The article attempts to highlight the development of the unity of medicine and philosophy in the context of combating epidemics of two early Greek thinkers Epimenides and Empedocles. The idea that Epimenides adheres to the divine origin of the disease is justified, but at the same time, in the process of ritual purification from the plague, it attracts elements of the Pythagorean view of healing, as well as close to Indo-Iranian traditions of the time. It is proved that (...) in the course of the development of ancient thought, the view of the disease also evolves “from myth to logos”, which leads to the understanding of this phenomenon in Empedocles as an ontological problem. Accordingly, it has been established that, for the Sicilian philosopher, mass diseases (epidemics) are caused primarily by the fact that he is more prevalent in the world. If the society is engulfed by hatred and malice, then diseases will inevitably emerge and increase. Instead, overcoming and disappearing of epidemics are possible because peace and harmony between people will prevail. The author substantiates the thesis that helping residents to overcome epidemics in various ancient cities, testifies to the great importance of the early Greek thinkers, who combined not only reflection but also praxis. (shrink)

From the scene of the singing cicadas in the _Phaedrus_, we will show the affinities between the mention of the dangerous sleep at noon (_Phdr_. 258e6-259d8) and a mythical episode in the life of Epimenides. Next, we will look at the possible affinities between the description of Dionysian madness (_Phdr_. 244d5-245a1) and the type of divination practiced by Epimenides of Crete (DK 3 B 1-25). From these approaches, we intend to describe and elucidate the common imaginary with which (...) Plato elaborates his reception and assimilation of the archaic poetic tradition in his philosophy. (shrink)

One of Marx‘s and Engels‘ main claims (hereafter ―original Marxism) in their account of the historical ―inevitability of the collapse of capitalism is that one‘s material (economic) conditions, not one‘s ideas, arguments or philosophy, determines one‘s ―consciousness and actions. However, the self-reference in this characterization of philosophical views generates a paradox analogous to the 7th century B.C. Epimenides ―Liar paradox. The Epimenides-paradox arises when Epimenides, a Cretan, states that all Cretans are liars. Epimenides-statement is paradoxical in (...) the sense that if it is true then it is false. Similarly, the Marxist claim that all philosophers who purport to state the cause of all social changes must be wrong, where Marx and Engels are themselves philosophers stating just such a claim, generates a paradox analogous to the ― Epimenides Liar paradox. This leads to what Engels himself calls a―false consciousness, i.e., a failure to understand the true causes of social change. This paradox can only be escaped by abandoning at least one of original Marxism‘s core doctrines. (shrink)

John Tucker; II.—Godel and Epimenides, Proceedings of the Aristotelian Society, Volume 59, Issue 1, 1 June 1959, Pages 25–48, https://doi.org/10.1093/aristoteli.

Our starting point is a somewhat obscure incident which has lately attracted some attention. The year is 429 B.C., and the place is Athens in the third year of the Peloponnesian war. The plague, which had broken out only a year before, was still claiming its victims. Yet military operations were in full swing, and the general Phormio operating in the Corinthian gulf against a Peloponnesian fleet was able to score an impressive victory. The Lacedaemonians were deeply dissatisfied. This was (...) the first sea-fight they had been engaged in, and they found it hard to believe that their fleet was so much inferior to that of the Athenians. They dispatched three advisers to Knemos, the admiral in charge, instructing them to make better preparations for another sea-fight. Additional ships were solicited from the allies, and those already at hand were prepared for battle. It is at this point that the incident in question occurred. Not to prejudge the issue, I quote the text in full leaving the controversial phrases untranslated: 4. And Phormio on his part sent messengers to Athens to give information of the enemy's preparations and to tell about the battle which they had won, urging them also to send to him speedily as many ships as possible, since there was always a prospect that a battle might be fought any day. 5. So they sent him twenty ships, but gave τ δ κυμξοντι special orders to sail first to Crete. Nικας γρ Kρς Γορτνιος πρξενος ν persuaded them to sail against Cydonia, a hostile town, promising to bring it over to the Athenians; but he was really asking them to intervene to gratify the people of Polichne, who are neighbours of the Cydonians. 6. So μν λαβν τς νας. went to Crete, and helped the Polichnitans to ravage the lands of the Cydonians, and by reason of winds and stress of weather wasted not a little time. (shrink)

