It is proposed that subconscious retro-predictions in conjunction with brain state update cycles are instrumental in the physiological generation of conscious sensations and perceptions, and in all abstract thought. In this paper the hypothesis is supported by conducting a detailed a re-evaluation of the self-referential statements in Set Theory and Formal Logic known as antinomies. This study concludes that the recursive behavior exhibited by abstract enigmas such as "Russell’s Paradox" is analogous to the oscillations typical of bistable perceptual phenomena.

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

ABSTRACT: This chapter offers a revenge-free solution to the liar paradox (at the centre of which is the notion of Gestalt shift) and presents a formal representation of truth in, or for, a natural language like English, which proposes to show both why -- and how -- truth is coherent and how it appears to be incoherent, while preserving classical logic and most principles that some philosophers have taken to be central to the concept of truth and our (...) use of that notion. The chapter argues that, by using a truth operator rather than truth predicate, it is possible to provide a coherent, model-theoretic representation of truth with various desirable features. After investigating what features of liar sentences are responsible for their paradoxicality, the chapter identifies the logic as the normal modal logic KT4M (= S4M). Drawing on the structure of KT4M (=S4M), the author proposes that, pace deflationism, truth has content, that the content of truth is bivalence, and that the notions of both truth and bivalence are semideterminable. (shrink)

The formalism of abstracted quantum mechanics is applied in a model of the generalized Liar Paradox. Here, the Liar Paradox, a consistently testable configuration of logical truth properties, is considered a dynamic conceptual entity in the cognitive sphere (Aerts, Broekaert, & Smets, [Foundations of Science 1999, 4, 115–132; International Journal of Theoretical Physics, 2000, 38, 3231–3239]; Aerts and colleagues[Dialogue in Psychology, 1999, 10; Proceedings of Fundamental Approachs to Consciousness, Tokyo ’99; Mind in Interaction]. Basically, the intrinsic contextuality of (...) the truth-value of the Liar Paradox is appropriately covered by the abstracted quantum mechanical approach. The formal details of the model are explicited here for the generalized case. We prove the possibility of constructing a quantum model of the m-sentence generalizations of the Liar Paradox. This includes (i) the truth–falsehood state of the m-Liar Paradox can be represented by an embedded 2m-dimensional quantum vector in a (2m) m -dimensional complex Hilbert space, with cognitive interactions corresponding to projections, (ii) the construction of a continuous ‘time’ dynamics is possible: typical truth and falsehood value oscillations are described by Schrödinger evolution, (iii) Kirchoff and von Neumann axioms are satisfied by introduction of ‘truth-value by inference’ projectors, (iv) time invariance of unmeasured state. (shrink)

The liar paradox is widely conceived as a problem for logic and semantics. On the basis of empirical studies presented here, we suggest that there is an underappreciated psychological dimension to the liar paradox and related problems, conceived as a problem for human thinkers. Specific findings suggest that how one interprets the liar sentence and similar paradoxes can vary in relation to one’s capacity for logical and reflective thought, acceptance of certain logical principles, and degree of philosophical (...) training, but also as a function of factors such as religious belief, gender, and whether the problem is treated as theoretical or practical. Though preliminary, these findings suggest that one reason the liar paradox resists a final resolution is that it engages both aspects described by so-called dual process accounts of human cognition. (shrink)

I argue that the paradoxes attributed to the Megarians, namely the Liar, the Sorites, presupposition ("Have you stopped beating your father,") and failure of substitution of co-referential terms in psychological verbs ("The Electra") were intended to be reasons to accept Parmenides view that non-being is an incoherent notion and that there is exactly One Being. That is, Eubulides and others were akin to Zeno, in indirectly supporting Parmenidean monism.

