This article informally presents a solution to the paradoxes of truth and shows how the solution solves classical paradoxes (such as the original Liar) as well as the paradoxes that were invented as counterarguments for various proposed solutions (“the revenge of the Liar”). This solution complements the classical procedure of determining the truth values of sentences by its own failure and, when the procedure fails, through an appropriate semantic shift allows us to express the failure in a (...) classical two-valued language. Formally speaking, the solution is a language with one meaning of symbols and two valuations of the truth values of sentences. The primary valuation is a classical valuation that is partial in the presence of the truth predicate. It enables us to determine the classical truth value of a sentence or leads to the failure of that determination. The language with the primary valuation is precisely the largest intrinsic fixed point of the strong Kleene three-valued semantics (LIFPSK3). The semantic shift that allows us to express the failure of the primary valuation is precisely the classical closure of LIFPSK3: it extends LIFPSK3 to a classical language in parts where LIFPSK3 is undetermined. Thus, this article provides an argumentation, which has not been present in contemporary debates so far, for the choice of LIFPSK3 and its classical closure as the right model for the truth predicate. In the end, an erroneous critique of Kripke-Feferman axiomatic theory of truth, which is present in contemporary literature, is pointed out. (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)

One recently proposed solution to the Liar paradox is the contextual theory of truth. Tyler Burge (1979) argues that truth is an indexical notion and that the extension of the truth predicate shifts during Liar reasoning. A Liar sentence might be true in one context and false in another. To many, contextualism seems to capture our pre-theoretic intuitions about the semantic paradoxes; this is especially due to its reliance on the so-called Revenge phenomenon. I, however, show (...) that Super-Liar sentences (where a Super-Liar sentence is a sentence which says of itself that it is not true in any context) generate a significant problem for Burge’s contextual theory of truth. (shrink)

Most work on the semantic paradoxes within classical logic has centered around what this essay calls “linguistic” accounts of the paradoxes: they attribute to sentences or utterances of sentences some property that is supposed to explain their paradoxical or nonparadoxical status. “No proposition” views are paradigm examples of linguistic theories, although practically all accounts of the paradoxes subscribe to some kind of linguistic theory. This essay shows that linguistic accounts of the paradoxes endorsing classical logic are subject to a particularly (...) acute form of the revenge paradox: that there is no exhaustive classification of sentences into “good” and “bad” such that the T-schema holds when restricted to the “good” sentences unless it is also possible to prove some “bad” sentences. The foundations for an alternative classical nonlinguistic approach is outlined that is not subject to the same kinds of problems. Although revenge paradoxes of different strengths can be formulated, they are found to be indeterminate at higher orders and not inconsistent. (shrink)

Note: The paper attached here is a "pre-review" version, not the final version that has now been published online first at the link below. -/- In “Nothing is True,” Will Gamester defends a form of alethic nihilism that still grants truth-talk a kind of legitimacy: an expressive role that is implemented via a pretense. He argues that this view has all of the strengths of deflationism, while also providing an elegant resolution of the Liar Paradox and its kin. For (...) the alethic nihilist, Liar and related sentences are not true, and that is the end of the story. No contradiction arises because it does not thereby follow that any of these sentences are also true, since nothing is. Gamester concludes that the simplicity of this response to the semantic paradoxes makes alethic nihilism an attractive approach. We disagree. In addition to providing insurmountable obstacles for his form of alethic nihilism, we contend that a certain form of non-nihilist deflationism is better placed to deal with the paradoxes and to account for truth-talk more generally. (shrink)

Given any proposition, is it possible to have rationally acceptable attitudes towards it? Absent reasons to the contrary, one would probably think that this should be possible. In this paper I provide a reason to the contrary. There is a proposition such that, if one has any opinions about it at all, one will have a rationally unacceptable set of propositional attitudes—or if one doesn’t, one will end up being cognitively imperfect in some other manner. The proposition I am concerned (...) with is a self-referential propositional attitude ascription involving the propositional attitude of rejection. Given a basic assumption about what constitutes irrationality, and a few assumptions about the nature of cognitively ideal agents, a paradox results. This paradox is superficially like the Liar, but it is importantly different in that no alethic notions are involved at all. As such, it stands independent of the Liar and is not a ‘revenge’ version of it. After setting out the paradox I discuss possible responses. After considering several I argue that one is best off simply accepting that the paradox shows us something surprising and interesting about rationality: that some cognitive shortfall is unavoidable even for ideal agents. I argue that nothing disastrous follows from accepting this conclusion. (shrink)