This article discusses the logic of the Epimenides Paradox using a graphical representation of the logical operators involved. The graphical representation of the Logical Operators is the one used in digital electronics. This method of investigation is very effective in revealing the hidden error in the reasoning that leads to the contradiction. The article explains the vicious circle that the mind goes through when trying to analyze the Paradox. Finally, the article proposes a solution of the Paradox with final (...) conclusions that are not paradoxical but simply counterintuitive. The endless deduction is generated by subsequent evaluations that take place on different levels. In its evaluation the Mind alternates a level of logical evaluation with a level of semantic evaluation. (shrink)

The liar analyzes in detail the genealogy of the paradox expressed by Epimenides when he claimed that all Cretans were liars. As he himself was a native of Crete, this expression was paradoxical since he expressed a truth by lying. Epimenides showed that it is possible to construct perfectly correct sentences according to grammatical and semantic rules, but that they in turn express a contradiction insofar as it is true and false indistinctly. Since the beginning of Western thought, (...) the liar's paradox has been resolved from dissimilar points of view. The book will analyze the different proposals developed in order to deactivate their pernicious consequences for any theory of truth. Thus, Aristotle proposed that the liar should be considered a fallacy, so he attempted to dissolve the presumed validity of his argument through insightful distinctions around the secundum quid et simpliciter fallacy. Subsequently, solutions were tested within the framework of discursive, dialectical and hypothetical models. In the book those propositions that change their truth value over time are analyzed, those called in the metapiptonta tradition. In medieval times the liar was assumed to be insolubious. Special attention was given to the discussion around the transcasus. Kant approached the liar from the point of view of the white lies generated by the antinomies of reason. In modern times, special care was taken to translate the liar into new expressive forms in order to pose it from a merely formal point of view. For this reason the study of him focused on showing and describing his circular, self-referential and reflective character. This work emphasizes the study of the liar within the framework of occasional expressions. The self-reference of the liar's paradox is derived from referential expressions that result from the information expressed circumstantially within the framework of a surrounding context. For this reason we propose a systematic study of the occasional in order to dissolve the liar. Our proposal proposes to characterize the surrounding expressions that determine the liar's referential meaning. (shrink)

With the help of renowned logician Taylor Swift, Theresa Helke introduces four fundamental paradoxes: the Liar, Epimenides’, the Truth-Teller, and the No-No.

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

Higher-order logic, with its type-theoretic apparatus known as the simple theory of types (STT), has increasingly come to be employed in theorizing about properties, relations, and states of affairs—or ‘intensional entities’ for short. This paper argues against this employment of STT and offers an alternative: ordinal type theory (OTT). Very roughly, STT and OTT can be regarded as complementary simplifications of the ‘ramified theory of types’ outlined in the Introduction to Principia Mathematica (on a realist reading). While STT, understood as (...) a theory of intensional entities, retains the Fregean division of properties and relations into a multiplicity of categories according to their adicities and ‘input types’ and discards the division of intensional entities into different ‘orders’, OTT takes the opposite approach: it retains the hierarchy of orders (though with some modifications) and discards the categorisation of properties and relations according to their adicities and input types. In contrast to STT, this latter approach avoids intensional counterparts of the Epimenides and related paradoxes. Fundamental intensional entities lie at the base of the proposed hierarchy and are also given a prominent part to play in the individuation of non-fundamental intensional entities. (shrink)

The significance of the semantical paradoxes for natural languages is examined. If Tarski’s reflections on the issue are correct, English is inconsistent. Paul Ziff responds to Tarskian reflections by arguing to the conclusion that no natural language is or can be inconsistent. The authors reject Ziff’s argument, but they defend something similar to its conclusion: no language, natural or otherwise, is or can be inconsistent in the way that Tarski holds languages capable of formulating the Epimenides are inconsistent.

Solutions to Russell’s paradox of propositions and to Kaplan’s paradox are proposed based on an extension of von Neumann’s method of avoiding paradox. It is shown that Russell’s ‘anti-Cantorian’ mappings can be preserved using this method, but Kaplan’s mapping cannot. In addition, several versions of the Epimenides paradox are discussed in light of von Neumann’s method.

1. Dioniso, Apollo, Eleusi, Orfeo, Museo, Iperborei, Enigma -- 2. Epimenide, Ferecide, Talete, Anassimandro, Annassimene, Onomacrito (2. ed., 1994) -- 3. Eraclito (2a ed., 1982).

