This paper propounds a systematic examination of the link between the Knower Paradox and provability interpretations of modal logic. The aim of the paper is threefold: to give a streamlined presentation of the Knower Paradox and related results; to clarify the notion of a syntactical treatment of modalities; finally, to discuss the kind of solution that modal provability logic provides to the Paradox. I discuss the respective strength of different versions of the Knower (...) class='Hi'>Paradox, both in the framework of first-order arithmetic and in that of modal logic with fixed point operators. It is shown that the notion of a syntactical treatment of modalities is ambiguous between a self-referential treatment and a metalinguistic treatment of modalities, and that these two notions are independent. I survey and compare the provability interpretations of modality respectively given by Skyrms, B. (1978, The Journal of Philosophy 75: 368–387) Anderson, C.A. (1983, The Journal of Philosophy 80: 338–355) and Solovay, R. (1976, Israel Journal of Mathematics 25: 287–304). I examine how these interpretations enable us to bypass the limitations imposed by the Knower Paradox while preserving the laws of classical logic, each time by appeal to a distinct form of hierarchy. (shrink)

The Knower Paradox has had a brief but eventful history, and principles of epistemic closure (which say that a subject automatically knows any proposition she knows to be materially implied, or logically entailed, by a proposition she already knows) have been the subject of tremendous debate in epistemic logic and epistemology more generally, especially because the fate of standard arguments for and against skepticism seems to turn on the fate of closure. As far as I can tell, however, (...) no one working in either area has emphasized the result I emphasize in this paper: the Knower Paradox just falsifies even the most widely accepted general principles of epistemic closure. After establishing that result, I discuss five of its more important consequences. (shrink)

The knower paradox states that the statement ‘We know that this statement is false’ leads to inconsistency. This article presents a fresh look at this paradox and some well-known solutions from the literature. Paul Égré discusses three possible solutions that modal provability logic provides for the paradox by surveying and comparing three different provability interpretations of modality, originally described by Skyrms, Anderson, and Solovay. In this article, some background is explained to clarify Égré’s solutions, all three (...) of which hinge on intricacies of provability logic and its arithmetical interpretations. To check whether Égré’s solutions are satisfactory, we use the criteria for solutions to paradoxes defined by Susan Haack and we propose some refinements of them. This article aims to describe to what extent the knower paradox can be solved using provability logic and to what extent the solutions proposed in the literature satisfy Haack’s criteria. Finally, the article offers some reflections on the relation between knowledge, proof, and provability, as inspired by the knower paradox and its solutions. (shrink)

The article states that the Knower paradox exposes the circularity of the conceptualization of knowledge. The article provides an explanation of the Knower paradox for the purpose of demonstrating how the paradox arises. A modification to the concept of knowledge is presented to solve the paradox and structure knowledge.

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)

I have argued that without an adequate solution to the knower paradox Fitch's Proof is- or at least ought to be-ineffective against verificationism. Of course, in order to follow my suggestion verificationists must maintain that there is currently no adequate solution to the knower paradox, and that the paradox continues to provide prima facie evidence of inconsistent knowledge. By my lights, any glimpse at the literature on paradoxes offers strong support for the first thesis, and (...) any honest, non-dogmatic reflection on the knower paradox provides strong support for the second. Whether verificationists want to go the route I've suggested is not for me todecide. As in the previous section my aim has been that of defending the mere viability of verificationism in the face of what many, many philosophers have taken to be its death-knell, namely Fitch's Proof. But, as the final objection makes clear, showing that verificationism can live in the face of Fitch's Proof is one thing; showing that it should live is another project. If nothing else, I hope that this papershows that verificationists still have a project to pursue; Fitch's Proof, contrary to popular opinion, need not bury verificationism.13. (shrink)

After introducing Fitch’s paradox of knowability and the knower paradox, the paper critically discusses the dialetheist unified solution to both problems that Beall and Priest have proposed. It is first argued that the dialetheist approach to the knower paradox can withstand the main objections against it, these being that the approach entails an understanding of negation that is intolerably weak and that it commits dialetheists to jointly accept and reject the same thing. The lesson of (...) the knower paradox, according to dialetheism, is that human knowledge is inconsistent. The paper also argues that this inconsistency has not been shown by dialetheists to be wide enough in its scope to justify their approach to Fitch’s problem. The connection between the two problems is superficial and therefore the proposed unified solution fails. (shrink)