Is there a notion of contradiction—let us call it, for dramatic effect, “absolute”—making all contradictions, so understood, unacceptable also for dialetheists? It is argued in this paper that there is, and that spelling it out brings some theoretical benefits. First it gives us a foothold on undisputed ground in the methodologically difficult debate on dialetheism. Second, we can use it to express, without begging questions, the disagreement between dialetheists and their rivals on the nature of truth. Third, dialetheism has an (...) operator allowing it, against the opinion of many critics, to rule things out and manifest disagreement: for unlike other proposed exclusion-expressing-devices (for instance, the entailment of triviality), the operator used to formulate the notion of absolute contradiction appears to be immune both from crippling expressive limitations and from revenge paradoxes—pending a rigorous nontriviality proof for a formal dialetheic theory including it. (shrink)

This paper decomposes the Liar Paradox into its semantic atoms using Meaning Postulates (1952) provided by Rudolf Carnap. Formalizing truth values of propositions as Boolean properties of these propositions is a key new insight. This new insight divides the translation of a declarative sentence into its equivalent mathematical proposition into three separate steps. When each of these steps are separately examined the logical error of the Liar Paradox is unequivocally shown.

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)

It seems that the most common strategy to solve the liar paradox is to argue that liar sentences are meaningless and, consequently, truth-valueless. The other main option that has grown in recent years is the dialetheist view that treats liar sentences as meaningful, truth-apt and true. In this paper I will offer a new approach that does not belong in either camp. I hope to show that liar sentences can be interpreted as meaningful, truth-apt and false, (...) but without engendering any contradiction. This seemingly impossible task can be accomplished once the semantic structure of the liar sentence is unpacked by a quantified analysis. The paper will be divided in two sections. In the first section, I present the independent reasons that motivate the quantificational strategy and how it works in the liar sentence. In the second section, I explain how this quantificational analysis allows us to explain the truth teller sentence and a counter-example advanced against truthmaker maximalism, and deal with some potential objections. (shrink)

In this paper I revisit an important response to the Moral Twin Earth (MTE) challenge: The Common Functional Role strategy (CFR). I argue that CFR is open to a revenge problem. MTE-cases allegedly show that two linguistic communities can be in genuine disagreement even when they are regulated by distinct families of properties. CFR provides a way to reconcile the intuition that the two communities are in genuine disagreement with the claim that the use of moral terms by both (...) communities is causally regulated by different families of properties. This is done by identifying a functional role that those families of properties both fulfill. Still, even if CFR is successful, its proponents need to face a serious revenge problem. Roughly, it could be that the families of properties that regulate each community are equally perfect realizers of the relevant higher-order functional state. I suggest that the proponent of CFR faces a dilemma: either CFR has controversial implications about first-order moral theory, or CFR needs to be coupled with substantive and parochial empirical/metaphysical assumptions to avoid those implications. (shrink)

This paper offers an analysis of a hitherto neglected text on insoluble propositions dating from the late XiVth century and puts it into perspective within the context of the contemporary debate concerning semantic paradoxes. The author of the text is the italian logician Peter of Mantua (d. 1399/1400). The treatise is relevant both from a theoretical and from a historical standpoint. By appealing to a distinction between two senses in which propositions are said to be true, it offers an unusual (...) solution to the paradox, but in a traditional spirit that contrasts a number of trends prevailing in the XiVth century. It also counts as a remarkable piece of evidence for the reconstruction of the reception of English logic in italy, as it is inspired by the views of John Wyclif. Three approaches addressing the Liar paradox (Albert of Saxony, William Heytesbury and a version of strong restrictionism) are first criticised by Peter of Mantua, before he presents his own alternative solution. The latter seems to have a prima facie intuitive justification, but is in fact acceptable only on a very restricted understanding, since its generalisation is subject to the so-called revenge problem. (shrink)

I propose an approach to liar and Curry paradoxes inspired by the work of Roger Swyneshed in his treatise on insolubles (1330-1335). The keystone of the account is the idea that liar sentences and their ilk are false (and only false) and that the so-called ''capture'' direction of the T-schema should be restricted. The proposed account retains what I take to be the attractive features of Swyneshed's approach without leading to some worrying consequences Swyneshed accepts. The approach and (...) the resulting logic (called ''Swynish Logic'') are non-classical, but are consistent and compatible with many elements of the classical picture including modus ponens, modus tollens, and double-negation elimination and introduction. It is also compatible with bivalence and contravalence. My approach to these paradoxes is also immune to an important kind of revenge challenge that plagues some of its rivals. (shrink)

