Logical paradoxes – like the Liar, Russell's, and the Sorites – are notorious. But in Paradoxes and Inconsistent Mathematics, it is argued that they are only the noisiest of many. Contradictions arise in the everyday, from the smallest points to the widest boundaries. In this book, Zach Weber uses “dialetheic paraconsistency” – a formal framework where some contradictions can be true without absurdity – as the basis for developing this idea rigorously, from mathematical foundations up. In doing so, Weber directly (...) addresses a longstanding open question: how much standard mathematics can paraconsistency capture? The guiding focus is on a more basic question, of why there are paradoxes. Details underscore a simple philosophical claim: that paradoxes are found in the ordinary, and that is what makes them so extraordinary. (shrink)

Philosophers often claim that forgiveness is a paradoxical phenomenon. I here examine two of the most widespread ways of dealing with the paradoxical nature of forgiveness. One of these ways, emblematized by Aurel Kolnai, seeks to resolve the paradox by appealing to the idea of repentance. Somehow, if a wrongdoer repents, then forgiving her is no longer paradoxical. I argue that this influential position faces more problems than it solves. The other way to approach the paradox, exemplified here (...) by the work of Jacques Derrida, is just too obscure to be by itself helpful. Yet, I argue that what I take to be its spirit is on the right track. I recommend distinguishing between the definition and the justification of forgiveness, and also between forgiveness understood as a mental phenomenon and an overt, communicative act. These distinctions are not given their due in the specialized literature, and I expose the nefarious consequences of this neglect. By focusing on forgiveness as a mental phenomenon I seek to analyze the root of the talk of paradoxes which surrounds the discussion of forgiveness. Finally, I present an analysis of forgiveness as a pure mental phenomenon, and argue that this analysis is the most important step in understanding forgiveness in any other sense. While my analysis reveals interesting aspects of forgiveness, it reveals, too, that forgiveness is not quite as paradoxical after all. (shrink)

Understandably absorbed in technical details, discussion of the semantic paradoxes risks losing sight of broad methodological principles. This chapter sketches a general approach to the comparison of rival logics, and applies it to argue that revision of classical propositional logic has much higher costs than its proponents typically recognize.

Husserl’s first work formulated what proved to be an algorithmically complete arithmetic, lending mathematical clarity to Kronecker’s reduction of analysis to finite calculations with integers. Husserl’s critique of his nominalism led him to seek a philosophical justification of successful applications of symbolic arithmetic to nature, providing insight into the “wonderful affinity” between our mathematical thoughts and things without invoking a pre-established harmony. For this, Husserl develops a purely descriptive phenomenology for which he found inspiration in Mach’s proposal of a “universal (...) physical phenomenology.” To account for applications to any domain, Husserl envisages a theory of all possible deductive systems, which he develops extensively in his Göttingen lectures wherein he engages with Hilbert’s work on deductive systems for geometry, real arithmetic, and physics. This leads Husserl to formulate claims of decidability and proofs of completeness for various arithmetics that result from his analysis of Kronecker’s general arithmetic. Careful attention to these proofs seem to show that Husserl was not oblivious to problems that underlie our incompleteness theorems, namely that of showing that some inversions of his algorithmic arithmetic are undefined. His growing preoccupation with the issue of a pre-established harmony between mathematical thought and reality motivate his pursuit of a “supramathematics” of all possible complete theory forms to demystify such harmony, by having such a form on hand for describing any empirical domain. He soon decides that a transcendental idealism of nature will reveal the wonderful affinity of thoughts and things comprising such harmony, to be a wonderful “parallelism of objective unities and constituted manifolds of consciousness.” But the paradoxes of logic and set theory cloud the clarity of mathematics, which Weyl would restore with Brouwer’s intuitionism and Hilbert with his metamathematics. Husserl informed Weyl that his student Becker had formulated a phenomenological foundation not only for Weyl’s generalization of relativity theory but also for the Brouwer-Weyl continuum. But Weyl eventually rejected much of Becker’s work, especially when it became clear that his phenomenological intuitionism could not account for the success of Hilbert’s transfinite mathematics in quantum physics. Becker responded to this “crisis of phenomenological method” with his mantic phenomenology celebrating the magic of mathematical mysticism, which Husserl finally rejects in favor of a pluralistic phenomenology of mathematics and nature. (shrink)