Paradoxes are mind-dependent in a number of ways. First, by definition, paradoxes offer surprises or apparent contradictions. Since surprise and appearance rely on subjective psychological reactions, paradoxes rely on psychological events. Second, propositional versions of the liar paradox must eventually appeal to sentences if they are to achieve traction, yet sentential versions of the liar paradox rely on language and hence on mentality. Third, belief paradoxes such as B, "No one believes B", transparently hinge on the existence of (...) mental states. (Belief paradoxes – extending work by Burge, Buridan, Grim, Sainsbury, and Sorensen – demonstrate a fundamental limitation on all cognitive systems: that none can hold all and only truths.) Finally, it is argued that belief paradoxes, like liar paradoxes, arise from the nature of semantic representation. (shrink)

Thanks to the work of Kendall Walton, appeals to the notion of pretence (or make-believe) have become popular in philosophy. Now the notion has begun to appear in accounts of truth. My aim here is to assess one of these accounts, namely the ‘constructive methodological deflationism’ put forward by Jc Beall. After introducing the view, I argue that Beall does not manage to overcome the problem of psychological implausibility. Although Beall claims that constructive methodological deflationism supports dialetheism, I argue that (...) it does not, and I show that it in fact provides a classical response to the Liar paradox. (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)

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)

Next SectionCharlie Pelling presents an impropriety paradox for the truth account of assertion. After solving his paradox I show that it is a version of the liar paradox. I then show that for any account of truth there is a strengthened liar-like paradox, and that for any solution to the strengthened liar paradox, there is a parallel solution to each of these “new” paradoxes.

Predictive processing, an increasingly popular paradigm in cognitive sciences, has focused primarily on giving accounts of perception, motor control and a host of psychological phenomena, including consciousness. But higher cognitive processes, like conceptual thought, language, and logic, have received only limited attention to date and PP still stands disconnected from a huge body of research in those areas. In this thesis, I aim to address this gap and I attempt to go some way towards developing and defending a cognitive-computational approach (...) to higher cognition within the predictive processing paradigm. To test its explanatory potential, I apply it to a range of linguistic and conceptual phenomena. I proceed in three steps. First, I lay out an account of concepts and suggest how concepts are represented, how they can be context-sensitively processed, and how the apparent diversity of formats arise. Secondly, I propose how paradigmatic higher cognitive competencies, like language and logical reasoning, could fit into the PP picture. Thirdly, I apply the PP account of concepts and language to a range of linguistic-conceptual phenomena as test cases, namely: metaphor, the semantic paradox (specifically the Liar Paradox) and copredication. Finally, I discuss some challenges and objections to the PP framework as applied to higher cognition and in general. (shrink)

Although most scholars trace the Liar Paradox to Plato’s contemporary, Eubulides, the paper argues that Plato builds something very like the Liar Paradox into the very structure of his dialogues with significant consequences for understanding his views. After a preliminary exposition of the liar paradox it is argued that Plato builds this paradox into the formulation of many of his central doctrines, including the “Divided Line” and the “Allegory of the Cave” and the “Ladder of Love”. Thus, (...) Plato may have been the first to formulate the view that Graham Priest calls dialetheism, roughly, the view that some contradictions are, in an illuminating way, inescapable and true. The paper argues that Plato builds this Liar paradox into the formulation of his signature views because he holds that the attempt by finite human beings to theorize about transcendent realities results in the simultaneous necessity, and impossibility, of transgressing the limits of language—leading to the paradoxes. Finally, it is argued that the existence of these paradoxes in these Platonic doctrines is the direct result of an intrinsic hermeneutical circle in Plato’s aforementioned signature views. (shrink)

The Liar paradox arises when we consider a sentence that says of itself that it is not true. If such self-referential sentences exist? and examples like?This sentence is not true? certainly suggest this?, then our logic and standard notion of truth allow to infer a contradiction: The Liar sentence is true and not true. What has gone wrong? Must we revise our notion of truth and our logic? Or can we dispel the common conviction that there are such (...) self-referential sentences? The present study explores the second path.0After comparing the Liar reasoning in formal and informal logic and showing that there are no Gödelian Liar sentences, the study moves on from the semantics of self-reference to the metaphysics of expressions and proposes a novel solution to the Liar paradox: Meaningful expressions are distinct from their syntactic bases and exist only relative to contexts. Detailed semantico-metaphysical arguments show that in this dynamic setting, an object can be referred to only after it has started to exist. Hence the circular reference needed in the Liar paradox cannot occur, after all. As this solution is contextualist, it evades the expressibility problems of other proposals. (shrink)