According to the perceptual view of language comprehension, listeners typically recover high-level linguistic properties such as utterance meaning without inferential work. The perceptual view is subject to the Objection from Context: since utterance meaning is massively context-sensitive, and context-sensitivity requires cognitive inference, the perceptual view is false. In recent work, Berit Brogaard provides a challenging reply to this objection. She argues that in language comprehension context-sensitivity is typically exercised not through inferences, but rather through top-down perceptual modulations or perceptual learning. (...) This paper provides a complete formulation of the Objection from Context and evaluates Brogaards reply to it. Drawing on conceptual considerations and empirical examples, we argue that the exercise of context-sensitivity in language comprehension does, in fact, typically involve inference. (shrink)

Logical pluralism is the view that there is more than one correct logic. Most logical pluralists think that logic is normative in the sense that you make a mistake if you accept the premisses of a valid argument but reject its conclusion. Some authors have argued that this combination is self-undermining: Suppose that L1 and L2 are correct logics that coincide except for the argument from Γ to φ, which is valid in L1 but invalid in L2. If you accept (...) all sentences in Γ, then, by normativity, you make a mistake if you reject φ. In order to avoid mistakes, you should accept φ or suspend judgment about φ. Both options are problematic for pluralism. Can pluralists avoid this worry by rejecting the normativity of logic? I argue that they cannot. All else being equal, the argument goes through even if logic is not normative. (shrink)

I use the principle of truth-maker maximalism to provide a new solution to the semantic paradoxes. According to the solution, AUS, its undecidable whether paradoxical sentences are grounded or ungrounded. From this it follows that their alethic status is undecidable. We cannot assert, in principle, whether paradoxical sentences are true, false, either true or false, neither true nor false, both true and false, and so on. AUS involves no ad hoc modification of logic, denial of the T-schema's validity, or obvious (...) revenge. (shrink)

This article examines the various Liar paradoxes and their near kin, Grelling’s paradox and Gödel’s Incompleteness Theorem with its self-referential Gödel sentence. It finds the family of paradoxes to be generated by circular definition–whether of statements, predicates, or sentences–a manoeuvre that generates the fatal disorders of the Liar syndrome: semantic vacuity, semantic incoherence, and predicative catalepsy. Afflicted statements, such as the self-referential Liar statement, fail to be genuine statements. Hence they say nothing, a point that invalidates the (...) reasoning on which the various paradoxes rest. The seeming plausibility of the paradoxes is due to the fact that the same sentence may be used to make both the pseudo-statement and a genuine statement about the pseudo-statement. Hence, if a formal system is to avoid ambiguity and consequent seeming paradox, it requires some sort of disambiguator to distinguish the two statements. Gödel’s Theorem presents a further complication in that the self-reference involved is sentential rather than statemental. Nevertheless, on the intended interpretation of the system as a formalization of arithmetic, the self-referential Gödel sentence can only be an ambiguous statement, one that is both a pseudo-statement and its genuine double. Consequently, the conclusions commonly drawn from Gödel’s theorem must be deemed unwarranted. Arithmetic might well be formalized in a proper system that either excludes circular definition or introduces disambiguators. (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)

A number of `no-proposition' approaches to the liar paradox find themselves implicitly committed to a moderate disquotational principle: the principle that if an utterance of the sentence `$P$' says anything at all, it says that $P$ (with suitable restrictions). I show that this principle alone is responsible for the revenge paradoxes that plague this view. I instead propose a view in which there are several closely related language-world relations playing the `semantic expressing' role, none of which is more (...) central to semantic theorizing than any other. I use this thesis about language and the negative result about disquotation to motivate the view that people do say things with utterances of paradoxical sentences, although they do not say the proposition you'd always expect, as articulated with a disquotational principle. (shrink)

In this paper, we do two things. First, we provide some support for adopting a version of the meaningless strategy with respect to the liar paradox, and, second, we extend that strategy, by providing, albeit tentatively, a solution to that paradox—one that is semantic, rather than logical.

A number of authors have objected to the application of non-classical logic to problems in philosophy on the basis that these non-classical logics are usually characterised by a classical metatheory. In many cases the problem amounts to more than just a discrepancy; the very phenomena responsible for non-classicality occur in the field of semantics as much as they do elsewhere. The phenomena of higher order vagueness and the revenge liar are just two such examples. The aim of this (...) paper is to show that a large class of non-classical logics are strong enough to formulate their own model theory in a corresponding non-classical set theory. Specifically I show that adequate definitions of validity can be given for the propositional calculus in such a way that the metatheory proves, in the specified logic, that every theorem of the propositional fragment of that logic is validated. It is shown that in some cases it may fail to be a classical matter whether a given sentence is valid or not. One surprising conclusion for non-classical accounts of vagueness is drawn: there can be no axiomatic, and therefore precise, system which is determinately sound and complete. (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)

