis shows that the function of reflective structures for the occurrence of antinomies has to be judged much more differentiated than previous opinions suggest. Not only are four forms of reflectivity to be distinguished in this context – ontic, semantic, pragmatic reflectivity, and especially the form of negative self-condition; but it is also apparent that these are intertwined with each other in a way that is difficult to be understood. The astonishing variety of relationships associated with this makes the irritation that has always emanated from the antinomy problem appear more comprehensible. In the developed pragmatic perspective furtheron parallels to the structure of self-consciousness become visible (chap.7). I conclude with considerations about the significance of the antinomic structure for the problem of dialectics, especially for the synthesis formation of mutually exclusive terms (chap.8). (shrink)

While it seems obvious that the embodied self is both a subject of experience and an object in the world, it is not clear how, or even whether, both of these senses of self can refer to thesameself. According to Husserl, the relation between these two senses of self is beset by the “paradox of human subjectivity.” Following Husserl’s lead, scholars have attempted to resolve the paradox of subjectivity. This paper categorizes the different formulations of the paradox (...) according to the dimension each pertains to and considers the prospects of each proposed resolution. It will be shown that, contrary to the claims of the respective authors, their attempted resolutions do not really resolve the paradox, but instead rephrase it or push it to the next dimension. This suggests that there is something deeper at work than a mere misunderstanding. This paper does not aim to resolve the paradox but instead initiates a new approach to it. Instead of seeing the paradox as a misapprehension that needs to be removed, I dig deeper to reveal its roots in ordinary consciousness. Investigating the proposed resolutions will reveal the fundamental role of the natural attitude, and I will argue that already the general thesis of the natural attitude makes the decisive cut that leads to what Sartre calls a “fissure” in pre-reflective self-awareness. The phenomenological reduction deepens the cut into what Husserl calls the “split of the self,” which in turn engenders the paradox of subjectivity. The paradox’s roots in the structure of ordinary consciousness not only constitute a reason for its persistence, but also suggest a new way to further investigate the embodied self. (shrink)

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

John Buridan was a fourteenth-century philosopher who enjoyed an enormous reputation for about two hundred years, was then totally neglected, and is now being 'rediscovered' through his relevance to contemporary work in philosophical logic. The final chapter of Buridan's Sophismata deals with problems about self-reference, and in particular with the semantic paradoxes. He offers his own distinctive solution to the well-known 'Liar Paradox' and introduces a number of other paradoxes that will be unfamiliar to most logicians. (...) Buridan also moves on from these problems to more general questions about the nature of propositions, the criteria of their truth and falsity and the concepts of validity and knowledge. This edition of that chapter is intended to make Buridan's ideas and arguments accessible to a wider range of readers. The volume should interest many philosophers, linguists and logicians, who are increasingly finding in medieval work striking anticipations of their own concerns. (shrink)

