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

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

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)

The ‘Dialectical school’ denotes a group of early Hellenistic philosophers that were loosely connected by philosophizing in the — Socratic — tradition of Eubulides of Megara and by their interest in logical paradoxes, propositional logic and dialectical expertise. . Its two best known members, Diodorus Cronus and Philo the Logician, made groundbreaking contributions to the development of theories of conditionals and modal logic. Philo introduced a version of material implication; Diodorus devised a forerunner of strict implication. Each developed a (...) system of modal notions that satisfies the basic logical requirements laid down by modern standard modal theories. In antiquity, Diodorus Cronus was famous for his so called Master Argument, which aims to prove that only the actual is possible. (shrink)

É comumente aceito, atualmente, que Aristóteles não teria enfrentado ou tentado seriamente resolver o famoso paradoxo do mentiroso, embora ele tenha sido formulado por Eubúlides de Mileto, membro da escola megárica e rival filosófico de Aristóteles. No máximo, assim reza a visão tradicional, ele parece apenas fazer uma menção desse paradoxo nas Refutações sofísticas, Capítulo 25, talvez esboçando a sua solução. O meu intento, no presente artigo, é desafiar essa opinião geral mostrando que o Estagirita fornece uma explicação implícita para (...) duas versões do paradoxo do mentiroso, a saber, a versão autorreferencial (que pode ser apresentada pela declaração: “esta declaração é falsa”), e a versão anafórica (que pode ser apresentada por meio de duas declarações mutuamente referentes como estas: “a próxima declaração é verdadeira” e “a declaração anterior é falsa”). A minha alegação é que a solução aristotélica para essas duas versões do paradoxo encontra-se no núcleo de sua refutação de duas teses, as quais denominei como tese da synalethia (que defende que toda declaração é verdadeira) e como tese da sympseudia (que defende que toda declaração é falsa). Tal refutação é realizada no oitavo capítulo do quarto Livro da Metafísica, um texto até agora subestimado pelos intérpretes modernos, mesmo sendo a parte final de um dos mais importantes escritos de Aristóteles. A solução aristotélica, assim defendo, é levada a cabo por meio dos seguintes princípios: (i) toda declaração é sempre precedida por um operador de verdade da forma ‘é verdade que...’, ou seja, toda declaração, qualquer que seja o que ela possa declarar a mais, primariamente assevera a sua própria verdade; e, em conformidade com o princípio anterior, (ii) toda declaração que assevera a sua própria falsidade ou acarreta a verdade de sua contraditória é necessariamente falsa. Através desses princípios, a refutação de Aristóteles da synalethia e da sympseudia é bem-sucedida. Mostrarei que obtemos uma boa solução para as versões do mentiroso acima mencionadas (e implicitamente presentes nas posições refutadas), apenas aplicando esses mesmos princípios a elas. Esse tipo de solução ao mentiroso tanto quanto para as teses antes citadas é muito parecido com aquele explicitamente encontrado nas obras de diversos filósofos, a saber, Guilherme de Sherwood, Tomás Bradwardine, João Buridano, Alberto da Saxônia, Paulo Venetus, Charles S. Peirce e Arthur Prior. Assim, também defendo que essa linhagem tem as suas raízes na solução de Aristóteles. (shrink)