Pluralists maintain that there is more than one truth property in virtue of which bearers are true. Unfortunately, it is not yet clear how they diagnose the liar paradox or what resources they have available to treat it. This chapter considers one recent attempt by Cotnoir (2013b) to treat the Liar. It argues that pluralists should reject the version of pluralism that Cotnoir assumes, discourse pluralism, in favor of a more naturalized approach to truth predication in real languages, (...) which should be a desideratum on any successful pluralist conception. Appealing to determination pluralism instead, which focuses on truth properties, it then proposes an alternative treatment to the Liar that shows liar sentences to be undecidable. (shrink)

We describe the earliest occurrences of the Liar Paradox in the Arabic tradition. e early Mutakallimūn claim the Liar Sentence is both true and false; they also associate the Liar with problems concerning plural subjects, which is somewhat puzzling. Abharī (1200-1265) ascribes an unsatisfiable truth condition to the Liar Sentence—as he puts it, its being true is the conjunction of its being true and false—and so concludes that the sentence is not true. Tūsī (1201-1274) argues that (...) self-referential sentences, like the Liar, are not truth-apt, and defends this claim by appealing to a correspondence theory of truth. Translations of the texts are provided as an appendix. (shrink)

This paper confronts the familiar prejudice in Western Marxism that Engels’ thought, as articulated in Anti-Duhring and the Dialectics of Nature, is of marginal interest and should be excised from Marxist theory. I argue that this view is mistaken. If we do not take seriously his insights about science, philosophy, nature, and history, his insights will take a fourfold revenge upon us. Natural science takes its revenge by unleashing technology that subjugates us in ways we cannot anticipate, understand (...) or control. Philosophy, in turn, takes revenge on science for neglecting the philosophical presuppositions of its own worldview. Nature itself takes its revenge upon those who consider it to be some formless and passive matter, deprived of history and negativity, responding to our productive activity in surprising ways that, without a rational form of regulation, could lead to our own extinction. Lastly, history takes revenge on those ‘well intentioned’ actors who try to impose their will upon it without a scientific knowledge of its internal, necessary, and objective forces. (shrink)

I have read many recent discussions of the limits of computation and the universe as computer, hoping to find some comments on the amazing work of polymath physicist and decision theorist David Wolpert but have not found a single citation and so I present this very brief summary. Wolpert proved some stunning impossibility or incompleteness theorems (1992 to 2008-see arxiv dot org) on the limits to inference (computation) that are so general they are independent of the device doing the computation, (...) and even independent of the laws of physics, so they apply across computers, physics, and human behavior. They make use of Cantor's diagonalization, the liar paradox and worldlines to provide what may be the ultimate theorem in Turing Machine Theory, and seemingly provide insights into impossibility, incompleteness, the limits of computation, and the universe as computer, in all possible universes and all beings or mechanisms, generating, among other things, a non- quantum mechanical uncertainty principle and a proof of monotheism. There are obvious connections to the classic work of Chaitin, Solomonoff, Komolgarov and Wittgenstein and to the notion that no program (and thus no device) can generate a sequence (or device) with greater complexity than it possesses. One might say this body of work implies atheism since there cannot be any entity more complex than the physical universe and from the Wittgensteinian viewpoint, ‘more complex’ is meaningless (has no conditions of satisfaction, i.e., truth-maker or test). Even a ‘God’ (i.e., a ‘device’with limitless time/space and energy) cannot determine whether a given ‘number’ is ‘random’, nor find a certain way to show that a given ‘formula’, ‘theorem’ or ‘sentence’ or ‘device’ (all these being complex language games) is part of a particular ‘system’. -/- Those wishing a comprehensive up to date framework for human behavior from the modern two systems view may consult my book ‘The Logical Structure of Philosophy, Psychology, Mind and Language in Ludwig Wittgenstein and John Searle’ 2nd ed (2019). Those interested in more of my writings may see ‘Talking Monkeys--Philosophy, Psychology, Science, Religion and Politics on a Doomed Planet--Articles and Reviews 2006-2019 2nd ed (2019) and Suicidal Utopian Delusions in the 21st Century 4th ed (2019) . (shrink)

One well known approach to the soritical paradoxes is epistemicism, the view that propositions involving vague notions have definite truth values, though it is impossible in principle to know what they are. Recently, Paul Horwich has extended this approach to the liar paradox, arguing that the liar proposition has a truth value, though it is impossible to know which one it is. The main virtue of the epistemicist approach is that it need not reject classical logic, and in (...) particular the unrestricted acceptance of the principle of bivalence and law of excluded middle. Regardless of its success in solving the soritical paradoxes, the epistemicist approach faces a number of independent objections when it is applied to the liar paradox. I argue that the approach does not offer a satisfying, stable response to the paradoxes—not in general, and not for a minimalist about truth like Horwich. (shrink)