A standard problem with the objectivity of social scientific theory in particular is that it is either self-referential, in which case it seems to undermine itself as ideology, or self-excepting, which seem pragmatically self-refuting. Using the example of Marx and his theory of ideology, I show how self-referential theories that include themselves in their scope of explanation can be objective. Ideology may be roughly defined as belief distorted by class interest. I show how Marx thought that (...) natural science was informed by class interest but not therefore necessarily ideology. Capitalists have an interest in understanding the natural world (to a point) so that they can manipulate it for profit. Their survival in the marketplace often depends on their competitive success in doing so. The fact that their interventions into nature, driven by class interest, often succeed, is evidence of the reliability and truth of their natural scientific theories. -/- With social science, capitalists have a partial interest in understanding the world, so that they may maintain their class power, ideological hegemony, and a reasonably stable and self-reproducing economy. Some bourgeois social science, Marx thinks, is therefore vindicated the same way that natural science is, because of, not despite, its success in promoting the class interests that cause it. But the capitalist class, Marx thinks, also has an interest in obfuscating the truth about the social world. It would undermine the stability of capitalism, for example, for the bourgeoisie to adopt what Marx thinks to be the correct social theory, Marxism, and proclaim to the world that capitalism is exploitative and unstable. Capitalism creates a a need for ideological social theories that, driven by class interest, represent capitalism as just, natural, inevitable, and unalterable. If Marxism is correct, while these theories may further capitalist interests, they will not withstand the test of time as capitalist exploitation and instability engenders countersystemic political action. -/- How, then can we know, according to Marx, that Marxism is correct, as applied to itself? In part it is whether it succeeds in further the class interests that cause it. If workers adopt bourgeois theories and Marxism is right, they will find themselves frustrated in pursuit of goals that they have, such as improving their well-being, and if Marxism is wrong, then those theories will help them further their own goals. Similarly with Marxism: if it is right, then workers who adopt it should in the long run have more success in furthering their own goals, and if not, then not. But it is question begging to say that our confidence in the reliability of Marxism is enhanced by its successful promotion of goals that capitalists do not have but (according to Marxism) workers do. To avoid this problem it is necessary to compare the relative success of each sort of theory in promoting the interests and needs that the respective classes have independently of the theory, as well as by the usual criteria of scientific theory choice. -/- Thus the Soviet variant of Marxism was fairly decisively refuted by its failure to generate the support of its own designated constituency necessary to grow and survive. Whether the same is true of other varieties of Marxism or of capitalist social theory, it is, as Zhou En Lai said when asked whether the French Revolution had succeeded, too soon to tell, at least in any definitive way. However, and this is the point of the paper, an objective test of Marxism is possible even though Marxism says that all theory is informed by class interest. The question is whether the interests are in discovering or obfuscating the truth. The point is not limited to Marx, but applies to any self-referential social scientific theory that includes itself in its scope. -/- Keywords: ideology, self-referential theory, self-reference, reliabilism, objectivity, Marx, Marxism, sociology of science, class interest, classes, capitalism, bourgeoisie, workers, working class, social theory of knowledge, confirmation of scientific theory. (shrink)

We provide a systematic recipe for eliminating self-reference from a simple language in which semantic paradoxes (whether purely logical or empirical) can be expressed. We start from a non-quantificational language L which contains a truth predicate and sentence names, and we associate to each sentence F of L an infinite series of translations h 0(F), h 1(F), ..., stated in a quantificational language L *. Under certain conditions, we show that none of the translations is self-referential, (...) but that any one of them perfectly mirrors the semantic behavior of the original. The result, which can be seen as a generalization of recent work by Yablo (1993, Analysis, 53, 251–252; 2004, Self-reference, CSLI) and Cook (2004, Journal of Symbolic Logic, 69(3), 767–774), shows that under certain conditions self-reference is not essential to any of the semantic phenomena that can be obtained in a simple language. (shrink)

The Problem of the Paradoxes came to the fore in philosophy and mathematics with the discovery of Russell's Paradox in 1901. It is the "forgotten" intellectual-scientific problem of the Twentieth Century, because for more than sixty years a pretence was maintained, by a consensus of logicians, that the problem had been "solved".

We know from more than two millenia of experience that self-referential statements, such as the liar's ("This very statement is false"), can be debated by philosophers and logicians for millenia without producing consensus on their solutions. We should not be surprised, then, if self-referential laws produce paradoxes which puzzle lawyers. What is surprising, though, is that some of these paradoxes bother only the logicians and philosophers who study law from outside, and do not bother lawyers at (...) all. This fact should interest philosophers of law even more than the paradoxes themselves. (shrink)

Stephen Read has advanced a solution of certain semantic paradoxes recently, based on the work of Thomas Bradwardine. One consequence of this approach, however, is that if Socrates utters only ‘Socrates utters a falsehood’ (a), while Plato says ‘Socrates utters a falsehood’ (b), then, for Bradwardine two different propositions are involved on account of (a) being self-referential, while (b) is not. Problems with this consequence are first discussed before a closely related analysis is provided that escapes it. Moreover, (...) this alternative analysis merely relies on quantification theory at the propositional level, so there is very little to question about it. The paper is the third in a series explaining the superior virtues of a referential form of propositional quantification. (shrink)