Language & Logic -- Glossary -- Aristotle's syllogisms -- Russell's paradox & Frege's logicism -- profile: Aristotle -- Russell's theory of description -- Frege's puzzle -- Gödel's theorem -- Epimenides' liar paradox -- Eubulides' heap -- Science & Epistemology -- Glossary -- I think therefore I am -- Gettier's counter example -- profile: Karl Popper -- The brain in a vat -- Hume's problem of induction -- Goodman's gruesome riddle -- Popper's conjectures & refutations -- Kuhn's scientific revolutions -- (...) Mind & Metaphysics -- Glossary -- Descartes mind-body problem -- Brentano's intentionality -- Fodor's language of thought -- Parfit's persons -- profile: René Descartes -- Chalmer's zombies -- Zeno's paradoxes -- Kant's left hand -- Theseus' ship -- Laplace's demon, determinism, & free will -- Ryle's ghost in the machine -- Ethics & Political Philosophy -- Glossary -- Aristotle's ethics -- States of nature and the social contract -- Kant's categorical imperative -- profile: Immanuel Kant -- Mill's utilitarianism -- Marx's historical materialism -- The trolley problem -- Religion -- Glossary -- Aquinas' five ways -- Anselm's ontological argument -- profile: Thomas Aquinas -- Epicurus' riddle -- Paley's watchmaker -- Pascal's wager -- Hume against miracles -- Grand Moments -- Glossary -- Socrates' method -- Plato's cave -- Aristotle's four causes -- Lucretius' atomism -- profile: Ludwig Wittgenstein -- Berkeley's idealism -- Kant's synthetic a priori -- Hegel's dialectic -- James' pragmatism -- Moore's common sense -- Wittgenstein's picture theory of language -- Continental Philosophy -- Glossary -- Nietzsche's Superman -- profile: Friedrich Nietzsche -- Derrida's deconstruction -- Heidegger's nothing -- Sartre's bad faith. (shrink)

É comumente aceito, atualmente, que Aristóteles não teria enfrentado ou tentado seriamente resolver o famoso paradoxo do mentiroso, embora ele tenha sido formulado por Eubúlides de Mileto, membro da escola megárica e rival filosófico de Aristóteles. No máximo, assim reza a visão tradicional, ele parece apenas fazer uma menção desse paradoxo nas Refutações sofísticas, Capítulo 25, talvez esboçando a sua solução. O meu intento, no presente artigo, é desafiar essa opinião geral mostrando que o Estagirita fornece uma explicação implícita para (...) duas versões do paradoxo do mentiroso, a saber, a versão autorreferencial, e a versão anafórica. A minha alegação é que a solução aristotélica para essas duas versões do paradoxo encontra-se no núcleo de sua refutação de duas teses, as quais denominei como tese da synalethia e como tese da sympseudia. Tal refutação é realizada no oitavo capítulo do quarto Livro da Metafísica, um texto até agora subestimado pelos intérpretes modernos, mesmo sendo a parte final de um dos mais importantes escritos de Aristóteles. A solução aristotélica, assim defendo, é levada a cabo por meio dos seguintes princípios: toda declaração é sempre precedida por um operador de verdade da forma ‘é verdade que...’, ou seja, toda declaração, qualquer que seja o que ela possa declarar a mais, primariamente assevera a sua própria verdade; e, em conformidade com o princípio anterior, toda declaração que assevera a sua própria falsidade ou acarreta a verdade de sua contraditória é necessariamente falsa. Através desses princípios, a refutação de Aristóteles da synalethia e da sympseudia é bem-sucedida. Mostrarei que obtemos uma boa solução para as versões do mentiroso acima mencionadas, apenas aplicando esses mesmos princípios a elas. Esse tipo de solução ao mentiroso tanto quanto para as teses antes citadas é muito parecido com aquele explicitamente encontrado nas obras de diversos filósofos, a saber, Guilherme de Sherwood, Tomás Bradwardine, João Buridano, Alberto da Saxônia, Paulo Venetus, Charles S. Peirce e Arthur Prior. Assim, também defendo que essa linhagem tem as suas raízes na solução de Aristóteles. (shrink)

The noctes Atticae of Aulus Gellius contain almost all the ancient paradoxes. Nevertheless, in comparison with his philosophical sources, the author shows a shift in the perspective of his approach. He analyses the `master argument' of Diodorus Chronus only from an ethical point of view and, among the seven paradoxes attributed to Eubulides of Milet, he quotes the `heap' as an absurdity (absurdum), the `horned one' and the `not-someone' as a trap (captio), the `liar' as a sophism (sophisma). Following (...) the advice of Cynics, Gellius mistrusts deceptive manoeuvres, which highlight gaps in binary logic. At the same time, however, he is interested in argumentative structures, which lead one of two opponents on to victory. The extensive report of the quarrel between Protagoras and Evathlus, and many observations of Gellius on convertible forms of reasoning in literary texts fall within this rhetorical field. (shrink)