In Beyond the Limits of Thought [2002], Graham Priest argues that logical and semantic paradoxes have the same underlying structure (which he calls the Inclosure Schema ). He also argues that, in conjunction with the Principle of Uniform Solution (same kind of paradox, same kind of solution), this is sufficient to 'sink virtually all orthodox solutions to the paradoxes', because the orthodox solutions to the paradoxes are not uniform. I argue that Priest fails to provide a non-question-begging method to 'sink (...) virtually all orthodox solutions', and that the Inclosure Schema cannot be the structure that underlies the Liar paradox. Moreover, Ramsey was right in thinking that logical and semantic paradoxes are paradoxes of different kinds. (shrink)

Here is the liar paradox. We have a sentence, (L), which somehow says of itself that it is false. Suppose (L) is true. Then things are as (L) says they are. (For it would appear to be a mere platitude that if a sentence is true, then things are as the sentence says they are.) (L) says that (L) is false. So, (L) is false. Since the supposition that (L) is true leads to contradiction, we can assert that (L) (...) is false. But since this is just what (L) says, (L) is then true. (For it would appear to be a mere platitude that if things are as a given sentence says they are, the sentence is true.) So (L) is true. So (L) is both true and false. Contradiction. (shrink)

The Liar Paradox is an argument that arrives at a contradiction by reasoning about a Liar Sentence. The classical Liar Sentence is the self-referential sentence “This sentence is false.”.

In this thesis, I both analyze the phenomenology of vision from a geometrical point of view, and also develop certain connections between that geometrical analysis and the mind body problem. In order to motivate the need for such an analysis, I first show, by means of a refutation of direct realism, that visual space is never identical with any of the physical objects being indirectly "seen" by constituting color arrangements in it. It thus follows that the geometry of visual space (...) may be quite different from the Euclidean geometry of physical space, and I proceed to analyze that geometry. ;I argue that topologically, visual space is two dimensional, inasmuch as regions of it are capable of being bounded by a line, such as the borders around the various objects constituted in it. An apparent paradox arises here though, inasmuch as we posess phenomenal depth perception, which is particularly striking during binocular vision, and thus the question arises as to how the binocular depth cue of retinal disparity is registered phenomenally in a two dimensional space. I resolve this apparent paradox by arguing that the internal metric struture of this space can be apprehended phenomenally, and can serve as such a phenomenal depth cue. It is shown that holistically, this metric structure is elliptical, since for example marginal distortions in wide-angle photography are not present in visual space, and it is also noted that there is a tendency towards size constancy in visual perception. It is shown from these geometrical considerations that visual space posseses a variable curvature, with that curvature being determined by the physical depths of objects constituted in the space. ;Finally, I investigate what bearing the preceding geometrical conclusions have on the question of how events in visual space may be causally determined by neural events in the brain. The classical isomorphic theory of Gestalt psychology is then reinterpreted in light of my analysis of the geometry of visual space. (shrink)

ABSTRACTTwo rival scholars from Shiraz in Persia, Dawānī and Dashtakī engaged in a bitter and extended dispute over a range of metaphysical and logical issues. One of these was the liar paradox. Their debate on this point marked the most extensive scrutiny of the paradox in Arabic until that time. Dashtakī’s solution was to deny that the statement ‘What I say is false’ is true or false, on the ground that there is one statement and one application of the (...) falsity predicate. Given that – ex hypothesi – there is no other statement, there is no basis for a reiteration of the truth or falsity predicate and describing the statement itself as true or false. Dawānī’s solution was to deny that ‘What I say is false’ is a statement at all, and he argued that it is instead akin to a performative utterance such as ‘I hereby sell you this’. (shrink)