Essential for the concept of the law of nature is not only spatio-temporal universality, but also functionality in the sense of the dependency on physical conditions of natural entities. In the following it is explained in detail that just the neglect of this functional property is to be understood as the real reason for the occurrence of the Goodman paradox – with the consequence, that the behavior of things seems to be completely at the mercy of change of unique (...) unrepeatable temporal points. It is exactly this (mis-)understanding that also generated the induction problem. From the intrinsic connection between universality and functionality, however, – that is my claim – the ontological consequence of a nature results, for which lawfulness is coupled to essentially functionally defined time sequences, thereby implying a potentiality dimension of nature, too. (shrink)

We examine two competing solutions to Benardete paradoxes: causal finitism, according to which nothing can have infinitely many causes, and the unsatisfiable pair diagnosis (UPD), according to which such paradoxes are logically impossible and no metaphysical thesis need be adopted to avoid them. We argue that the UPD enjoys notable theoretical advantages over causal finitism. Causal finitists, however, have levelled two main objections to the UPD. First, they urge that the UPD requires positing a ‘mysterious force’ that prevents paradoxes from (...) arising. Since such a force is implausible, the UPD is in trouble. Second, they employ recombination or patchwork principles to argue that paradoxical situations would be possible if causal finitism were false. Since such situations are not possible, causal finitism is true, and so a substantive metaphysical thesis is needed to avoid the paradoxes. We argue that the UPD proponent can successfully respond to these objections. (shrink)

This paper argues that we should solve paradoxes for propositions (such as the Russell–Myhill paradox) in essentially the same way that we solve Russellian paradoxes for sets. That is, the standard, iterative approach to sets is extended to include properties, and then the resulting hierarchy of sets and properties is used to construct propositions. Propositions on this account are structured in the sense of mirroring the sentences that express them, and they would seem to serve the needs of philosophers (...) of language and metaphysicians who rely on such propositions. The resulting account has limitations, comparable to those faced by the iterative approach to sets, but it is argued to be in important ways preferable to others that have been proposed. (shrink)

Evolutionary fitness threats and rewards are associated with subjectively unpleasant and pleasant sensations, respectively. Initially, these correlations appear explainable via adaptation by natural selection. But here I analyse the major metaphysical perspectives on consciousness – physicalism, dualism, and panpsychism – and conclude that none help to understand the adaptive-seeming correlations via adaptation. I also argue that a recently proposed explanation, the phenomenal powers view, has major problems that mean it cannot explain the adaptive-seeming correlations via adaptation either. So the mystery (...) – call it the evolutionary paradox of consciousness – remains. Some have used this mystery to argue for non-naturalistic (e.g. theistic) explanations. But I propose a naturalistic, non-adaptive explanation of the adaptive-seeming correlations: namely, ‘sensational associative learning’ during development. In this perspective, pairing of particular sensations with unconditioned stimuli – fitness rewards or threats – cause the sensations themselves to come to be interpreted as good or bad, respectively. Sensations, like colours, that are not reliably paired with either fitness rewards or threats remain largely unvalenced. Sensational associative learning also provides explanations for adaptive-seeming structural aspects of sensations, such as the observation that sounds of different pitch are experienced as ordinal in correspondence to their wavelengths while the same is not true of colours of different hue. The sensational associative learning perspective appears compatible with physicalism, panpsychism, and dualism (though not epiphenomenalism). (shrink)

Benardete paradoxes involve a beginningless set each member of which satisfies some predicate just in case no earlier member satisfies it. Such paradoxes have been wielded on behalf of arguments for the impossibility of an infinite past. These arguments often deploy patchwork principles in support of their key linking premise. Here I argue that patchwork principles fail to justify this key premise.

A paradox can be defined as an unacceptable conclusion derived by apparently acceptable reasoning from apparently acceptable premises. Many paradoxes raise serious philosophical problems, and they are associated with crises of thought and revolutionary advances. The expanded and revised third edition of this intriguing book considers a range of knotty paradoxes including Zeno's paradoxical claim that the runner can never overtake the tortoise, a new chapter on paradoxes about morals, paradoxes about belief, and hardest of all, paradoxes about truth. (...) The discussion uses a minimum of technicality but also grapples with complicated and difficult considerations, and is accompanied by helpful questions designed to engage the reader with the arguments. The result is not only an explanation of paradoxes but also an excellent introduction to philosophical thinking. (shrink)

[[[ (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)

Supererogatory acts—good deeds “beyond the call of duty”—are a part of moral common sense, but conceptually puzzling. I propose a unified solution to three of the most infamous puzzles: the classic Paradox of Supererogation (if it’s so good, why isn’t it just obligatory?), Horton’s All or Nothing Problem, and Kamm’s Intransitivity Paradox. I conclude that supererogation makes sense if, and only if, the grounds of rightness are multi-dimensional and comparative.