In this paper I shall present three solutions to the Knower Paradox which, despite important points in common, differ in several respects. The first solution, proposed by C. A. Anderson [1] is a hierarchical solution, developed in the framework of first-order arithmetic. However I will try toshow that this solution is based on an incorrect argument. The second solution, inspired by a book of R.M. Smullyan [14], is developed in the framework of modal logic and it is based (...) on the idea of interpreting one of the basic systems of the modal logic of provability in an epistemic way. Ishall give arguments in support of this solution. The third solution, proposed by P. Egrèé [8] attempts to connect the first and the second solutions. I will show that this attempt fails for philosophical and formal reasons. (shrink)

This essay corrects an error in the presentation of the Paradox of the Knowledge-Plus Knower, which is the variant of Kaplan and Montague’s Knower Paradox presented in C. Cross 2001: ‘The Paradox of the Knower without Epistemic Closure,’ MIND, 110, pp. 319–33. The correction adds a universally quantified transitivity principle for derivability as an additional assumption leading to paradox. This correction does not affect the status of the Knowledge-Plus paradox as a rebuttal (...) to an argument against epistemic closure, since the quantified transitivity principle is true in the standard model of arithmetic and therefore innocuous. (shrink)

In this essay I present a new version of the Paradox of the Knower and show that this new paradox vitiates a certain argument against epistemic closure. I then prove a theorem that relates the new paradox to epistemological scepticism. I conclude by assessing the use of the Knower in arguments against syntactical treatments of knowledge.

In “The Paradox of the Knower without Epistemic Closure”, MIND 110:319-33, 2001, I develop a version of the Knower Paradox which does not assume epistemic closure, and I use it to argue that the original Knower Paradox does not support an argument against epistemic closure. In “The Paradox of the Knower without Epistemic Closure?”, MIND 113:95-107, 2004, Gabriel Uzquiano, using his own result, argues that my rebuttal to the anti-closure argument is not (...) successful. I respond here by arguing that in order to use Uzquiano’s result in an argument against closure, one must assume an implausible skepticism about arithmetic. (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)

Predicates are term-to-sentence devices, and operators are sentence-to-sentence devices. What Kaplan and Montague's Paradox of the Knower demonstrates is that necessity and other modalities cannot be treated as predicates, consistent with arithmetic; they must be treated as operators instead. Such is the current wisdom.A number of previous pieces have challenged such a view by showing that a predicative treatment of modalities neednot raise the Paradox of the Knower. This paper attempts to challenge the current wisdom in (...) another way as well: to show that mere appeal to modal operators in the sense of sentence-to-sentence devices is insufficient toescape the Paradox of the Knower. A family of systems is outlined in which closed formulae can encode other formulae and in which the diagonal lemma and Paradox of the Knower are thereby demonstrable for operators in this sense. (shrink)

Let us sum up. The paradox of the Knower poses a direct and formal challenge to the coherence of common notions of knowledge and truth. We've considered a number of ways one might try to meet that challenge: propositional views of truth and knowledge, redundancy or operator views, and appeal to hierarchy of various sorts. Mere appeal to propositions or operators, however, seems to be inadequate to the task of the Knower, at least if unsupplemented by an (...) auxiliary recourse to hierarchy. But the cost of hierarchy appears to be an abandonment of any notion of all truth or of omniscience. What the contradictions of the Knower seem to demand, then, is at least an abandonment of these. As noted in the introduction, the argument is complicated enough that one must be wary of dogmatic and precipitate conclusions. One may legitimately wonder whether some new response, or some variation on an old one, will yet offer a way out.Far too often, however, it is asked what has gone wrong with paradox rather than what paradox may have to teach us. What the Knower may have to teach us, I think, is that there really can be no coherent notion of all truth and really can be no coherent notion of omniscience. In its own way that conclusion is perhaps as humbling as is any traditional notion of God. (shrink)