A historically popular response to the liar paradox (“this sentence is false”) is to say that the liar sentence is meaningless (or semantically defective, or malfunctions, or…). Unfortunately, like all other supposed solutions to the liar, this approach faces a revenge challenge. Consider the revenge liar sentence, “this sentence is either meaningless or false”. If it is true, then it is either meaningless or false, so not true. And if it is not true, then it can’t (...) be either meaningless or false, so it must be true. Either way, we are back in a paradox. This paper provides a detailed and exhaustive discussion of the options for responding to revenge on behalf of “meaningless” theories. Though I attempt to discuss all of the options fairly, I will ultimately opt for one specific response and discuss some of its challenges. Various technical and logical matters will be discussed throughout the paper, but my focus will be philosophical, throughout. My overall conclusion is that the “meaningless” strategy is at least as well off in the face of revenge as any other approach to the liar and related paradoxes. (shrink)

In this paper we concentrate on the nature of the liar paradox asa cognitive entity; a consistently testable configuration of properties. We elaborate further on a quantum mechanical model (Aerts, Broekaert and Smets, 1999) that has been proposed to analyze the dynamics involved, and we focus on the interpretation and concomitant philosophical picture. Some conclusions we draw from our model favor an effective realistic interpretation of cognitive reality.

A semantic solution to the liar paradox (“This statement is not true”) is presented in this article. Since the liar paradox seems to evince a contradiction, the principle of non-contradiction is preliminarily discussed, in order to determine whether dismissing this principle may be reason enough to stop considering the liar paradox a problem. No conclusive outcome with respect to the value of this principle is aspired to here, so that the inquiry is not concluded at this point (...) and the option to explore an alternative, semantic, solution remains open. This proposed solution is focused on what the liar paradox expresses and what it fails to express. (shrink)

Do logical paradoxes, like Eubulides’s Liar Paradox (the claim that the sentence “I am now lying” is true if and only if it is false), have any “existential” significance or are they mere brain puzzles for the mathematically minded? The paper argues that Randall Jarrell’s poem, “Eighth Air Force”, contains a poetic use of Eubulides’ Liar Paradox, spoken by Pontius Pilate’s wife in her statements about the “murder” of Jesus, in order to capture, symbolically, the inherent universal duplicity (...) (inauthenticity) of human life, specifically, the fact that human life, even in its true statements about fundamental moral-existential issues, is an inseparable blend of “truth” and “lies.”. (shrink)

In his 1935 book Principles of Gestalt Psychology, Kurt Koffka stated that empirical research in perceptual psychology should begin with “a phenomenological analysis,” which in turn would put constraints on the “true theory.” In this paper, I take this statement as a point of departure to investigate in what sense Gestalt psychologists practiced a phenomenological analysis and how they saw it related to theory construction. I will contextualize the perceptual research in Gestalt psychology vis-a-vis Husserlian phenomenology on (...) the one hand and mainstream psychophysics on the other, and I will argue that Gestalt psychologists practiced a form of “frontloading” phenomenology: Instead of requiring experimental subjects to engage in experiential reflections, such reflections were—in a sense—already engrained in the experimental designs used by researchers. This type of phenomenology was decidedly anti-“introspectionist” and as such was compatible with some of Husserl’s basic commitments, while at the same time bearing a surprising resemblance with the methods employed by psychophysicists like E. Boring and S.S. Stevens. This latter point will prompt me to explore what the difference between Gestalt-psychology and psychophysics amounted to. My analysis will reveal some disagreements and misunderstandings, especially with regard to the notions of isomorphism and introspection. (shrink)

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

Here I present a new objection to the material or "hook" analysis of indicative conditionals - the thesis that an indicative conditional 'If A then C' has the truth-conditions of the so-called material conditional - based on Liar-like reasoning. This objection seems invulnerable to any Grice-Lewis-Jackson-inspired pragmatic rejoinder.

