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)
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)
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)
This paper considers the phenomenon of lying and the implications it has for those subjects who are capable of lying. It is argued that lying is not just intentional untruthfulness, but is intentional untruthfulness plus an insincere invocation of trust. Understood in this way, lying demands of liars a sophistication in relation to themselves, to language, and to those to whom they lie which exceeds the demands on mere truth-tellers.
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)
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 pseudo-statements afflicted with the Liar syndrome: semantic vacuity, semantic incoherence, and predicative catalepsy. Such statements, e.g., the self-referential Liar statement, are meaningless, and hence fail to say anything, a point that invalidates the reasoning on which (...) the various paradoxes rest. The seeming plausibility of the paradoxes is due to the fact that often the sentence used to make the pseudo-statement is ambiguous in that it may also be used to make a genuine statement about the pseudo-statement. Hence, if a formal system is to avoid ambiguity and consequent paradox and contradiction, it must distinguish between the two statements the sentence may be used to make. 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)
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)
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.
This chapter investigates the conflict between thought and speech that is inherent in lying. This is the conflict of saying what you think is false. The chapter shows how stubbornly saying what you think is false resists analysis. In traditional analyses of lying, saying what you think is false is analyzed in terms of saying something and believing that it is false. But standard cases of unconscious or divided belief challenge these analyses. Classic puzzles about belief from Gottlob Frege and (...) Saul Kripke show that suggested amendments involving assent instead of belief do not fare better. I argue that attempts to save these analyses by appeal to guises or Fregean modes of presentation will also run into trouble. I then consider alternative approaches to untruthfulness that focus on (a) expectations for one’s act of saying/asserting and (b) the intentions involved in one’s act of saying/asserting. Here I introduce two new kinds of case, which I call “truth serum” and “liar serum” cases. Consideration of these cases reveals structural problems with intention- and expectation-based approaches as well. Taken together, the string of cases presented suggests that saying what you think is false, or being untruthful, is no less difficult and interesting a subject for analysis than lying itself. Tackling the question of what it is to say what you think is false illuminates ways in which the study of lying is intertwined with fundamental issues in the nature of intentional action. (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)
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 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)
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 counter-arguments for various proposed solutions (``the revenge of the Liar''). Any solution to the paradoxes of truth necessarily establishes a certain logical concept of truth. 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 a content-wise 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 logical concept of truth. In the end, an erroneous critique of Kripke-Feferman axiomatic theory of truth, which is present in contemporary literature, is pointed out. (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)
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)
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)
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)
This is the original English version of a paper that has been published only in Chinese translation. (For the published, Chinese version, see "透視悖論說謊者的幽默指南", in page 37-44 on 拒絕再Hea──真理與意義的追尋) The paper was originally written as a lecture given at the University of Macau in April 2010. The paper argues that humor is essentially a form of paradoxical deception.
We discuss misinformation about “the liar antinomy” with special reference to Tarski’s 1933 truth-definition paper [1]. Lies are speech-acts, not merely sentences or propositions. Roughly, lies are statements of propositions not believed by their speakers. Speakers who state their false beliefs are often not lying. And speakers who state true propositions that they don’t believe are often lying—regardless of whether the non-belief is disbelief. Persons who state propositions on which they have no opinion are lying as much as those (...) who state propositions they believe to be false. Not all lies are statements of false propositions—some lies are true; some have no truth-value. People who only occasionally lie are not liars: roughly, liars repeatedly and habitually lie. Some half-truths are statements intended to mislead even though the speakers “interpret” the sentences used as expressing true propositions. Others are statements of propositions believed by the speakers to be questionable but without revealing their supposed problematic nature. The two “formulations” of “the antinomy of the liar” in [1], pp.157–8 and 161–2, have nothing to do with lying or liars. The first focuses on an “expression” Tarski calls ‘c’, namely the following. -/- c is not a true sentence -/- The second focuses on another “expression”, also called ‘c’, namely the following. -/- for all p, if c is identical with the sentence ‘p’, then not p -/- Without argumentation or even discussion, Tarski implies that these strange “expressions” are English sentences. [1] Alfred Tarski, The concept of truth in formalized languages, pp. 152–278, Logic, Semantics, Metamathematics, papers from 1923 to 1938, ed. John Corcoran, Hackett, Indianapolis 1983. -/- https://www.academia.edu/12525833/Sentence_Proposition_Judgment_Statement_and_Fact_Speaking_about_th e_Written_English_Used_in_Logic. (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)
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.