The concept of truth serves in logic not only as an instrument but also as an object of study. Eubulides of Miletus (fl. fourth century BCE), a Megarian logician, discovered the paradox known as ‘the Liar,’ and, ever since his discovery, logicians down the ages ‐ Aristotle and Chrysippus, John Buridan and William Heytesbury, and Alfred Tarski and Saul Kripke, to mention just a few ‐ have tried to understand the puzzling behavior of the concept of truth.

De 1805 a 1830, Hegel professe neuf series de cours sur l'histoire de la philosophie. Explorant et meditant les pensees de ses predecesseurs, il en nourrit sa pensee et les eclaire en retour de la sienne. A ce titre, K.L. Michelet, a qui l'on doit la restitution de ces lecons a partir des notes de Hegel et de celles de ses auditeurs, voit dans ce texte la meileure cle pour la comprehension de son oeuvre. C'est par le berceau de la (...) philosophie, la Grece, que Hegel commence son exploration de l'histoire de la philosophie. Divisant la pensee grecque en trois periodes (la premiere s'etend de Thales a Aristote; la seconde englobe epicurisme, stoicisme et scepticisme; la troisieme, Platon et Aristote), il s'agit pour lui de partir du commencement de la pensee philosophante pour aboutir au stade ou l'idee prend la forme de la totalite. Ce deuxieme tome presente, au sein de la premiere periode, les lecons dediees aux sophistes (Protagoras, Gorgias), a Socrate et aux trois grandes ecoles socratiques: megarique (Euclide, Eubulide, Stilpon), cyrenaique (Aristippe, Theodore, Hegesias, Anniceris), cynique (Antisthene, Diogene et cyniques posterieurs). (shrink)

Many philosophical doctrines have been suggested as the target Eubulides intended his Heap and Bald Man to destroy: the coherence of empirical concepts, the law of noncontradiction, the Law of Excluded Middle, pluralism, Aristotle's theory of infinity or of the mean. Aristotle betrays no clear awareness of sorites reasoning in any of his extant works. Sorites puzzles became a standard weapon of Skeptics in their attacks on Stoic philosophy. The Stoics distinguished between sentences and the propositions they are used (...) to assert. The Stoics were prepared to apply bivalence to sorites reasoning and swallow the consequences: any difficulty in answering the sorites questions must come from our ignorance of the right answers, not their non‐existence. More recently, sorites puzzles have been discussed in the form of apparently sound arguments with apparently false conclusions, and philosophers such as Michael Dummett and Crispin Wright have advanced grounds for the premises. (shrink)

The essence of the argument of the beard (so-called by some logic textbooks) is the tactic used by a respondent to reply to a proponent, "The criterion you used to define a key term in your argument is vague, therefore your use of this term in your argument is illegitimate, and your argument is refuted." This familiar kind of argument tactic is similar to the much more famous heap (sorites) argument of Eubulides, closely associated with the slippery slope argument. (...) This article provides a system of classification for sorting out these three arguments, and related types of argument of interest in informal logic. (shrink)

The Hooded Man Paradox of Eubulides concerns the apparent failure of the substitutivity of identicals in epistemic (and other intentional) contexts. This paper formulates a number of different versions of the paradox and shows how these may be solved using semantics for quantified epistemic logic. In particular, two semantics are given which invalidate substitution, even when rigid designators are involved.