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

Dorothy Edgington’s work has been at the centre of a range of ongoing debates in philosophical logic, philosophy of mind and language, metaphysics, and epistemology. This work has focused, although by no means exclusively, on the overlapping areas of conditionals, probability, and paradox. In what follows, I briefly sketch some themes from these three areas relevant to Dorothy’s work, highlighting how some of Dorothy’s work and some of the contributions of this volume fit in to these debates.

Ryan Wasserman explores a range of fascinating puzzles raised by the possibility of time travel, with entertaining examples from physics, science fiction, and popular culture, and he draws out their implications for our understanding of time, tense, freedom, fatalism, causation, counterfactuals, laws of nature, persistence, change, and mereology.

Au détour de l'ordre géométrique, dans un scolie de la Quatrième partie de l'Éthique faisant suite à l'énoncé de la règle fondamentale qui associe l'utilité du corps humain, et par conséquent le bien de l'individu, à la recherche d'une constance fondamentale dans le rapport de ses parties, surgit un scolie baroque, où passe l'ombre de la mort et qui débouche sur d'inquiétantes possibilités de mutation, voire de transmutation de l'identité : « Il arrive qu'un homme subit de tels changements, que (...) je ne dirai pas aisément qu'il est le même. C'est ce que j'ai entendu raconter de certain poète espagnol qui avait été atteint de maladie et qui, bien qu'il en fût guéri, demeura cependant dans un tel oubli de sa vie passée, qu'il ne croyait pas que les nouvelles et les tragédies qu'il avait faites fussent de lui ; et certes on eût pu le tenir pour un nourrisson adulte, s'il eût oublié aussi sa langue maternelle... » De ce texte perturbateur et de sa « contradiction » centrale, qui ont semé le trouble chez les commentateurs, François Zourabichvili qui en propose une explication systématique fait le fil conducteur d'une relecture complète des relations qui associent la métaphysique spinozienne à son anthropologie et à sa politique, centrée sur la question de la transformation comme « oubli », voire amnésie d'une forme antérieure, et « imagination », chimérique ou non, d'une nouvelle aptitude du corps. Il démontre ainsi la rigoureuse correspondance qui, d'un bout à l'autre de l'œuvre, associe la question d'une sortie de l'enfance à celle d'une émancipation de l'imaginaire monarchique. A l'encontre d'une lecture naïvement « révolutionnaire » du spinozisme, surgit alors ce qu'on peut appeler un conservatisme : mais dont le paradoxe est éclatant, car il tend moins à préserver l'état de choses existant qu'à inventer les conditions d'une vraie conservation de soi (neutralisation de la mort et de la servitude). Pages de début Avertissement Introduction Première étude. Envelopper une autre nature / envelopper la nature Introduction 1. La transition éthique dans le Court traité 2. La transition éthique dans le Traité de la réforme de l'entendement Deuxième étude. L'image rectifiée de l'enfance Introduction 3. La figure de l'infans adultus 4. Enfance et philosophie 5. Enfance et mémoire Conclusion sur le rapport à l'enfance Troisième étude. Puissance de Dieu et puissance des rois Introduction 6. La confusion des deux puissances et la dérive baroque du cartésianisme 7. Le rêve transformiste de la monarchie absolue 8. Qu'est-cequ'une multitude libre? Guerre et civilisation Bibliographie Index. (shrink)

The laws of logic and two of the broader theories of truth are fundamental components that are responsible for espousing an ontology and meaningfulness in matters of analytic philosophy. In this respect they have persisted as conventional attitudes or modes of thought which most, if not all, of analytic philosophy uses to philosophize. However, despite the conceptual productivity of these components they are unable to account for matters that are beyond them. These matters would include certain theological beliefs, for instance, (...) that transcend the purview of analytic ontology and the meaningfulness it ensues. Any attempt in making rational sense of such beliefs that are insusceptible to these methodological components would conventionally prohibit (restrict) us from rationally believing in them. This is because we would be unable to make sense of such beliefs with the aid of these methodological components. As a result of this, religious beliefs of this particular nature would be deemed irrational. I shall demonstrate this point by applying both of these components to an absolutely ineffable God of Islam. This would entail, attempting to make sense of an absolutely ineffable God of Islam in virtue of the laws of logic and two broad categories of truth theories, namely, substantive and insubstantive theories. I hope to establish that applying both of these methodological components in attempting to make sense of an absolutely ineffable God of Islam would not be conceptually viable. It would result in a contradictory notion which I shall allude to as the paradox of ineffability. (shrink)