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)
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)
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)
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)
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)
Saya telah membaca banyak diskusi baru-baru ini batas komputasi dan alam semesta sebagai komputer, berharap untuk menemukan beberapa komentar pada karya menakjubkan fisikawan polimatematika dan teori keputusan David Wolpert tetapi belum menemukan satu rujukan dan jadi aku menyajikan ringkasan ini sangat singkat. Wolpert terbukti beberapa impotensi yang menakjubkan atau teorema ketidaklengkapan (1992 untuk 2008-Lihat arxiv dot org) pada batas untuk kesimpulan (perhitungan) yang begitu umum mereka independen dari perangkat melakukan komputasi, dan bahkan independen dari hukum fisika, sehingga mereka berlaku di (...) seluruh komputer, fisika, dan perilaku manusia. Mereka memanfaatkan diagonalisasi Cantor, paradoks liar dan worldlines untuk memberikan apa yang mungkin menjadi teorema utama dalam teori mesin Turing, dan tampaknya memberikan wawasan ketidakmungkinan, ketidaklengkapan, batas komputasi, dan alam semesta sebagai komputer, di semua semesta yang mungkin dan semua makhluk atau mekanisme, menghasilkan, antara lain, non-kuantum prinsip ketidakpastian mekanik dan bukti monoteisme. Ada hubungan yang jelas dengan karya klasik Chaitin, Solomonoff, Komolgarov dan Wittgenstein dan dengan anggapan bahwa tidak ada program (dan dengan demikian tidak ada perangkat) dapat menghasilkan urutan (atau perangkat) dengan kompleksitas yang lebih besar daripada memiliki. Orang mungkin mengatakan bahwa tubuh kerja menyiratkan ateisme karena tidak dapat ada entitas yang lebih kompleks daripada alam semesta fisik dan dari sudut pandang Wittgensteinian, ' lebih kompleks ' tidak berarti (tidak memiliki kondisi kepuasan, yaitu, pembuat kebenaran atau tes). Bahkan ' Allah ' (yaitu, sebuah ' device'dengan waktu tak terbatas/ruang dan energi) tidak dapat menentukan apakah yang diberikan ' nomor ' adalah ' acak ', atau menemukan cara tertentu untuk menunjukkan bahwa diberikan ' formula ', ' teorema ' atau ' kalimat ' atau ' perangkat ' (semua ini menjadi permainan bahasa yang kompleks) adalah bagian dari ' sistem ' tertentu. Mereka yang ingin komprehensif up to date kerangka perilaku manusia dari dua systems tampilan modern dapat berkonsultasi buku saya 'struktur Logis filsafat, psikologi, mind dan bahasa dalam Ludwig wittgenstein dan John Searle ' 2nd Ed (2019). Mereka yang tertarik pada tulisan saya lebih mungkin melihat 'berbicara monyet--filsafat, psikologi, ilmu, agama dan politik di planet yang ditakdirkan--artikel dan ulasan 2006-2019 2nd Ed (2019) dan bunuh diri utopian delusi di 21st Century 4th Ed (2019). (shrink)