The epistemic paradox of 'belief instability' has recently received notable attention from many philosophers. Understanding this paradox is very important because belief is a central notion of psychologically motivated semantic theories in philosophy, linguistics, and cognitive science, and this paradox poses serious problems for these theories. In this dissertation I criticize previous proposals and offer a new proposal, which I call a 'revision theory of belief'. ;My revision theory of belief is in many respects an application of (...) Gupta's and Belnap's revision theory of truth, which is proposed to deal with the Liar paradox. They argue that truth is a circular notion because Tarski biconditionals provide circular, partial definitions of truth. And this circularity of truth is the source of the Liar paradox. I offer a similar proposal for handling the paradox of belief instability. In particular, I argue that our notion of belief involved in the paradox of belief instability is circular, and that is why this paradox arises. ;If the notion of belief involved in the paradox is circular, we have to employ a hypothetical evaluation of the belief predicate, and if we do so through a revision process, we can avoid the contradiction which seems to be generated by some paradoxical belief sentences. But it is not easy to show that our notion of belief is circular. Especially, there is nothing like Tarski biconditionals in the case of belief. Nonetheless, I show in this dissertation that there is a certain schema, which I call the B-schema, whose instances can be taken as circular, partial definitions of a notion of belief, and it is that notion of belief which is involved in the paradox of belief instability. In this dissertation I also show that the revision approach can be extended for handling the Knower paradox. I argue that the Knower paradox arises because our notion of knowledge involved in the paradox is circular. (shrink)

At some step in proving the Liar Paradox in natural language, a sentence is derived that seems overdetermined with respect to its semantic value. This is complemented by Tarski’s Theorem that a formal language cannot consistently contain a naive truth predicate given the laws of logic used in proving the Liar paradox. I argue that proofs of the Eubulidean Liar either use a principle of truth with non-canonical names in a fallacious way or make a fallacious use of (...) substitution of identicals. Tarski never committed the first fallacy and may have himself considered it fallacious. Nevertheless, I clarify that it is fallacious. I then argue substitution of identicals needs to be restricted within the scope of the truth predicate. A logic for truth implementing this restriction is a monotonic extension of a classical first order logic, or indeed a formalizable fragment of natural language. Proofs of Tarski’s Indefinability of Truth theorem are invalid in this logic. This approach generalizes to invalidate proofs of Liar-like paradoxes, particularly the predicate form of the Knower paradox. Consequently, such a logic can be further extended in a way that avoids Montague’s theorem for such a system. Yet, the semantic status of a Liar sentence is not fully resolved. It is no longer overdetermined; it is now underdetermined. (shrink)

The epistemic paradox of 'belief instability' has recently received notable attention from many philosophers. Understanding this paradox is very important because belief is a central notion of psychologically motivated semantic theories in philosophy, linguistics, and cognitive science, and this paradox poses serious problems for these theories. In this dissertation I criticize previous proposals and offer a new proposal, which I call a 'revision theory of belief'. -/- My revision theory of belief is in many respects an application (...) of Gupta's and Belnap's revision theory of truth, which is proposed to deal with the Liar paradox. They argue that truth is a circular notion because Tarski biconditionals provide circular, partial definitions of truth. And this circularity of truth is the source of the Liar paradox. I offer a similar proposal for handling the paradox of belief instability. In particular, I argue that our notion of belief involved in the paradox of belief instability is circular, and that is why this paradox arises. -/- If the notion of belief involved in the paradox is circular, we have to employ a hypothetical evaluation of the belief predicate, and if we do so through a revision process, we can avoid the contradiction which seems to be generated by some paradoxical belief sentences. But it is not easy to show that our notion of belief is circular. Especially, there is nothing like Tarski biconditionals in the case of belief. Nonetheless, I show in this dissertation that there is a certain schema, which I call the B-schema, whose instances can be taken as circular, partial definitions of a notion of belief, and it is that notion of belief which is involved in the paradox of belief instability. In this dissertation I also show that the revision approach can be extended for handling the Knower paradox. I argue that the Knower paradox arises because our notion of knowledge involved in the paradox is circular. (shrink)