The paradox of pain refers to the idea that the folk concept of pain is paradoxical, treating pains as simultaneously mental states and bodily states. By taking a close look at our pain terms, this paper argues that there is no paradox of pain. The air of paradox dissolves once we recognize that pain terms are polysemous and that there are two separate but related concepts of pain rather than one.

Paradoxes are more than just intellectual puzzles - they raise substantive philosophical issues and offer the promise of increased philosophical knowledge. In this introduction to paradox and paradoxes, Doris Olin shows how seductive paradoxes can be, why they confuse and confound, and why they continue to fascinate. Olin examines the nature of paradox, outlining a rigorous definition and providing a clear and incisive statement of what does and does not count as a resolution of a paradox. The (...) view that a statement can be both true and false, that contradictions can be true, is seen to provide a challenge to the account of paradox resolution, and is explored. With this framework in place, the book then turns to an in-depth treatment of the Prediction Paradox, versions of the Preface/Fallibility Paradox, the Lottery Paradox, Newcomb's Problem, the Prisoner's Dilemma and the Sorites Paradox. Each of these paradoxes is shown to have considerable philosophical punch. Olin unpacks the central arguments in a clear and systematic fashion, offers original analyses and solutions, and exposes further unsettling implications for some of our most deep-seated principles and convictions. (shrink)

Paradoxes are more than just intellectual puzzles - they raise substantive philosophical issues and offer the promise of increased philosophical knowledge. In this introduction to paradox and paradoxes, Doris Olin shows how seductive paradoxes can be, why they confuse and confound, and why they continue to fascinate. Olin examines the nature of paradox, outlining a rigorous definition and providing a clear and incisive statement of what does and does not count as a resolution of a paradox. The (...) view that a statement can be both true and false, that contradictions can be true, is seen to provide a challenge to the account of paradox resolution, and is explored. With this framework in place, the book then turns to an in-depth treatment of the Prediction Paradox, versions of the Preface/Fallibility Paradox, the Lottery Paradox, Newcomb's Problem, the Prisoner's Dilemma and the Sorites Paradox. Each of these paradoxes is shown to have considerable philosophical punch. Olin unpacks the central arguments in a clear and systematic fashion, offers original analyses and solutions, and exposes further unsettling implications for some of our most deep-seated principles and convictions. (shrink)

_Paradoxes from A to Z, Third edition_ is the essential guide to paradoxes, and takes the reader on a lively tour of puzzles that have taxed thinkers from Zeno to Galileo, and Lewis Carroll to Bertrand Russell. Michael Clark uncovers an array of conundrums, such as Achilles and the Tortoise, Theseus’ Ship, and the Prisoner’s Dilemma, taking in subjects as diverse as knowledge, science, art and politics. Clark discusses each paradox in non-technical terms, considering its significance and looking at (...) likely solutions. This third edition is revised throughout, and adds nine new paradoxes that have important bearings in areas such as law, logic, ethics and probability. Paradoxes from A to Z, Third edition is an ideal starting point for those interested not just in philosophical puzzles and conundrums, but anyone seeking to hone their thinking skills. (shrink)

Classical logic, of first or higher order, is extended with sentential operators and quantifiers, interpreted substitutionally over unrestricted substitution class. Operators mark a single layered, consistent metalanguage. Self-reference, arising from substitutional quantification over sentences, allows to express paradoxes which, unlike contradictions, do not lead to explosion. Semantics of the resulting language, using semi-kernels of digraphs, is non-explosive yet two-valued and has classical semantics as a special case for clasically consistent theories. A complete reasoning is obtained by extending LK with two (...) rules for sentential quantifiers. Adding (cut) yields a complete system for the explosive semantics. (shrink)