I develop a genealogy of the concept of ‘energy’ in western philosophy and science, focusing on how energy concepts (e.g., energeia, vis viva, kinetic/potential energy) have been theorized in relation to time. Looking especially to the ideas of Gilles Deleuze, Henri Bergson, Friedrich Nietzsche, and Martin Heidegger, I argue that the thread that connects energy concepts through time is the epistemological tendency to derive conceptual accounts of change from a prior ontological sameness or essence. I then attempt to lay the (...) groundwork for a process metaphysics that harmonizes with contemporary findings in the physical sciences, while also extending the concept of energy to account for the presence of subjectivity in nature. (shrink)

Consider the reaction of Trayvon Martin’s family to the jury verdict. They were devastated that George Zimmerman, the defendant, was found not guilty of manslaughter or murder. Whatever the merits of this outcome, what does the Martin family’s emotional reaction mean? What does it say about criminal punishment – especially the reasons why we punish? Why did the Martin family want to see George Zimmerman go to jail? And why were – and are – they so upset that he didn’t? (...) -/- This Article will argue for three points. First, what fuels this kind of outrage is vengeance: the desire to see defendants like George Zimmerman be forced to “pay” for the harms that they needlessly and culpably inflict on others. While this point may seem obvious, it isn’t. Most people repudiate revenge and therefore the notion that it plays any role in the criminal justice system. -/- Second, this attitude toward revenge is misguided and needs to change. We need to recognize that vengeance not only does but should play a significant role in motivating criminal punishment. Our vengeful reactions to harmful crimes are not ugly or shameful; on the contrary, they manifest a deep valuation of victims and a bitter denunciation of individuals who actively renounce this valuation through their criminal behavior. -/- Third, these two points have significant implications for the two main theories of criminal punishment: “retributivism,” which says that criminals should be punished in order to give them their “just deserts,” and “consequentialism,” which says that criminals should be punished in order to bring about such good consequences as deterrence, incapacitation, and rehabilitation. Traditionally, these two theories have been at war with one another. But I will show how recognizing revenge as a motivation and justification for punishment can help to end this war and bring these two theories together. (shrink)

Confronting the Liar Paradox is commonly viewed as a prerequisite for developing a theory of truth. In this paper I turn the tables on this traditional conception of the relation between the two. The theorist of truth need not constrain his search for a “material” theory of truth, i.e., a theory of the philosophical nature of truth, by committing himself to one solution or another to the Liar Paradox. If he focuses on the nature of truth (leaving issues (...) of formal consistency for a later stage), he can arrive at material principles that prevent the Liar Paradox from arising in the first place. I argue for this point both on general methodological grounds and by example. The example is based on a substantivist theory of truth that emphasizes the role of truth in human cognition. The key point is that truth requires a certain complementarity of “immanence” and “transcendence”, and this means that some hierarchical structure is inherent in truth. Approaching the Liar Paradox from this perspective throws new light on its existent solutions: their differences and commonalities, their purported ad-hocness, and the relevance of natural language and bivalence to truth and the Liar. (shrink)

'Ghosting' or the unethical practice of having someone other than the student registered in the course take the student's exams, complete their assignments and write their essays has become a common method of cheating in today's online higher education learning environment. Internet-based teaching technology and deceit go hand-in-hand because the technology establishes a set of perverse incentives for students to cheat and institutions to either tolerate or encourage this highly unethical form of behavior. For students, cheating becomes an increasingly attractive (...) option as pre-digital safeguards-for instance, in-person exam proctoring requirements and face-to-face mentoring-are quietly phased out and eventually eliminated altogether. Also, as the punishments for violating academic integrity policies are relaxed, the temptation to cheat increases accordingly. For institutions, tolerating, normalizing and encouraging one type of student cheating, ghosting, improves the profitability of their online divisions by bolstering student enrolments and retention. In universities and colleges across the globe, online divisions and programs have become thriving profit centers, not because of the commonly attributed reasons (student ease, safety during health crises and convenience of taking courses online), but due to a single strategic insight: Ubiquitous opportunities for ghosting improve profit margins and maximize revenue. (shrink)

Stephen Barker presents a novel approach to solving semantic paradoxes, including the Liar and its variants and Curry’s paradox. His approach is based around the concept of alethic undecidability. His approach, if successful, renders futile all attempts to assign semantic properties to the paradoxical sentences, whilst leaving classical logic fully intact. And, according to Barker, even the T-scheme remains valid, for validity is not undermined by undecidable instances. Barker’s approach is innovative and worthy of further consideration, particularly by those (...) of us who aim to find a solution without logical revisionism. As it stands, however, the approach is unsuccessful, as I shall demonstrate below. (shrink)