Heraclitus accepts as a principle that any particular insight into things is necessarily partial and perspectival. Edward Halper has discussed how, for this reason, it is in principle impossible for a particular thinker to attain the perspective of the Logos by which the whole can be made intelligible. So, metaphysics itself tells us that metaphysics is impossible. According to Halper, Heraclitus was wrong to take the Logos as applying to itself, as the Logos should properly be understood as applying only (...) to what is not a product of human agency. I argue that Halper’s move cannot serve as a corrective patch to Heraclitus’ metaphysical thought, since it posits a distinction between the human and the rest of reality which Heraclitus could never accept. Although not a radical monist who denies the reality of all multiplicity, a fundamental principle of his thought is that all distinctions and oppositions are grounded in a more fundamental unity. I instead approach the Heraclitean paradox by appealing to the strategy, familiar from a number of ancient Greek philosophers, of making a distinction between different levels of knowledge inherent within the same knower. (shrink)

The goal of this paper is to explore the significance of Montague’s paradox—that is, any arithmetical theory $T\supseteq Q$ over a language containing a predicate $P$ satisfying $P\rightarrow \varphi $ and $T\vdash \varphi \,\therefore\,T\vdash P$ is inconsistent—as a limitative result pertaining to the notions of formal, informal, and constructive provability, in their respective historical contexts. To this end, the paradox is reconstructed in a quantified extension $\mathcal {QLP}$ of Artemov’s logic of proofs. $\mathcal {QLP}$ contains both explicit modalities (...) $t:\varphi $ and also proof quantifiers $x:\varphi $. In this system, the basis for the rule NEC is decomposed into a number of distinct principles governing how various modes of reasoning about proofs and provability can be internalized within the system itself. A conceptually motivated resolution to the paradox is proposed in the form of an argument for rejecting the unrestricted rule NEC on the basis of its subsumption of an intuitively invalid principle pertaining to the interaction of proof quantifiers and the proof-theorem relation expressed by explicit modalities. (shrink)

The last twenty years of English-speaking Nietzsche scholarship have been dominated by the paradox of perspectivism. Perspectivism is the view that any claim to knowledge is bound to the perspective formed by the contingent “interests” of the knower. Nearly all existing interpretations fall within one of two categories. On the one hand, this relativity to perspective is thought to underwrite a generalized skepticism: we are irretrievably locked up in a perspective which may distort our apprehension of reality. On (...) the other hand, perspectivism is interpreted as anti-essentialism: there is no independent reality the apprehension of which our perspective might distort; accordingly, our judgments are less a matter of correspondence to objective reality than expression of subjective attitudes. Unsurprisingly, this anti-essentialism is often associated with relativism. (shrink)

This is a defense and extension of Stephen Yablo's claim that self-reference is completely inessential to the liar paradox. An infinite sequence of sentences of the form 'None of these subsequent sentences are true' generates the same instability in assigning truth values. I argue Yablo's technique of substituting infinity for self-reference applies to all so-called 'self-referential' paradoxes. A representative sample is provided which includes counterparts of the preface paradox, Pseudo-Scotus's validity paradox, the Knower, and other enigmas (...) of the genre. I rebut objections that Yablo's paradox is not a genuine liar by constructing a sequence of liars that blend into Yablo's paradox. I rebut objections that Yablo's liar has hidden self-reference with a distinction between attributive and referential self-reference and appeals to Gregory Chaitin's algorithmic information theory. The paper concludes with comments on the mystique of self-reference. (shrink)

The last twenty years of English-speaking Nietzsche scholarship have been dominated by the paradox of perspectivism. Perspectivism is the view that any claim to knowledge is bound to the perspective formed by the contingent “interests” of the knower. Nearly all existing interpretations fall within one of two categories. On the one hand, this relativity to perspective is thought to underwrite a generalized skepticism: we are irretrievably locked up in a perspective which may distort our apprehension of reality. On (...) the other hand, perspectivism is interpreted as anti-essentialism: there is no independent reality the apprehension of which our perspective might distort; accordingly, our judgments are less a matter of correspondence to objective reality than expression of subjective attitudes. Unsurprisingly, this anti-essentialism is often associated with relativism. (shrink)

Fitch's Paradox and the Paradox of the Knower both make use of the Factivity Principle. The latter also makes use of a second principle, namely the Knowledge-of-Factivity Principle. Both the principle of factivity and the knowledge thereof have been the subject of various discussions, often in conjunction with a third principle known as Closure. In this paper, we examine the well-known Surprise Examination paradox considering both the principles on which this paradox rests and some formal (...) characterisations of the surprise notion, crucial in this paradox. Standard formalizations of the Surprise Examination paradox in modal logic do not seem, at first glance, to depend on either factivity or knowledge-of-factivity, but we will argue that both factivity and knowledge-of-factivity play a key implicit role in the paradox. Namely, they are implicitly, perhaps unintentionally, used in order to simplify the definition of surprise. We analyze modal logical formalizations of three versions of the paradox concluding that the Surprise Examination paradox is the result of two flaws: the assumption of knowledge-of-factivity, and the over-simplification of the definition of "surprise" accordingly. By fixing these two flaws, the Surprise Examination paradox vanishes. (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..