This paper reconsiders certain of Kierkegaard's criticisms of Hegel's theoretical philosophy in the light of recent interpretations of the latter. The paper seeks to show how these criticisms, far from being merely parochial or rhetorical, turn on central issues concerning the nature of thought and what it is to think. I begin by introducing Hegel's conception of "pure thought" as this is distinguished by his commitment to certain general requirements on a properly philosophical form of inquiry. I then outline Hegel's (...) strategy for resolving a crucial problem he takes himself to face. For his account of the nature of thought depends upon the idea of a form of inquiry in which nothing whatsoever is presupposed; but this idea appears basically paradoxical inasmuch as the mere act of beginning to inquire in a certain way embodies an assumption about how it is appropriate to begin. Turning to Kierkegaard, I consider a key objection to the effect that Hegel's strategy for resolving this paradox depends on the incoherent idea of a purely reflexive act of thinking. Finally, I draw out some central features of the alternative account of "situated" thought and inquiry which Kierkegaard presents as distinctively Socratic. (shrink)

Essential for the concept of the law of nature is not only spatio-temporal universality, but also functionality in the sense of the dependency on physical conditions of natural entities. In the following it is explained in detail that just the neglect of this functional property is to be understood as the real reason for the occurrence of the Goodman paradox. As a consequence, the behavior of things seems to be completely at the mercy of the temporal change of unique (...) absolute temporal points. It is exactly this (mis-)understanding that also generated the induction problem. From the intrinsic connection between universality and functionality, however, - that is my claim - the ontological consequence of a nature results, for which the potentiality of lawfulness is coupled to essentially functionally defined time sequences. (shrink)

Philosophers have long argued that duties to oneself are paradoxical, as they seem to entail an incoherent power to release oneself from obligations. I argue that self-release is possible, both as a matter of deontic logic and of metaethics.

I distinguish paradoxes and hypodoxes among the conundrums of time travel. I introduce ‘hypodoxes’ as a term for seemingly consistent conundrums that seem to be related to various paradoxes, as the Truth-teller is related to the Liar. In this article, I briefly compare paradoxes and hypodoxes of time travel with Liar paradoxes and Truth-teller hypodoxes. I also discuss Lewis’ treatment of time travel paradoxes, which I characterise as a Laissez Faire theory of time travel. Time travel paradoxes are impossible according (...) to Laissez Faire theories, while it seems hypodoxes are possible. (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)

Grunbaum claims that the remedial failure of atreatment's characteristic factors is thegeneric, objective property of a placebo. Hestipulates that a treatment is placebic if thisremedial failure exacerbates the targetdisorder. This stipulation can subsume asplacebic effects that might be solelypharmacological, e.g., paradoxical reactions tocertain psychiatric drugs. If that exacerbationcan be explained pharmacologically, then wemight question whether Grunbaum's definitionalscheme captures the core identity of what weusually intend by the placebo concept. Ipropose that this core identity is bestcaptured by a symbolic meaning hypothesis (...) inwhich psychological factors exert thedeterminative influence. (shrink)

I hope to show that each of 1, 2, and 3 are plausible, yet we can derive 4: 1. It is epistemically permissible to believe that our preferred views in multi-proposition disputes are true, or at least more likely true than not. 2. If it is epistemically permissible to believe that our preferred views in multi-proposition disputes are true, or at least more likely true than not, then it is epistemically permissible for us to believe that we are über epistemic (...) superiors to our disagreeing colleagues in multi-proposition disputes. 3. It is not epistemically permissible to believe that we are über epistemic superiors to our disagreeing colleagues in multi-proposition disputes. 4. At least one of 1, 2, or 3, is false. (shrink)

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

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

This book develops a framework for analysing strategic rationality, a notion central to contemporary game theory, which is the formal study of the interaction of rational agents and which has proved extremely fruitful in economics, political theory and business management. The author argues that a logical paradox lies at the root of a number of persistent puzzles in game theory, in particular those concerning rational agents who seek to establish some kind of reputation. Building on the work of Parsons, (...) Burge, Gaifman and Barwise and Etchemendy, Robert Koons constructs a context-sensitive solution to the whole family of liar-like paradoxes including, for the first time, a detailed account of how the interpretation of paradoxical statements is fixed by context. This analysis provides an understanding of how the rational agent model can account for the emergence of rules, practices and institutions. (shrink)