मैं कंप्यूटर के रूप में गणना और ब्रह्मांड की सीमा के कई हाल ही में चर्चा पढ़ लिया है, polymath भौतिक विज्ञानी और निर्णय सिद्धांतकार डेविड Wolpert के अद्भुत काम पर कुछ टिप्पणी खोजने की उम्मीद है, लेकिन एक भी प्रशस्ति पत्र नहीं मिला है और इसलिए मैं यह बहुत संक्षिप्त मौजूद सारांश. Wolpert कुछ आश्चर्यजनक असंभव या अधूरापन प्रमेयों साबित कर दिया (1992 से 2008-देखें arxiv dot org) अनुमान के लिए सीमा पर (कम्प्यूटेशन) कि इतने सामान्य वे गणना कर (...) डिवाइस से स्वतंत्र हैं, और यहां तक कि भौतिकी के नियमों से स्वतंत्र, इसलिए वे कंप्यूटर, भौतिक विज्ञान और मानव व्यवहार में लागू होते हैं. वे कैंटर विकर्णीकरण का उपयोग करते हैं, झूठा विरोधाभास और worldlines प्रदान करने के लिए क्या ट्यूरिंग मशीन थ्योरी में अंतिम प्रमेय हो सकता है, और प्रतीत होता है असंभव, अधूरापन, गणना की सीमा में अंतर्दृष्टि प्रदान करते हैं, और ब्रह्मांड के रूप में कंप्यूटर, सभी संभव ब्रह्मांडों और सभी प्राणियों या तंत्र में, उत्पादन, अन्य बातों के अलावा, एक गैर क्वांटम यांत्रिक अनिश्चितता सिद्धांत और एकेश्वरवाद का सबूत. वहाँ Chaitin, Solomonoff, Komolgarov और Wittgenstein के क्लासिक काम करने के लिए स्पष्ट कनेक्शन कर रहे हैं और धारणा है कि कोई कार्यक्रम (और इस तरह कोई डिवाइस) एक दृश्य उत्पन्न कर सकते हैं (या डिवाइस) अधिक से अधिक जटिलता के साथ यह पास से. कोई कह सकता है कि काम के इस शरीर का अर्थ नास्तिकता है क्योंकि भौतिक ब्रह्मांड से और विटगेनस्टीनियन दृष्टिकोण से कोई भी इकाई अधिक जटिल नहीं हो सकती है, 'अधिक जटिल' अर्थहीन है (संतोष की कोई शर्त नहीं है, अर्थात, सत्य-निर्माता या परीक्षण)। यहां तक कि एक 'भगवान' (यानी, असीम समय/स्थान और ऊर्जा के साथ एक 'डिवाइस' निर्धारित नहीं कर सकता है कि क्या एक दिया 'संख्या' 'यादृच्छिक' है, और न ही एक निश्चित तरीका है दिखाने के लिए कि एक दिया 'सूत्र', 'प्रमेय' या 'वाक्य' या 'डिवाइस' (इन सभी जटिल भाषा जा रहा है) खेल) एक विशेष 'प्रणाली' का हिस्सा है. आधुनिक दो systems दृश्यसे मानव व्यवहार के लिए एक व्यापक अप करने के लिए तारीख रूपरेखा इच्छुक लोगों को मेरी पुस्तक 'दर्शन, मनोविज्ञान, मिनडी और लुडविगमें भाषा की तार्किक संरचना से परामर्श कर सकते हैं Wittgenstein और जॉन Searle '2 एड (2019). मेरे लेखन के अधिक में रुचि रखने वालों को देख सकते हैं 'बात कर रहेबंदर- दर्शन, मनोविज्ञान, विज्ञान, धर्म और राजनीति पर एक बर्बाद ग्रह --लेख और समीक्षा 2006-2019 2 ed (2019) और आत्मघाती यूटोपियान भ्रम 21st मेंसदी 4वें एड (2019) . (shrink)
This paper motivates and defends alethic nihilism, the theory that nothing is true. I first argue that alethic paradoxes like the Liar and Curry motivate nihilism; I then defend the view from objections. The critical discussion has two primary outcomes. First, a proof of concept. Alethic nihilism strikes many as silly or obviously false, even incoherent. I argue that it is in fact well-motivated and internally coherent. Second, I argue that deflationists about truth ought to be nihilists. Deflationists maintain (...) that the utility of the truth predicate is exhausted by its expressive role, and I argue that the truth predicate can still play this expressive role even if nothing is true. As such, deflationists do not stand to lose anything by accepting nihilism. Since they also stand to gain an elegant solution to the alethic paradoxes, on balance deflationists ought to