I have read many recent discussions of the limits of computation and the universe as computer, hoping to find some comments on the amazing work of polymath physicist and decision theorist David Wolpert but have not found a single citation and so I present this very brief summary. Wolpert proved some stunning impossibility or incompleteness theorems (1992 to 2008-see arxiv.org) on the limits to inference (computation) that are so general they are independent of the device doing the computation, and even (...) independent of the laws of physics, so they apply across computers, physics, and human behavior. They make use of Cantor's diagonalization, the liar paradox and worldlines to provide what may be the ultimate theorem in Turing Machine Theory, and seemingly provide insights into impossibility,incompleteness, the limits of computation,and the universe as computer, in all possible universes and all beings or mechanisms, generating, among other things,a non-quantum mechanical uncertainty principle and a proof of monotheism. (shrink)

This paper describes the ways in which trolls and bots impede the acquisition of knowledge online. I distinguish between three ways in which trolls and bots can impede knowledge acquisition, namely, by deceiving, by encouraging misplaced skepticism, and by interfering with the acquisition of warrant concerning persons and content encountered online. I argue that these threats are difficult to resist simultaneously. I argue, further, that the threat that trolls and bots pose to knowledge acquisition goes beyond the mere threat of (...) online misinformation, or the more familiar threat posed by liars offline. Trolls and bots are, in effect, fake persons. Consequently, trolls and bots can systemically interfere with knowledge acquisition by manipulating the signals whereby individuals acquire knowledge from one another online. I conclude with a brief discussion of some possible remedies for the problem of fake persons. (shrink)

Section 1 reviews Strawson’s logic of presuppositions. Strawson’s justification is critiqued and a new justification proposed. Section 2 extends the logic of presuppositions to cases when the subject class is necessarily empty, such as (x)((Px & ~Px) → Qx) . The strong similarity of the resulting logic with Richard Diaz’s truth-relevant logic is pointed out. Section 3 further extends the logic of presuppositions to sentences with many variables, and a certain valuation is proposed. It is noted that, given this valuation, (...) Gödel’s sentence becomes neither true nor false. The similarity of this outcome with Goldstein and Gaifman’s solution of the Liar paradox, which is discussed in section 4, is emphasized. Section 5 returns to the definition of meaningfulness; the meaninglessness of certain sentences with empty subjects and of the Liar sentence is discussed. The objective of this paper is to show how all of the above-mentioned concepts are interrelated. (shrink)

Some infamous memoirs have turned out to be chock-full of fibs. Should we care? Why not say—as many have—that all autobiography is fiction, that accurate memory is impossible, that we start lying as soon as we start narrating, and that it doesn’t matter anyway, since made-up stories are just as good as true ones? Because, well, every part of that is misleading. First, we don’t misremember absolutely everything; second, we have other sources to draw on; third, story form affects only (...) significance, not facts; fourth, fiction and nonfiction offer different affordances, benefits, and delights. And since we need both kinds of writing, we have to insist on honesty in memoir; we have to stop saying that everything is invention and that fibs don’t matter. If memoirs could never be trusted, who would still read them? In a world without truth, what exactly would we speak to power? (shrink)

The truth-functional hypothesis states that indicative conditional sentences and the material implication have the same truth conditions. Haze (2011) has rejected this hypothesis. He claims that a self-referential conditional, coupled with a plausible assumption about its truth-values and the assumption that the truth-functional hypothesis is true, lead to a liar’s paradox. Given that neither the self-referential conditional nor the assumption about its truth-values are problematic, the culprit of the paradox must be the truth-functional hypothesis. Therefore, we should reject it. (...) In this paper I argue that, contrary to what Haze thinks, the truth-functional hypothesis is not to blame. In fact, no liar’s paradox emerges when the truth-functional hypothesis is true; it emerges only if it is false. (shrink)

