Academic literature on the topic 'Epimenides paradox'

Abstract Many logicians and exegetes have read Titus 1,12 as an example of the Liar’s Paradox without paying sufficient attention to the nature of ancient oracular utterance. Instead of reading the verse as a logical puzzle, it should be read from its ancient context in the history of religions—a context of which ancient Christian scholars were aware. The Syriac scholars preserved a shocking Cretan tradition about Zeus’s death that probably goes back to Theodore of Mopsuestia. The god responsible for Epimenides’ oracle presumably rejected the Cretan tradition of Zeus’s death and tomb. The truth value of 1,12 consequently depends on the oracle and not the human being (i. e., Epimenides) who delivers the oracle. A reading sensitive to the history of religions preserves the Pauline author’s perspective in Titus 1,13: ἡ μαρτυρία αὕτη ἐστὶν ἀληθής. There is, consequently, a strong analogy between Caiaphas’s words in John 11:49–50 and those of Epimenides in Titus 1,12.

AbstractThe proposition Cretans are always liars" is not a socio-contingent proposition about Cretans in Titus 1:12,13. It has nothing to do with stereotyping Cretans, but, placed as it is on the lips of a Cretan speaker, constitutes a purely logical or formal proposition which expresses a paradox. A careful tracing of the functions of logical paradox from Zeno and the other Greeks to modern mathematical logic demonstrates its frequent function as meta-language, to break out of a vicious circularity which may arise from within a single-level system of propositions. In Titus, the context substantiates the view which also emerges from philosophical analysis that paradox may expose a logical asymmetry between first-person utterances of a kind which are necessarily embedded in life through given commitments and third-person utterances which do not entail any given stake in life. The paradox of Titus 1:12 brings into focus the self-defeating and often fruitless escalation of claims in purely verbal exchanges which may be transposed to a constructive level if truth-claims made by the elders or bishops can be perceived as drawing currency from blameless conduct. They are not to be "empty talkers" who "profess to know God but deny him by their deeds" (1:8,10,16). A clumsy confusion arose in Patristic exegesis and thereafter between the logically necessary and logically contingent status of the proposition in Titus 1:12 for reasons which are explained here, including the blurring of two distinct traditions about "Epimenides" of Crete, with whom the paradox of the liar is strongly associated. Counterarguments to this proposal are considered and addressed, including the special function of the postscript "this testimony is true" (Titus 1:13a).

The subject of the research is the question of what texts of Plato could become a stimulus for the formation of skeptical ideas in the Academy. Can we, in particular, raise the question of the presence in the texts of Plato of something similar to the principle of the “epoche”, which is the most important methodological sign of skepticism? Can be compared with skepticism the elenchic strategy of Socrates? In our opinion, there are a number of moments in the works of Plato, which brings him closer to skeptical discourse (although this does not make him a skeptic). We dwell only on two of them. The first is the ability of the protagonists of his dialogues to hold in their arguments the two opposite sides of the subject in their undoubted difference and, at the same time, in mutual necessity. This is the Platonic dialectic in its true expression, examples of which we see in the Sophistes and the Parmenides. The second specific aspect of Plato's thought is in the formulation by Plato of a number of logical paradoxes. In its classic version, it became known, however, a little later, in the works of representatives of the Megarian school. We shall deal in more detail with the paradox of the liar, or “the thesis of Epimenides”, which is often seen as a classic example of a self-referential statement. The article will show analogies to the paradox of the liar in Plato's texts. The key point is the last argument from the Theaetetus, where Socrates examines the definition of knowledge as a true opinion with the addition of a specifying attribute (Thaet 201c-208d), as well as the 7th and 8th hypotheses of the Parmenides (Parm. 164b-166c). It seems to us that this moment of the Platonic dialectic also turns out to be a definite resource for the future “skeptical turn” in the Academy. Especially in the situation when the dialogues of Plato were discussed in terms of interest in the arguments of Pyrrho and the Megarians, for whom paradoxes were one of the important methodological tools.

My thesis aims at contributing to classifying the Liar-like paradoxes (and related Truth-teller-like expressions) by clarifying distinctions and relationships between these expressions and arguments. Such a classification is worthwhile, firstly, because it makes some progress towards reducing a potential infinity of versions into a finite classification; secondly, because it identifies a number of new paradoxes, and thirdly and most significantly, because it corrects the historically misplaced distinction between semantic and set-theoretic paradoxes. I emphasize the third result because the distinction made by Peano [1906] and supported by Ramsey [1925] has been used to warrant different responses to the semantic and set-theoretic paradoxes. I find two types among the paradoxes of truth, satisfaction and membership, but the division is shifted from where it has historically been drawn. This new distinction is, I believe, more fundamental than the Peano-Ramsey distinction between semantic and set-theoretic paradoxes. The distinction I investigate is ultimately exemplified in a difference between the logical principles necessary to prove the Liar and those necessary to prove Grelling’s and Russell’s paradoxes. The difference relates to proofs of the inconsistency of naive truth and satisfaction; in the end, we will have two associated ways of proving each result. ¶ Another principled division is intuitively anticipated. I coin the term 'hypodox' (adj.: 'hypodoxical') for a generalization of Truth-tellers across paradoxes of truth, satisfaction, membership, reference, and where else it may find applicability. I make and investigate a conjecture about paradox and hypodox duality: that each paradox (at least those in the scope of the classification) has a dual hypodox.¶ In my investigation, I focus on paradoxes that might intuitively be thought to be relatives of the Liar paradox, including Grelling’s (which I present as a paradox of satisfaction) and, by analogy with Grelling’s paradox, Russell’s paradox. I extend these into truth-functional and some non-truth-functional variations, beginning with the Epimenides, Curry’s paradox, and similar variations. There are circular and infinite variations, which I relate via lists. In short, I focus on paradoxes of truth, satisfaction and some paradoxes of membership. ¶ Among the new paradoxes, three are notable in advance. The first is a non-truth functional variation on the Epimenides. This helps put the Epimenides on a par with Curry’s as a paradox in its own right and not just a lesser version of the Liar. I find the second paradox by working through truth-functional variants of the paradoxes. This new paradox, call it ‘the ESP’, can be either true or false, but can still be used to prove some other arbitrary statement. The third new paradox is another paradox of satisfaction, distinctly different from Grelling’s paradox. On this basis, I make and investigate the new distinction between two different types of paradox of satisfaction, and map one type back by direct analogy to the Liar, and the other by direct analogy to Russell's paradox.

My thesis aims at contributing to classifying the Liar-like paradoxes (and related Truth-teller-like expressions) by clarifying distinctions and relationships between these expressions and arguments. Such a classification is worthwhile, firstly, because it makes some progress towards reducing a potential infinity of versions into a finite classification; secondly, because it identifies a number of new paradoxes, and thirdly and most significantly, because it corrects the historically misplaced distinction between semantic and set-theoretic paradoxes. I emphasize the third result because the distinction made by Peano [1906] and supported by Ramsey [1925] has been used to warrant different responses to the semantic and set-theoretic paradoxes. I find two types among the paradoxes of truth, satisfaction and membership, but the division is shifted from where it has historically been drawn. This new distinction is, I believe, more fundamental than the Peano-Ramsey distinction between semantic and set-theoretic paradoxes. The distinction I investigate is ultimately exemplified in a difference between the logical principles necessary to prove the Liar and those necessary to prove Grelling’s and Russell’s paradoxes. The difference relates to proofs of the inconsistency of naive truth and satisfaction; in the end, we will have two associated ways of proving each result. ¶ ...