be nihilists. (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 note we shall argue that Milne’s new effort does not refute Truthmaker Maximalism. According to Truthmaker Maximalism, every truth has a truthmaker. Milne has attempted to refute it using the following self-referential sentence M: This sentence has no truthmaker. Essential to his refutation is that M is like the Gödel sentence and unlike the Liar, and one way in which Milne supports this assimilation is through the claim that his proof is essentially object-level and not semantic. In (...) Section 2, we shall argue that Milne is still begging the question against Truthmaker Maximalism. In Section 3, we shall argue that even assimilating M to the Liar does not force the truthmaker maximalist to maintain the ‘dull option’ that M does not express a proposition. There are other options open and, though they imply revising the logic in Milne’s reasoning, this is not one of the possible revisions he considers. In Section 4, we shall suggest that Milne’s proof requires an implicit appeal to semantic principles and notions. In Section 5, we shall point out that there are two important dissimilarities between M and the Gödel sentence. Section 6 is a brief summary and conclusion. (shrink)
In Vagueness and Contradiction (2001), Roy Sorensen defends and extends his epistemic account of vagueness. In the process, he appeals to connections between vagueness and semantic paradox. These appeals come mainly in Chapter 11, where Sorensen offers a solution to what he calls the no-no paradox—a “neglected cousin” of the more famous liar—and attempts to use this solution as a precedent for an epistemic account of the sorites paradox. This strategy is problematic for Sorensen’s project, however, since, as we (...) establish, he fails to resolve the semantic pathology of the no-no paradox. (shrink)
In this essay (for undergraduates) I introduce three of the famous semantic paradoxes: the Liar, Grelling’s, and the No-No. Collectively, they seem to show that the notion of truth is highly paradoxical, perhaps even contradictory. They seem to show that the concept of truth is a bit akin to the concept of a married bachelor—it just makes no sense at all. But in order to really understand those paradoxes one needs to be very comfortable thinking about how lots of (...) interesting sentences talk about not dogs or cats or elections or baseball but sentences. That is, we need to get familiar analyzing sentences that talk about sentences. (shrink)
Peter Milne has tried to refure Truthmaker Maximalism. the thesis that every truth has a truthmaker, by producing a simple and direct counterexample to it, the sentence M: This sentence has no truthmaker. I argue that, contrary to what Milne argues, on Truthmaker Maximalism M is equivalent to the Liar, which gives the truthmaker maximalist a way to defend his position from Milne's counterexample: to argue that M expresses no proposition.