Feminist philosophers are often concerned with rejecting Cartesian notions of objectivity which eliminate all subjectivity on the part of knowers. However, this rejection of a notion of pure (non-subjective) neutrality has led the dilemma that Louise Antony calls the “bias paradox” (Antony 1993, 188-90). At the heart of this paradox lies the seeming choice between objectivism and relativism. It has two fundamental commitments that clearly focus this dilemma: (1) the explicit rejection of the concept of impartial objectivity and (...) (2) the desire to assert the reality of women’s oppression. The problem is that in the absence of impartiality (at least as an ideal), there appears to be a lack of principled, normative criteria for evaluating beliefs across differing epistemic perspectives. While this tension is dealt with most straightforwardly in discussions of naturalized feminist epistemology and feminist philosophy of science, the bias paradox, nonetheless, is not merely a problem for feminists. Any view that rejects the Cartesian ideals of pure objectivity and value-neutrality will ultimately be forced to confront the dilemma that seemingly results from the paradox; namely, to either endorse pure impartiality or accept an “anything goes” relativism. (shrink)

A variation of Fitch’s paradox is given, where no special rules of inference are assumed, only axioms. These axioms follow from the familiar assumptions which involve rules of inference. We show (by constructing a model) that by allowing that possibly the knower doesn’t know his own soundness (while still requiring he be sound), Fitch’s paradox is avoided. Provided one is willing to admit that sound knowers may be ignorant of their own soundness, this might offer a way (...) out of the paradox. (shrink)

In a recent paper, Alexander argues that relaxing the requirement that sound knowers know their own soundness might provide a solution to Fitch’s paradox and introduces a suitable axiomatic system where the paradox is avoided. In this paper an analysis of this solution is proposed according to which the effective move for solving the paradox depends on the axiomatic treatment of the ontic modality rather than the limitations imposed on the epistemic one. It is then shown that, (...) once the ontic modality is standardly introduced, the paradox still follows and, in addition, some puzzling consequences arise. (shrink)

The nature of psychoanalysis seems contradictory - deeply personal, subjective and intuitive, yet requiring systematic theory and principles of technique. The objective quality of psychoanalytic knowledge is paradoxically dependent on the personal engagement of the knower with what is known. In The Dove that Returns, The Dove that Vanishes , Michael Parsons explores the tension of this paradox. As they respond to it, and struggle to sustain it creatively, analysts discover their individual identities. The work of outstanding clinicians (...) such as Marion Milner and John Klauber is examined in detail. The reader also encounters oriental martial arts, Greek Tragedy, the landscape painting of John Constable, a Winnicottian theory of creativity and a discussion of the significance of play in psychoanalysis. From such varied topics evolves a deepening apprehension of the nature of the clinical experience. Illustrated throughout with clinical examples, The Dove that Returns, The Dove that Vanishes will prove valuable to those in the field of psychoanalysis, and to those in the arts and humanities who are interested in contemporary psychoanalytic thinking. (shrink)

The Knower paradox purports to place surprising a priori limitations on what we can know. According to orthodoxy, it shows that we need to abandon one of three plausible and widely-held ideas: that knowledge is factive, that we can know that knowledge is factive, and that we can use logical/mathematical reasoning to extend our knowledge via very weak single-premise closure principles. I argue that classical logic, not any of these epistemic principles, is the culprit. I develop a consistent (...) theory validating all these principles by combining Hartry Field's theory of truth with a modal enrichment developed for a different purpose by Michael Caie. The only casualty is classical logic: the theory avoids paradox by using a weaker-than-classical K3 logic. I then assess the philosophical merits of this approach. I argue that, unlike the traditional semantic paradoxes involving extensional notions like truth, its plausibility depends on the way in which sentences are referred to--whether in natural languages via direct sentential reference, or in mathematical theories via indirect sentential reference by Gödel coding. In particular, I argue that from the perspective of natural language, my non-classical treatment of knowledge as a predicate is plausible, while from the perspective of mathematical theories, its plausibility depends on unresolved questions about the limits of our idealized deductive capacities. (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)