This paper aims to present how logic may undermine a parliamentary assault on democratic institutions based on the analysis conducted with reference to the so-called Polish constitutional crisis. I analyse whether a law can be reviewed on the basis of this law itself. The Polish Constitutional Tribunal faced such a problem while passing the verdict of 9th March, 2016, regarding the constitutionality of the amendment to the Statute on the Constitutional Tribunal from 22nd December, 2015. This problem, called a ‘verdict (...) paradox’, was claimed to be a type of the Liar paradox. I argue that, contrary to the common view, the problem of the verdict paradox is not based on the Liar paradox; for this purpose, a logical analysis is applied to four variants of a reasoning with regard to the constitutionality of the said amendment. The distinction between two levels of analysis concerning emerging reasonings, namely an abstract level and a concrete level placed in the context of the legal system, is also introduced. This paper demonstrates that although only two variants of the reasoning concerning a law’s judicial review based on the law itself involve logical contradiction, the possibility of employing reasonings from other variants must be excluded, albeit due to alternative reasons. Therefore, the Constitutional Tribunal’s decision to avoid the verdict paradox by passing over the reviewed provisions in the review process was correct and might be perceived as an example of how logic and reason can defend the institutional guarantees of political freedom. (shrink)

The purpose of this note is to present a strong form of the liar paradox. It is strong because the logical resources needed to generate the paradox are weak, in each of two senses. First, few expressive resources required: conjunction, negation, and identity. In particular, this form of the liar does not need to make any use of the conditional. Second, few inferential resources are required. These are: (i) conjunction introduction; (ii) substitution of identicals; and (iii) the inference: (...) From ¬(p ∧ p), infer ¬ p. It is, interestingly enough, also essential to the argument that the ‘strong’ form of the diagonal lemma be used: the one that delivers a term λ such that we can prove: λ = ¬ T(⌈λ⌉); rather than just a sentence Λ for which we can prove: Λ ≡ ¬T(⌈Λ⌉). The truth-theoretic principles used to generate the paradox are these: ¬(S ∧ T(⌈¬S⌉); and ¬(¬S ∧ ¬T(⌈¬S⌉). These are classically equivalent to the two directions of the T-scheme, but they are intuitively weaker. The lesson I would like to draw is: There can be no consistent solution to the Liar paradox that does not involve abandoning truth-theoretic principles that should be every bit as dear to our hearts as the T-scheme. So we shall have to learn to live with the Liar, one way or another. (shrink)

Gestalt psychology of perception was one of the main inspirations behind the philosophical work of the Hungarian polymath Michael Polanyi. Seeing scientists and philosophers backing away from its implications, he proposed instead to take those implications seriously. I detail three ways in which he did so, the result of which was his theory of ‘tacit knowing’. This can be thought of as a gestalt epistemology, because it takes the figure/ground relation as the model for all knowing. Polanyi took (...) his gestalt epistemology to apply widely. I argue that it is more successful with some of the problems to which he applied it than with others, and thus that Polanyi was wrong to think that they all exhibit a common pattern. Polanyi’s epistemological work led him to a position alongside phenomenology. He compared his project to the work of Husserl and Merleau-Ponty in a positive way. But, while he sympathised with the phenomenological method, and strongly endorsed its anti-reductionist conclusions, he criticised phenomenologists for acquiescing in a positivistic or mechanistic view of the natural sciences, and he went on to develop a metaphysics or ontology which he considered to have gone beyond phenomenology. However, Polanyi did sometimes follow certain phenomenologists in an existentialist direction, to conclusions about meaningfulness and its ‘destruction’, and to his related account of the various degrees or levels of ‘indwelling’. I conclude by arguing that, in the places where he did this, Polanyi’s thought over-extends, and that this raises a problem for his entire theory of tacit knowing. (shrink)

John Barker, in two recent essays, raises a variety of intriguing criticisms to challenge my interpretation of the liar paradox and the type of solution I proposein ‘Denying the Liar’ and ‘Denying the Liar Reaffirmed.’ Barker continues to believe that I have misunderstood the logical structure of the liar sentence and itsexpression, and that as a result my solution misfires. I shall try to show that on the contrary my analysis is correct, and that Barker does (...) not properly grasp what mysolution to the liar paradox involves. Additionally, I argue that Barker makes fundamental errors in the explanation of liar sentence formulations in intensional contexts and in the classical metatheory he invokes to support his criticisms. (shrink)

The liar paradox is a famous and ancient paradox related to logic and philosophy. It shows it is perfectly possible to construct sentences that are correct grammatically and semantically but that cannot be true or false in the traditional sense. In this paper the authors show four approaches to interpreting paradoxes that illustrate the influence of: the levels of language, their belonging to indeterminate compatible propositions or indeterminate propositions, being based on universal antinomy and the theory of dialetheism.