‘Puzzles’, ‘word games’, ‘logical anomalies’, whatever we call them, they perplex us and challenge our familiar patterns of reasoning. One of these puzzles, among many others, originated from the mind of an ancient Megarian logician, Eubulides of Miletus, and endures to the modern day.1 Its name, ‘sorites’, can be traced to the Greek word soros, meaning ‘heap.’ The answer to whether one grain of sand ‘is a heap’ or ‘is not a heap’ seems quite simple: it is not a (...) heap. However, as we add grains to the one, at what future point does the non-heap become a heap? Our decision is fraught with uncertainty. Are the objects or the language we are using to describe them vague? In academic philosophy, the ancient Greek puzzle has gained the status of a paradox, as philosophers apply stoic and modern logic to these propositions considered to have vague predicates. The current debate has developed quite serious and wide-ranging implications, such as whether sorites issues provide adequate grounds for abandoning our standard ontology (or our understanding of what really exists), 2 and (germinating into another discipline) whether vagueness in the language of legal rules can generate disagreement as to whether there are right answers to questions of law. 3 Several unique solutions to the paradox have been proposed, yet all suffer from specific inadequacies that might, upon further reflection, disappear in the event that we endeavour to produce a synthesis. When we say that we are attempting to derive a synthesis, we seek to combine elements of two solutions for the sake of creating a new (and hopefully, though not necessarily, a better) one. The paradox of the sorites, or ‘the heap’, appeals to us because it challenges our assumption that we may categorically describe clear cases and their negations, yet fail to distinguish the borderline ones. I will demonstrate that some combinations of solutions are easy fits while others are extremely weak and awkward as attempts at resolving the paradox. Nonetheless, the process of synthesis produces three noteworthy combinations. (shrink)

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

Since classical antiquity, theorists have struggled with the problem of self-reference originating in the Liar Paradox of Eubulides: “Does someone who says ‘I am lying’ lie?” Does he speak truly or falsely? The consensus resolution has been to dismiss the contention “This statement is false” as meaningless incoherent on grounds of self-contradiction. Leibniz also deemed the claim incoherent, but not on grounds of self-contradiction incoherence however on grounds of embarking on an infinite and incompletable series of meaningfulness-presuppositions. He thus (...) introduced a novel and constructive mode of semantical analysis. (shrink)

Since classical antiquity, theorists have struggled with the problem of self-reference originating in the Liar Paradox of Eubulides: “Does someone who says ‘I am lying’ lie?” Does he speak truly or falsely? The consensus resolution has been to dismiss the contention “This statement is false” as meaningless incoherent on grounds of self-contradiction. Leibniz also deemed the claim incoherent, but not on grounds of self-contradiction incoherence however on grounds of embarking on an infinite and incompletable series of meaningfulness-presuppositions. He thus (...) introduced a novel and constructive mode of semantical analysis. (shrink)

Paradoxes and their Resolutions is a ‘thematic compilation’ by Avi Sion. It collects in one volume the essays that he has written in the past (over a period of some 27 years) on this subject. It comprises expositions and resolutions of many (though not all) ancient and modern paradoxes, including: the Protagoras-Euathlus paradox (Athens, 5th Cent. BCE), the Liar paradox and the Sorites paradox (both attributed to Eubulides of Miletus, 4th Cent. BCE), Russell’s paradox (UK, 1901) and its derivatives (...) the Barber paradox and the Master Catalogue paradox (also by Russell), Grelling’s paradox (Germany, 1908), Hempel's paradox of confirmation (USA, 1940s), and Goodman’s paradox of prediction (USA, 1955). This volume also presents and comments on some of the antinomic discourse found in some Buddhist texts (namely, in Nagarjuna, India, 2nd Cent. CE; and in the Diamond Sutra, date unknown, but probably in an early century CE). (shrink)

Lying is an ubiquitous element of communication. Amazingly enough, the topic is almost completely ignored by traditional logic. The usual example, Eubulides’ antinomy, is not a good one: intuitively, “the Liar” doesn’t lie. There are not many further approaches to be found in the literature. Why is this? There are quite a few reasons. We will consider them one by one and disclose further properties of lies at the same time. We sketch a general framework for the formal analysis (...) of lying. As a result we observe that non-adjunctive calculi fits in here quite comfortably. (shrink)