We present a new logic -based approach to the reasoning about knowledge which is independent of possible worlds semantics.? k is a non- Fregean logic whose models consist of propositional universes with subsets for true, false and known propositions. Knowledge is, in general, not closed under rules of inference; the only valid epistemic principles are the knowledge axiom K i??? and some minimal conditions concerning common knowledge in a group. Knowledge is explicit and all forms of the logical omniscience problem (...) are avoided. Various stronger epistemic properties such as positive and/or negative introspection, the K-axiom, closure under logical connectives, etc, can be restored by imposing additional semantic constraints. This yields corresponding sublogics for which we present sound and complete axiomatizations. As a useful tool for general model constructions we study abstract versions of some 3-valued logics in which we interpret truth as knowledge. We establish a connection between? k and the well-known syntactic approach to explicit knowledge proving a result concerning equi-expressiveness. Furthermore, we discuss some self - referential epistemic statements, such as the knower paradox, as relaxations of variants of the liar paradox and show how these epistemic "paradoxes" can be solved in? k. Every specific? k - logic is defined as a certain extension of some underlying classical abstract logic. (shrink)

In discussions of Fitch’s paradox, it is usually assumed without further argument that knowledge is factive, that if a subject knows that p, then p is true. It is argued that this common assumption is not as well-founded as it should be, and that there in fact are certain reasons to be suspicious of the unrestricted version of the factiveness claim. There are two kinds of reason for this suspicion. One is that unrestricted factiveness leads to paradoxes and unexpected (...) results, the other is that the usual arguments for factiveness are not as compelling as is commonly thought. There may in fact be some kinds of contexts, where factiveness doesn’t hold for knowledge—the usual arguments for factiveness don’t suffice to support the claim that knowledge is unrestrictedly factive. Perhaps all that can be shown is that knowledge is at times factive, or that it is default factive, as it were: this doesn’t show that there can’t be counterexamples, however. Certain aspects of knowledge without unrestricted factiveness are examined briefly. (shrink)

It is epistemological orthodoxy that the object of propositional knowledge is the truth of propositions. This traditional view is based on what I call the ‘KT-schema’, viz, ‘S knows that p, iff, S knows that “p” is true’. The purpose of this paper is to reject the KT-schema. By showing the paradoxical upshot of the KT-schema and providing counterexamples to the KT-schema, this paper argues that ‘knowing that p’ is more than ‘knowing that “p” is true’. Consequently, we shall rethink (...) the object problem of propositional knowledge – if knowing that p is not merely knowing that ‘p’ is true, then what is indeed the object of propositional knowledge? I will also attempt to solve this problem by proposing a complementary answer: knowing that p requires at least knowing the truth of p, plus, understanding the content of p. (shrink)

We present a new logic-based approach to the reasoning about knowledge which is independent of possible worlds semantics. \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$${\in_K}$$\end{document} is a non-Fregean logic whose models consist of propositional universes with subsets for true, false and known propositions. Knowledge is, in general, not closed under rules of inference; the only valid epistemic principles are the knowledge axiom Kiφ → φ and some minimal conditions concerning common knowledge in a group. Knowledge is explicit (...) and all forms of the logical omniscience problem are avoided. Various stronger epistemic properties such as positive and/or negative introspection, the K-axiom, closure under logical connectives, etc. can be restored by imposing additional semantic constraints. This yields corresponding sublogics for which we present sound and complete axiomatizations. As a useful tool for general model constructions we study abstract versions of some 3-valued logics in which we interpret truth as knowledge. We establish a connection between \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$${\in_K}$$\end{document} and the well-known syntactic approach to explicit knowledge proving a result concerning equi-expressiveness. Furthermore, we discuss some self-referential epistemic statements, such as the knower paradox, as relaxations of variants of the liar paradox and show how these epistemic “paradoxes” can be solved in \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$${\in_K}$$\end{document}. Every specific \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$${\in_K}$$\end{document}-logic is defined as a certain extension of some underlying classical abstract logic. (shrink)