A new solution to the liar paradox is developed using the insight that it is illegitimate to even suppose (let alone assert) that a liar sentence has a truth-status (true or not) on the grounds that supposing this sentence to be true/not-true essentially defeats the telos of supposition in a readily identifiable way. On that basis, the paradox is blocked by restricting the Rule of Assumptions in Gentzen-style presentations of the sequent-calculus. The lesson of the liar is (...) that not all assumptions are for free. One merit of this proposal is that it is free from the revenge problem. (shrink)

There is no need to prove the significance to philosophy of the famous liar paradox. Attempts to solve it have not ceased over the course of many centuries, from hoary antiquity to our own day. The failure of attempts undertaken within the bounds of everyday, natural languages has led many philosophers, particularly of the positivist trend, to pessimistic conclusions with respect to the potentials of such languages. This is very clearly evident, for example, in the statement of A. Tarski, (...) who writes: "The liar paradox made its first appearance in our discussions as a kind of evil force possessed of great destructive energy. It compels us to reject all attempts to explicate the notion of truth for natural languages and to confine ourselves to the formalized languages of scientific reasoning." Tarski's viewpoint has been repeatedly criticized. We should prefer not to cast doubt on the significance of that highly valuable criticism. However, we cannot fail to observe that Tarski's notion retains its force so long as its basic argument - the insolubility of the liar paradox within the confines of natural languages - remains standing. (shrink)

The liar paradox is still an open philosophical problem. Most contemporary answers to the paradox target the logical principles underlying the reasoning from the liar sentence to the paradoxical conclusion that the liar sentence is both true and false. In contrast to these answers, Buddhist epistemology offers resources to devise a distinctively epistemological approach to the liar paradox. In this paper, I mobilise these resources and argue that the liar sentence is what Buddhist epistemologists call (...) a contradiction with one’s own words. I situate my argument in the works of Dignāga and Dharmakīrti and show how Buddhist epistemology answers the paradox. (shrink)

Al-Taftāzānī introduces the Liar Paradox, in a commentary on al-Rāzī, in a short passage that is part of a polemic against the ethical rationalism of the Muʿtazila. In this essay, we consider his remarks and their place in the history of the Liar Paradox in Arabic Logic. In the passage, al-Taftāzānī introduces Liar Cycles into the tradition, gives the paradox a puzzling name—the fallacy of the “irrational root” —which became standard, and suggests a connection between the paradox (...) and what it tells us about truth and falsehood, and arguments for divine voluntarism and what they tell us about the nature of goodness and badness. On this last point, we also discuss a passage from al-Rāzī, which suggests similar connections. (shrink)

Network motifs are small patterns of connections, found over‐represented in gene regulatory networks. An example is the negative feedback loop (e.g. factor A represses itself). This opposes its own state so that when ‘on’ it tends towards ‘off’ – and vice versa. Here, we argue that such self‐opposition, if considered dimensionlessly, is analogous to the liar paradox: ‘This statement is false’. When ‘true’ it implies ‘false’ – and vice versa. Such logical constructs have provided philosophical consternation for over 2000 (...) years. Extending the analogy, other network topologies give strikingly varying outputs over different dimensions. For example, the motif ‘A activates B and A. B inhibits A’ can give switches or oscillators with time only, or can lead to Turing‐type patterns with both space and time (spots, stripes or waves). It is argued here that the dimensionless form reduces to a variant of ‘The following statement is true. The preceding statement is false’. Thus, merely having a static topological description of a gene network can lead to a liar paradox. Network diagrams are only snapshots of dynamic biological processes and apparent paradoxes can reveal important biological mechanisms that are far from paradoxical when considered explicitly in time and space. (shrink)

In this commentary, I discuss the effects of the liar paradox on Floridi’s definition on semantic information. In particular, I show that there is at least one sentence that creates a contradictory result for Floridi’s definition of semantic information that does not affect the standard definition.