This paper presents and motivates a new philosophical and logical approach to truth and semantic paradox. It begins from an inferentialist, and particularly bilateralist, theory of meaning---one which takes meaning to be constituted by assertibility and deniability conditions---and shows how the usual multiple-conclusion sequent calculus for classical logic can be given an inferentialist motivation, leaving classical model theory as of only derivative importance. The paper then uses this theory of meaning to present and motivate a logical system---ST---that conservatively extends (...) classical logic with a fully transparent truth predicate. This system is shown to allow for classical reasoning over the full (truth-involving) vocabulary, but to be non-transitive. Some special cases where transitivity does hold are outlined. ST is also shown to give rise to a familiar sort of model for non-classical logics: Kripke fixed points on the Strong Kleene valuation scheme. Finally, to give a theory of paradoxical sentences, a distinction is drawn between two varieties of assertion and two varieties of denial. On one variety, paradoxical sentences cannot be either asserted or denied; on the other, they must be both asserted and denied. The target theory is compared favourably to more familiar related systems, and some objections are considered. (shrink)

Challenging prevailing interpretations of the development of modern philosophy, this book proposes a reinterpretation of the transcendental tradition, as represented primarily by Kant and Husserl, and counters Heidegger's influential reading of these philosophers. Author David Carr defends their subtle and complex transcendental investigations of the self and the life of subjectivity, and seeks to revive an understanding of what Husserl calls "the paradox of subjectivity"--an appreciation for the rich and sometimes contradictory character of experience.

Paradoxes are arguments that lead from apparently true premises, via apparently uncontroversial reasoning, to a false or even contradictory conclusion. Paradoxes threaten our basic understanding of central concepts such as space, time, motion, infinity, truth, knowledge, and belief. In this volume Roy T Cook provides a sophisticated, yet accessible and entertaining, introduction to the study of paradoxes, one that includes a detailed examination of a wide variety of paradoxes. The book is organized around four important types of paradox: the (...) semantic paradoxes involving truth, the set-theoretic paradoxes involving arbitrary collections of objects, the Soritical paradoxes involving vague concepts, and the epistemic paradoxes involving knowledge and belief. In each of these cases, Cook frames the discussion in terms of four different approaches one might take towards solving such paradoxes. Each chapter concludes with a number of exercises that illustrate the philosophical arguments and logical concepts involved in the paradoxes. _Paradoxes_ is the ideal introduction to the topic and will be a valuable resource for scholars and students in a wide variety of disciplines who wish to understand the important role that paradoxes have played, and continue to play, in contemporary philosophy. (shrink)

Moore's paradox is a paradox in which certain kinds of belief or assertion, such as a belief that ?it is raining and I do not believe that it is raining?, are irrational despite involving no obvious contradiction in what is believed. But is there a parallel paradox involving other kinds of attitude, in particular desire? I argue that certain kinds of desire would be irrational to have for similar, distinctive reasons that having Moorean beliefs would be irrational (...) to have. Hence, I argue that such desires, a desire that ?one have a particular desire that was frustrated? or a desire that ?some state of affairs obtain about which one was indifferent?, are a parallel Moorean paradox of desire. I further argue that this analogous paradox has implications for practical reasoning, in particular by presenting a problem for instrumentalism about the objects of desire. (shrink)

A commitment to truth requires that you are open to receiving new evidence, even if that evidence contradicts your current beliefs. You should be open to changing your mind. However, this truism gives rise to the paradox of empathy. The paradox arises with the possibility of mental corruption through transformative change, and has consequences for how we should understand tolerance, disagreement, and the ability to have an open mind. I close with a discussion of how understanding this (...) class='Hi'>paradox provides a new explanation for a certain kind of standoff between the believer and the skeptic with regard to religious belief. (shrink)

The present work outlines a logical and philosophical conception of propositions in relation to a group of puzzles that arise by quantifying over them: the Russell-Myhill paradox, the Prior-Kaplan paradox, and Prior's Theorem. I begin by motivating an interpretation of Russell-Myhill as depending on aboutness, which constrains the notion of propositional identity. I discuss two formalizations of of the paradox, showing that it does not depend on the syntax of propositional variables. I then extend to propositions a (...) modal predicative response to the paradoxes articulated by an abstraction principle for propositions. On this conception, propositions are “shadows” of the sentences that express them. Modal operators are used to uncover the implicit relation of dependence that characterizes propositions that are about propositions. The benefits of this approach are shown by application to other intensional puzzles. The resulting view is an alternative to the plenitudinous metaphysics of impredicative comprehension principles. (shrink)

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