Russell’s substitutional theory conferred philosophical advantages over the simple type theory it was to emulate. However, it faced propositional paradoxes, and in a 1906 paper “On ‘Insolubilia’ and Their Solution by Symbolic Logic”, he modified the theory to block these paradoxes while preserving Cantor’s results. My aim is to draw out several quandaries for the interpretation of the role of substitution in Russell’s logic. If he was aware of the substitutional (_p_0_a_0) paradox in 1906, why did he advertise “Insolubilia” as (...) a solution to the Epimenides? If he was dissatisfied with the solution, as his correspondence suggests, why did he go on to publish it? Why did substitution reappear with orders in “Mathematical Logic as Based on the Theory of Types” if he had rejected a hierarchy of orders as intolerable? I offer the following as possible explanations: he construed the “logical Epimenides” as a version of the _p_0_a_0 paradox; his dissatisfaction with the “Insolubilia” solution was philosophical, not technical; and substitution re-emerged because he hoped for a new philosophical gloss on orders. Whether or not my explanations are correct, these issues must be addressed in accounting for Russell’s reasons for ramification. (shrink)

i. a poetic solution of the Goldbach Conjecture; ii. several responses to the Epimenides Paradox; iii. the volitional solution to Russell's Paradox.

After a brief and informal explanation of the Gödel’s theorem as a version of the Epimenides’ paradox applied to Elementary Number Theory formulated in first-order logic, Lucas shows some of the most relevant consequences of this theorem, such as the impossibility to define truth in terms of provability and so the failure of Verificationist and Intuitionist arguments. He shows moreover how Gödel’s theorem proves that first-order arithmetic admits non-standard models, that Hilbert’s programme is untenable and that second-order logic is (...) not mechanical. There are furthermore some more general consequences: the difference between being reasonable and following a rule and the possibility that one man’s insight differs from another’s without being wrong. Finally some consequences concerning moral and political philosophy can arise from Gödel’s theorem, because it suggests that – instead of some fundamental principle from which all else follows deductively – we can seek for different arguments in different situations. (shrink)

Este artigo examina a trajetória do pensamento filosófico, histórico e matemático de Alexandre Koyré, destacando a relação com Husserl seja em seus estudos iniciais sobre os paradoxos de Zenão e Epimênides, seja em sua leitura tardia sobre a Revolução Científica, Galileu e Newton. Além disso, explora a evolução do pensamento de Koyré e o impacto sobre as suas concepções teológicas e ontológicas em relação ao realismo matemático. O artigo conclui ressaltando a dualidade entre o mundo da ciência e o mundo (...) da vida, resultante da revolução científica, e sugere uma perspectiva histórica e epistemológica alternativa para abordar essa dualidade. (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)

The main objective of this paper is to examine how theories of truth and reference that are in a broad sense Fregean in character are threatened by antinomies; in particular by the Epimenides paradox and versions of the so-called Russell-Myhill antinomy, an intensional analogue of Russell’s more well-known paradox for extensions. Frege’s ontology of propositions and senses has recently received renewed interest in connection with minimalist theories that take propositions (thoughts) and senses (concepts) as the primary bearers of truth (...) and reference. In this paper, I will present a rigorous version of Frege’s theory of sense and denotation and show that it leads to antinomies. I am also going to discuss ways of modifying Frege’s semantical and ontological framework in order to avoid the paradoxes. In this connection, I explore the possibility of giving up the Fregean assumption of a universal domain of absolutely all objects, containing in addition to extensional objects also abstract intensional ones like propositions and singular concepts. I outline a cumulative hierarchy of Fregean propositions and senses, in analogy with Gödel’s hierarchy of constructible sets. In this hierarchy, there is no domain of all objects. Instead, every domain of objects is extendible with new objects that, on pain of contradiction, cannot belong to the given domain. According to this approach, there is no domain containing absolutely all propositions or absolutely all senses. (shrink)

Lucas introduces this paper by an account of how he began to be interested to questions about Materialism and Mechanism. Then he suggests a simple version of the Incompleteness theorem of Gödel, showing how this theorem proposes a version of the Epimenides’ paradox able to avoid the circularity of this paradox by means of the possibility to express meta-mathematics in terms of arithmetical propositions and by substituting questions concerning truth by questions concerning provability.