The semantic paradoxes are a family of arguments – including the liar paradox, Curry’s paradox, Grelling’s paradox of heterologicality, Richard’s and Berry’s paradoxes of definability, and others – which have two things in common: first, they make an essential use of such semantic concepts as those of truth, satisfaction, reference, definition, etc.; second, they seem to be very good arguments until we see that their conclusions are contradictory or absurd. These arguments raise serious doubts concerning the coherence of the (...) concepts involved. This article will offer an introduction to some of the main theories that have been proposed to solve the paradoxes and avert those doubts. Included is also a brief history of the semantic paradoxes from Eubulides to Tarski and Curry. (shrink)
I distinguish paradoxes and hypodoxes among the conundrums of time travel. I introduce ‘hypodoxes’ as a term for seemingly consistent conundrums that seem to be related to various paradoxes, as the Truth-teller is related to the Liar. In this article, I briefly compare paradoxes and hypodoxes of time travel with Liar paradoxes and Truth-teller hypodoxes. I also discuss Lewis’ treatment of time travel paradoxes, which I characterise as a Laissez Faire theory of time travel. Time travel paradoxes are (...) impossible according to Laissez Faire theories, while it seems hypodoxes are possible. (shrink)
The paper presents Alfred Tarski’s debate with the semantic antinomies: the basic Liar Paradox, and its more sophisticated versions, which are currently discussed in philosophy: Strengthen Liar Paradox, Cyclical Liar Paradox, Contingent Liar Paradox, Correct Liar Paradox, Card Paradox, Yablo’s Paradox and a few others. Since Tarski, himself did not addressed these paradoxes—neither in his famous work published in 1933, nor in later papers in which he developed the Semantic Theory of Truth—therefore, We try to (...) defend his concept of truth against these antinomies. It is demonstrated that Tarskian theory of truth is resistant to the paradoxes and it is still the best solution to avoid the antinomies and remain within a classical logic, that is, accepting the laws of noncontradiction, excluded middle, and the principle of bivalence. Thus, the goal of the paper is double—firstly, to show that none of the versions of the Liar Paradox’s is a serious threat to Tarski’s concept of truth, and secondly, that Semantic Theory of Truth allows to remain within classical logic, and at the same time, avoid antinomies—which makes it the most attractive among classical theories of truth. (shrink)
In Replacing Truth, Scharp takes the concept of truth to be fundamentally incoherent. As such, Scharp reckons it to be unsuited for systematic philosophical theorising and in need of replacement – at least for regions of thought and talk which permit liar sentences and their ilk to be formulated. This replacement methodology is radical because it not only recommends that the concept of truth be replaced, but that the word ‘true’ be replaced too. Only Tarski has attempted anything like (...) it before. I dub such a view Conceptual Marxism. In assessing this view, my goals are fourfold: to summarise the many components of Scharp’s theory of truth; to highlight what I take to be some of the excess baggage carried by the view; to assess whether, and to what extent, the extreme methodology on offer is at all called for; finally, to briefly propose a less radical replacement strategy for resolving the liar paradox. (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)
According to Emma Borg, minimalism is (roughly) the view that natural language sentences have truth conditions, and that these truth conditions are fully determined by syntactic structure and lexical content. A principal motivation for her brand of minimalism is that it coheres well with the popular view that semantic competence is underpinned by the cognition of a minimal semantic theory. In this paper, I argue that the liar paradox presents a serious problem for this principal motivation. Two lines of (...) response to the problem are discussed, and difficulties facing those responses are raised. I close by issuing a challenge: to construe the principal motivation for BM in such a way so as to avoid the problem of paradox. (shrink)
Aristotle’s words in the Metaphysics: “to say of what is that it is, or of what is not that it is not, is true” are often understood as indicating a correspondence view of truth: a statement is true if it corresponds to something in the world that makes it true. Aristotle’s words can also be interpreted in a deflationary, i.e., metaphysically less loaded, way. According to the latter view, the concept of truth is contained in platitudes like: ‘It is true (...) that snow is white iff snow is white’, ‘It is true that neutrinos have mass iff neutrinos have mass’, etc. Our understanding of the concept of truth is exhausted by these and similar equivalences. This is all there is to truth. In his book Truth (Second edition 1998), Paul Horwich develops minimalism, a special variant of the deflationary view. According to Horwich’s minimalism, truth is an indefinable property of propositions characterized by what he calls the minimal theory, i.e., all (nonparadoxical) propositions of the form: It is true that p if and only if p. Although the idea of minimalism is simple and straightforward, the proper formulation of Horwich’s theory is no simple matter. In this paper, I shall discuss some of the difficulties of a logical nature that arise. First, I discuss problems that arise when we try to give a rigorous characterization of the theory without presupposing a prior understanding of the notion of truth. Next I turn to Horwich’s treatment of the Liar paradox and a paradox about the totality of all propositions that was first formulated by Russell (1903). My conclusion is that Horwich’s minimal theory cannot deal with these difficulties in an adequate way, and that it has to be revised in fundamental ways in order to do so. Once such revisions have been carried out the theory may, however, have lost some of its appealing simplicity. (shrink)
It is shown that Russell's Paradox can be solved without advocating the Theory of Types, and also that the Liar's Paradox can be solved in much the same way. Neither solution requires that any of our commonsense-based beliefs be revised, let alone jettisoned. It is also shown that the Theory of Types is false.