我最近读过许多关于计算极限和宇宙作为计算机的讨论,希望找到一些关于多面体物理学家和决策理论家大卫·沃尔珀特的惊人工作的评论,但没有发现一个引文,所以我提出这个非常简短的总结。Wolpert 证明了一些惊人的不可能或不完整的定理(1992-2008-见arxiv dot org)对推理(计算)的限制,这些极限非常一般,它们独立于执行计算的设备,甚至独立于物理定律,因此,它们适用于计算机、物理和人类行为。他们利用Cantor的对角线、骗子悖论和世界线来提供图灵机器理论的 终极定理,并似乎提供了对不可能、不完整、计算极限和宇宙的见解。计算机,在所有可能的宇宙和所有生物或机制,产生,除其他外,非量子力学不确定性原理和一神论的证明。与柴廷、所罗门诺夫、科莫尔加罗夫和维特根斯 坦的经典作品以及任何程序(因此没有设备)能够生成比它拥有的更大复杂性的序列(或设备)的概念有着明显的联系。有人可能会说,这一工作意味着无政府主义,因为没有比物质宇宙更复杂的实体,从维特根斯坦的观点来看 ,"更复杂的"是毫无意义的(没有满足的条件,即真理制造者或测试)。即使是"上帝"(即具有无限时间/空间和能量的"设备")也无法确定给定的&q uot;数字"是否为"随机",也无法找到某种方式来显示给定的"公式"、"定理"或"句子"或"设备&q uot;(所有这些语言都是复杂的语言)游戏)是特定"系统"的一部分。 那些希望从现代两个系统的观点来看为人类行为建立一个全面的最新框架的人,可以查阅我的书《路德维希的哲学、心理学、Mind 和语言的逻辑结构》维特根斯坦和约翰·西尔的《第二部》(2019年)。那些对我更多的作品感兴趣的人可能会看到《会说话的猴子——一个末日星球上的哲学、心理学、科学、宗教和政治——文章和评论2006-201 9年第二次(2019年)》和《自杀乌托邦幻想》第21篇世纪4日 (2019).

ABSTRACTCurrent evolutionary models of revenge focus on its complex deterrent functions. Nevertheless, there are some retaliatory behaviors in nonhuman animals that do not appear to have a deterren...

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)

Lewis Carroll, both logician and writer, suggested a logical paradox containing furthermore two connotations (connotations or metaphors are inherent in literature rather than in mathematics or logics). The paradox itself refers to implication demonstrating that an intermediate implication can be always inserted in an implication therefore postponing its ultimate conclusion for the next step and those insertions can be iteratively and indefinitely added ad lib, as if ad infinitum. Both connotations clear up links due to the shared formal structure with (...) other well-known mathematical observations: (1) the paradox of Achilles and the Turtle; (2) the transitivity of the relation of equality. Analogically to (1), one can juxtapose the paradox of the Liar (for Lewis Carroll’s paradox) and that of the arrow (for “Achilles and the Turtle”), i.e. a logical paradox, on the one hand, and an aporia of motion, on the other hand, suggesting a shared formal structure of both, which can be called “ontological”, on which basis “motion” studied by physics and “conclusion” studied by logic can be unified being able to bridge logic and physics philosophically in a Hegelian manner: even more, the bridge can be continued to mathematics in virtue of (2), which forces the equality (for its property of transitivity) of any two quantities to be postponed analogically ad lib and ad infinitum. The paper shows that Hilbert arithmetic underlies naturally Lewis Carroll’s paradox admitting at least three interpretations linked to each other by it: mathematical, physical and logical. Thus, it can be considered as both generalization and solution of his paradox therefore naturally unifying the completeness of quantum mechanics (i.e. the absence of hidden variables) and eventual completeness of mathematics as the same and isomorphic to the completeness of propositional logic in relation to set theory as a first-order logic (in the sense of Gödel (1930)’s completeness theorems). (shrink)

The paper shows how ideas that explain the sense of an expression as a method or algorithm for finding its reference, preshadowed in Frege’s dictum that sense is the way in which a referent is given, can be formalized on the basis of the ideas in Thomason (1980). To this end, the function that sends propositions to truth values or sets of possible worlds in Thomason (1980) must be replaced by a relation and the meaning postulates governing the behaviour of (...) this relation must be given in the form of a logic program. The resulting system does not only throw light on the properties of sense and their relation to computation, but also shows circular behaviour if some ingredients of the Liar Paradox are added. The connection is natural, as algorithms can be inherently circular and the Liar is explained as expressing one of those. Many ideas in the present paper are closely related to those in Moschovakis (1994), but receive a considerably lighter formalization. (shrink)