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)

The field of study we call Classics is an ideological construction. It assumes that the Greece and Rome of antiquity belong to the modern West in some singular, privileged way, as our antiquity, their works our classics, and that these civilizations were largely self-invented. In this antiquity there are no diaspora, no hybrids, no minorities, often no women or slaves. Democratic, philosophical Athens is the antitype of a cosmopolis: hermetic, autochthonous, owing nothing to the civilizations of Africa, India, or the (...) Near East. But the classical lines of demarcation and exclusion have eroded under globalization. We are beginning to understand how antiquity was everywhere mixed and riven by difference. DuBois envisions a new classical studies, less insular, engaged with larger debates in the humanities. She brings a classical scholar’s expert knowledge on Alexander, Epimenides, Oedipus, Sparticus, and St. Paul to bear on questions in the work of Agamben, Badiou, Butler, Negri, and Rancière. She reads Sapho, and exposes the impulse of scholarship to efface the traces of the past, transfixed by an imaginary original. They might better study the forces of fragmentation and the genealogy of canons. She studies the politics and religion of dramatic tragedy in Athens, and finds resources to undermine a neoconservative account of the stability, superiority, and homogeneity of Western civilization. (shrink)

The title of this book is misleading; the subtitle indicates the content more faithfully. Only the last chapter is concerned with paradoxes, namely, with the semantic paradoxes. But the argument there is based on the general theory of assertion and predication defended in the preceding six chapters, which constitute the heart of the book. Cargile rejects the familiar answers to the semantic paradoxes mainly on the grounds that they require restricting the universality of the laws of logic, which involve self-reference (...) just as much as do the paradoxical sentences. What is Cargile’s answer? His treatment of the Epimenides is representative. A Cretan who asserts that all Cretan assertions are false is asserting a different proposition from the proposition a non-Cretan would assert with the same sentence. What assertion is being made with such a sentence depends on the predications, performed by the assertion, of truth or falsity of the propositions "non-assessably" asserted in the original, "assessable" assertion. The Cretan’s assertion predicates falsity of itself, as well as of every other Cretan assertion, but the non-Cretan’s assertion does not. The latter is presumably false and in any case nonparadoxical. The former is self-contradictory, therefore false, therefore also nonparadoxical, since, among other things, it asserts that it is false that all Cretan assertions are false. Other semantic paradoxes require different treatments, also provided by Cargile, but on the basis of the same general theory of assertion and predication. (shrink)

It seems that the Truth-teller is either true or false, but there is no accepted principle determining which it is. From this point of view, the Truth-teller is a hypodox. A hypodox is a conundrum like a paradox, but consistent. Sometimes, accepting an additional principle will convert a hypodox into a paradox. Conversely, in some cases, retracting or restricting a principle will convert a paradox to a hypodox. This last point suggests a new method of avoiding inconsistency. This article provides (...) a significant example. The Liar paradox can be defused to a hypodox by relatively minimally restricting three principles: the T-schema, substitution of identicals and universal instantiation. These restrictions are not arbitrary. For each, I identify the source of a contradiction given some presumptions. Then I propose each restriction as a reasonable way to deal with that source of contradiction. (shrink)

One way of resolving a paradox is to defuse it to a hypodox. This way is relatively unknown though. The goal of this paper is to explain this way with varied examples. The hypodoxes are themselves a broad class: both the Truth-teller and the 21st birthday of someone born on 29th February can be construed as hypodoxes. The most familiar kind of relation between paradoxes and hypodoxes is exemplified by the relation between the Liar and the Truth-teller. This article concerns (...) a second kind where a paradox is defused to a hypodox by restricting or rejecting some granted principles. The Liar paradox has this second kind of relation to a Liar hypodox, which will be introduced. In some cases, defusing a paradox to a hypodox is only a partial resolution, as the hypodox itself may then need resolving. Even so, such a partial resolution decomposes a complex problem into more easily understood problems. Moreover, I compare the result of defusing a paradox to a hypodox with the results of resolving paradoxes in other ways. I give four examples. The first is mainly pedagogic, concerning a birthday. The second is a lightweight legal case, presenting a parking voucher paradox. The third is a formal system in which a Liar and Liar-like sentences are hypodoxical. The fourth is a philosophical critique of ways of solving Bertrand’s chord paradox. (shrink)

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