Can the so-ca\led first incompleteness theorem refer to itself? Many or maybe even all the paradoxes in mathematics are connected with some kind of self-reference. Gбdel built his proof on the ground of self-reference: а statement which claims its unprovabllity. So, he demonstrated that undecidaЬle propositions exist in any enough rich axiomatics (i.e. such one which contains Peano arithmetic in some sense). What about the decidabllity of the very first incompleteness theorem? We can display that it fulfills its conditions. That's (...) why it can Ье applied to itself, proving that it is an undecidaЬle statement. It seems to Ье а too strange kind of proposition: its validity implies its undecidabllity. If the validity of а statement implies its untruth, then it is either untruth (reductio ad absurdum) or an antinomy (if also its negation implies its validity). А theory that contains а contradiction implies any statement. Appearing of а proposition, whose validity implies its undecidabllity, is due to the statement that claims its unprovability. Obviously, it is а proposition of self-referential type. Ву Gбdel's words, it is correlative with Richard's or liar paradox, or even with any other semantic or mathematical one. What is the cost, if а proposition of that special kind is used in а proof? ln our opinion, the price is analogous to «applying» of а contradictory in а theory: any statement turns out to Ье undecidaЬ!e. Ifthe first incompleteness theorem is an undecidaЬ!e theorem, then it is impossiЬle to prove that the very completeness of Peano arithmetic is also an tmdecidaЬle statement (the second incompleteness theorem). Hilbert's program for ап arithmetical self-foundation of matheшatics is partly rehabllitated: only partly, because it is not decidaЬ!e and true, but undecidaЬle; that's wby both it and its negation шау Ье accepted as true, however not siшultaneously true. The first incompleteness theoreш gains the statute of axiom of а very special, semi-philosophical kind: it divides mathematics as whole into two parts: either Godel шathematics or Нilbert matheшatics. Нilbert's program of self-foundation ofmatheшatic is valid only as to the latter. (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.
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)
The aim of this dissertation is to offer and defend a correspondence theory of truth. I begin by critically examining the coherence, pragmatic, simple, redundancy, disquotational, minimal, and prosentential theories of truth. Special attention is paid to several versions of disquotationalism, whose plausibility has led to its fairly constant support since the pioneering work of Alfred Tarski, through that by W. V. Quine, and recently in the work of Paul Horwich. I argue that none of these theories meets the correspondence (...) intuition---that a true sentence or proposition in some way corresponds to reality---despite the explicit claims by each to capture this intuition. I distinguish six versions of the correspondence theory, and defend two against traditional objections, standardly taken as decisive against them, and show, plainly, that these two theories capture the correspondence intuition. Due to the importance of meeting this intuition, only these two theories stands a chance of being a satisfactory theory of truth. I argue that the version of the correspondence theory incorporating a simple semantic representation relation is preferable to its rival, for which the representation relation is complex. I present and argue for a novel version of this correspondence theory according to which truth is a correspondence property sensitive to semantic context. One consequence of this context-sensitivity is that an ungrounded sentence does not express a proposition. In addition to accounting for the similarity between the Liar and Truth-Teller sentences, this theory of truth is immune to the Liar Paradox, including empirical versions. It is argued that the Liar Paradox is devastating to all of the other theories above, and even formal theories of truth designed to solve it, such as the revision and vagueness theories. Customized versions of the Liar Paradox besetting this theory are handled by its context-sensitivity, and by enforcing the distinction between truth and truth value. This same pair of considerations also yields solutions to Lob's Paradox and Grelling's Paradox. Arguments similar to those given to defend this correspondence theory show that with one minor alteration, Kripke's fixed point theory may be used to model this correspondence notion of truth. (shrink)
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