The article critically examines the heuristic capacity and methods of using separate tools of Wittgenstein’s philosophical grammar to treat various semantic pathologies (paradoxes of Liar, Truth-Teller, etc.). According to Wittgenstein, philosophical confusion associated with the analysis of such semantic pathologies arises on the grounds of our intuitive faith that we are able to express in language any property that interests us. For instance, we believe that the property “to have a length of exactly one metre” can be meaningfully attributed (...) to any extended object. However, such a faith is fundamentally wrong, since an object like a standard metre, which plays an exclusive role as the criterion of length in our measuring practices based on the metric system, is an example of an extended object about which one can say neither that it is one metre long, nor that it is not one metre long. A correct understanding of the language-game concept shows that the criterion by which we form a set of objects that meet the standards established by the criterion cannot be described in the same way as objects of this set. Language-games using predicates of truth and falsehood are similar to our practice of measuring length using the metric system. In cases of Liar and Truth-Teller sentences, we encounter resembling examples of philosophical confusion. Beyond the context of their usage, “This sentence is false” and “This sentence is true” sentences seem to us paradoxes. But, according to Wittgenstein’s philosophical grammar, a correct method of treating such “paradoxical” sentences demands to find the lack- ing context for their usage, i.e. pay attention to the language-game in which they are emplloyed. Like in the case of the standard metre, we can claim that the sentence “This sentence is false” (“This sentence is true”) is neither false (true), nor not false (true). In an analogous way, Liar and Truth-Teller sentences should be interpreted as peculiar standards of falsehood and truth that we use in our language-games to judge about the truth value of other sentences. (shrink)

To become a public figure or celebrity, I claim, is to exist alongside a zombie version of yourself. This zombie shares the same name and physical likeness but operates independently of its flesh-and-blood counterpart. In fact, public figures do not have any special authority over the zombie version of themselves, and in some contexts, they enjoy less authority over their zombie counterparts than others do. In the US, for example, public figures are not legally entitled to protections against criticism via (...) parody, which can include unauthorized use of their likeness for offensive images, insulting jokes, and other forms of public mockery. As Michel Foucault observed, a work is entitled to become the “murderer” of its author, which suggests that the author’s name exists among the living dead. An artist’s works can bear their name yet operate independently of their attitudes or mental states. In June of 2019, the master rights to Taylor Swift’s first six albums were sold without her knowledge or consent, effectively “murdering” her rights as their author. Swift’s 2019 decision to re-record her first six studio albums can thus be understood as an act of institutional revenge, a way to get back at the people who have wielded power over her and the institutions that enable exploitation—a battle with her zombified works: the “stolen” original albums. In this chapter I sketch an institutional theory of celebrity names to explain the institutional, personal, and political significance of self-appropriation, using Taylor Swift’s act of re-recording her own music as a paradigm case. (shrink)

Since Saul Kripke’s influential work in the 1970s, the revisionary approach to semantic paradox—the idea that semantic paradoxes must be solved by weakening classical logic—has been increasingly popular. In this paper, we present a new revenge argument to the effect that the main revisionary approaches breed new paradoxes that they are unable to block.

This paper explores the liar paradox and its implications for logic and philosophical reasoning. It analyzes the paradox using classical logic principles and paraphrases it as "affirmation of the falsity of the very affirmation." The study draws connections between the liar paradox and Hegel's speculative sentence and suggests it functions as a "quasi-speculative sentence." Additionally, it examines parallels with the logocentric predicament and the determinist's assertion, highlighting their paradoxical nature. Through these analyses, the paper aims to illuminate the (...) fundamental paradoxes in our reasoning and logic. (shrink)

In their (2008) article Liar-Like Paradox and Object Language Features C.S. Jenkins and Daniel Nolan (henceforth, JN) argue that it is possible to construct Liar-like paradox in a metalanguage even though its object language is not semantically closed. I do not take issue with this claim. I find fault though with the following points contained in JN’s article: First, that it is possible to construct Liar-like paradox in a metalanguage, even though this metalanguage is not semantically closed. (...) Second, that the presented examples of Liar-like paradox are supposed to be counterexamples to Tarski’s diagnosis of the classic Liar paradox. Third, that JN fail to notice Tarski’s postulate. And finally, that JN fail to recognize that the world they are pondering is not among the possible worlds. (shrink)

By pooling together exhaustive analyses of certain philosophical paradoxes, we can prove a series of fascinating results regarding philosophical progress, agreement on substantive philosophical claims, knockdown arguments in philosophy, the wisdom of philosophical belief, the epistemic status of metaphysics, and the power of philosophy to refute common sense. As examples, this Element examines the Sorites Paradox, the Liar Paradox, and the Problem of the Many – although many other paradoxes can do the trick too.

Sam Berstler has recently argued for a fairness-based moral difference between lying and misleading. According to Berstler, the liar, but not the misleader, unfairly free rides on the Lewisian conventions which ground public-language meaning. Although compelling, the pragmatic and metasemantic backdrop within which this moral reason is located allows for the generation of a vicious explanatory circle. Simply, this backdrop entails that no speaker has ever performed an assertion. As I argue, escaping the circle requires rejecting Berstler’s fairness-based reason (...) against lying. The problem is a general one: the wrong of lying cannot be founded on the goods of language. (shrink)