In lieu of an abstract, here is a brief excerpt of the content:Book Reviews Die Megariker: Kommentierte Sammlung der Testimonien. By Klaus D~ring. (Amsterdam : Verlag B. R. Griiner N.V., 1972. Pp. xii q- 185) D~Sring has assembled the first complete collection of textual fragments concerning the Megarian philosophers of the fourth and third centuries B.c., together with a commentary. The fragments are divided by the author into four groups, each centered around one of the better-known figures of the school: (...) Euclid, Eubulides, Diodorus Cronus, Stilpo. Evidences concerning lesser-known personalities are included under the figure to whose "circle" they belonged. A fifth group of texts appears in an Anhang devoted to the sophist Bryson (often mistakenly associated with the Megarians) and his student Polyxenus. Divisions in the commentary parallel those in the text. The author also adds a stemma summarizing his conclusions about teacher-pupil relationships within the school, and there is a selective bibliography and a SteUenregister. An index, which in view of the work's organization would be helpful, is not included. Simply as a collection of texts, this is a major addition to the scholarship in its field; with the author's commentary, it is the most important work on the Megarians since Kurt von Fritz's Real-Encyclopiidie article.1 D~Sringpresents convincing evidence that some widely disseminated opinions about the school have little or no foundation. Some of his alternative views have important consequences, and not only for the history of the Megarians. DSring rejects the dates customarily assigned to the school's founder Euclid (ca. 450ca. 380), pointing out that there is actually no good evidence for them (pp. 73-74). His own figures (ca. 435-ca. 365) rely on the evidence of Plato's Theaetetus to give the year 369 as a terminus post quem for Euclid's death. The first consequence of this chronology is that the story of Euclid stealing into Athens disguised as a woman in order to avoid the anti-Megarian decree of 432 must be rejected; Dfiring feels that it is probably one of a family of tales elaborated by later writers "urn die Macht der Philosophie zu demonstrieren " (p. 74). A more important consequence is in store when this chronology is combined with a reassessment of the evidence relating to Euclid's philosophical position. D6ring rejects the traditional description of Euclid as a "neo-Eleatic" who attempted to combine a strict Parmenidean monism with Socrates' ethical views by identifying the "One" with the "Good." Following yon Fritz, he sees this as "eine ziemlich gewaltsame antike Doxographenkonstruktion" (p. 83). His own view reverses the importance of Socratic and Eleatic elements in Euclid's thought, making him "[ein] Sokratiker, der die dem Sokratischen Denken inh~ente eleatische Komponente weiterentwickelt hat" (p. 87). Together with the revision of Euclid's dates, this would appear to eliminate decisively Kr~imer's thesis that Euclid originated the "Gleichsetzung ontologischer und axiologischer Momente''e fundamental to Platonic metaphysics. First, Euclid was only a few years older than Plato (not "at least two decades," as KrOner requires); second, there is no evidence whatever that he had studied the Eleatic doctrines before meeting Socrates; and finally, the purported "Gleichsetzung" appears to be rather the work of doxographers (pp. 87-89). When we add DSring's skeptical assessment of the story of Plato's Megarian period (p. 76), there remains little evidence to support the theory that Euclid was the ultimate source of Plato'S metaphysics. The most famous achievements of the M~garians were in the sphere of logic. Here, x Suppl. V (1931), s. v. "Megariker." H. J. Kr~mer, Arete bei Platon und Aristoteles (Heidelberg, 1959), p. 506. [52H 522 HISTORY OF PHILOSOPHY Dtring's work should provide the impetus for further research; his collection of texts is much more comprehensive than anything previously available, and his commentary, although deliberately limited to an overview, at least provides a good account of the status quaestionis. The material on the paradoxes attributed to the Megarians (pp. 106-114) is particularly valuable; he gives a good conspectus of the extensive literature on the "Liar" and "sorites," and his remarks on the lesser-known paradoxes (the "Man Who Escapes Notice," the "Electra," the "Hooded... (shrink)

ABSTRACT: Discussion (in German) of Robert Muller's "Les Megariques, Fragments et temoignages". Traduit et commentes. Paris, Vrin 1985, with focus on his commentary on ancient paradoxes.