The main goal of this article is to investigate the mythical symbolic form in Cassirer’s Philosophy of Symbolic Form regarding its connection with visual perception. The article argues that mythical symbolic form is rooted in Gestalt principles of perception for organizing the perceptual field, and shows that these principles shape the main features of space and time in Cassirer’s mythical symbolic form. This argument challenges Heidegger’s critique of Cassirer’s definition of a mythical symbolic form that it is directionless and (...) not grounded in man’s being. The combination of Gestalt principles and mythical symbolic forms supports the argument about the active role of visual perception, and clarifies Cassirer’s application and re-definition of Kantian and Neo-Kantian concepts. The investigation opens a perspective for comprehending the mythic-religious phenomenon as well as for comprehending visual perception. (shrink)

This volume includes a target paper, taking up the challenge to revive, within a modern (formal) framework, a medieval solution to the Liar Paradox which did ...

The story goes that Epimenides, a Cretan, used to claim that all Cretans are always liars. Whether he knew it or not, this claim is odd. It is easy to see it is odd by asking if it is true or false. If it is true, then all Cretans, including Epimenides, are always liars, in which case what he said must be false. Thus, if what he says is true, it is false. Conversely, suppose what Epimenides said is false. Then (...) some Cretan at some time speaks truly. This might not tell us anything about Epimenides. But if, to make the story simple, he were the only Cretan ever to speak, and this was the only thing he ever said, then indeed, he would have to speak truly. And we would then have shown that if what he said was false, it must be true. (shrink)

The first sentence in this essay is a lie. There is something odd about saying so, as has been known since ancient times. To see why, remember that all lies are untrue. Is the first sentence true? If it is, then it is a lie, and so it is not true. Conversely, suppose that it is not true. As we (viz., the authors) have said it, presumably with the intention of you believing it when it is not true, it is (...) a lie. But then it is true! (shrink)

The Gestalt psychologists adopted a set of positions on mind-body issues that seem like an odd mix. They sought to combine a version of naturalism and physiological reductionism with an insistence on the reality of the phenomenal and the attribution of meanings to objects as natural characteristics. After reviewing basic positions in contemporary philosophy of mind, we examine the Gestalt position, characterizing it m terms of phenomenal realism and programmatic reductionism. We then distinguish Gestalt philosophy of mind (...) from instrumentalism and computational functionalism, and examine Gestalt attributions of meaning and value to perceived objects. Finally, we consider a metatheoretical moral from Gestalt theory, which commends the search for commensurate description of mental phenomena and their physiological counterparts. (shrink)

In this paper we explain our pretense account of truth-talk and apply it in a diagnosis and treatment of the Liar Paradox. We begin by assuming that some form of deflationism is the correct approach to the topic of truth. We then briefly motivate the idea that all T-deflationists should endorse a fictionalist view of truth-talk, and, after distinguishing pretense-involving fictionalism (PIF) from error- theoretic fictionalism (ETF), explain the merits of the former over the latter. After presenting the basic (...) framework of our PIF account of truth-talk, we demonstrate a few advantages it offers over T-deflationist accounts that do not explicitly acknowledge pretense at work in the discourse. In turning to the Liar Paradox, we explain how the quasi-anaphoric functioning that our account attributes to truth-talk provides a diagnosis of the Liar Paradox (and other instances of semantic pathology) as having no content—in the sense of not specifying any of what we call M-conditions. At the same time, however, we vindicate the intuition that we can understand liar sentences, thereby avoiding one standard objection to “meaningless strategy” responses to the Liar Paradox. With this diagnosis in place, we then, by way of treatment, introduce a new predicate, ‘semantically defective’, and show how the explanation we give for its application allows for a consistent, yet revenge-immune, (dis)solution of the Liar Paradox, and semantic pathology generally. (shrink)