John Rawls’s difference principle says that we should change our economy if doing so is better for the worst-off group, on the condition that certain basic rights are secured. This paper presents a kind of case that challenges the principle. If we modify the principle to cope with the challenge, we open the way to a Sorites paradox.

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)

This short article pairs the realms of “Mathematics”, “Philosophy”, and “Poetry”, presenting some corners of intersection of this type of scientocreativity. Poetry have long been following mathematical patterns expressed by stern formal restrictions, as the strong metrical structure of ancient Greek heroic epic, or the consistent meter with standardized rhyme scheme and a “volta” of Italian sonnets. Poetry was always connected to Philosophy, and further on, notable mathematicians, like the inventor of quaternions, William Rowan Hamilton, or Ion Barbu, the (...) creator of the Barbilian spaces, have written appreciated poems. We will focus here on an avant-garde movement in literature, art, philosophy, and science, called Paradoxism, founded in Romania in 1980 by a mathematician, philosopher and poet, and on the laboured writing exercises of the Oulipo group, founded in Paris in 1960 by mathematicians and poets, both of them still in act. (shrink)

A sorites argument is a symptom of the vagueness of the predicate with which it is constructed. A vague predicate admits of at least one dimension of variation (and typically more than one) in its intended range along which we are at a loss when to say the predicate ceases to apply, though we start out confident that it does. It is this feature of them that the sorites arguments exploit. Exactly how is part of the subject of this paper. (...) The majority of philosophers writing on vagueness take it to be a kind of semantic phenomenon. If we are right, they are correct in this assumption, which is surely the default position, but they have not so far provided a satisfactory account of the implications of this or a satisfactory diagnosis of the sorites arguments. Other philosophers have urged more exotic responses, which range from the view that the fault lies not in our language, but in the world, which they propose to be populated with vague objects which our semantics precisely reflects, to the view that the world and language are both perfectly in order, but that the fault lies with our knowledge of the properties of the words we use (epistemicism). In contrast to the exotica to which some philosophers have found themselves driven in an attempt to respond to the sorites puzzles, we undertake a defense of the commonsense view that vague terms are semantically vague. Our strategy is to take fresh look at the phenomenon of vagueness. Rather than attempting to adjudicate between different extant theories, we begin with certain pre-theoretic intuitions about vague terms, and a default position on classical logic. The aim is to see whether (i) a natural story can be told which will explain the vagueness phenomenon and the puzzling nature of soritical arguments, and, in the course of this, to see whether (ii) there arises any compelling pressure to give up the natural stance. We conclude that there is a simple and natural story to be told, and we tell it, and that there is no good reason to abandon our intuitively compelling starting point. The importance of the strategy lies in its dialectical structure. Not all positions on vagueness are on a par. Some are so incredible that even their defenders think of them as positions of last resort, positions to which we must be driven by the power of philosophical argument. We aim to show that there is no pressure to adopt these incredible positions, obviating the need to respond to them directly. If we are right, semantic vagueness is neither surprising, nor threatening. It provides no reason to suppose that the logic of natural languages is not classical or to give up any independently plausible principle of bivalence. Properly understood, it provides us with a satisfying diagnosis of the sorites argumentation. It would be rash to claim to have any completely novel view about a topic so well worked as vagueness. But we believe that the subject, though ancient, still retains its power to inform and challenge us. In particular, we will argue that taking seriously the central phenomenon of predicate vagueness—the “boundarylessness” of vague predicates—on the commonsense assumption that vagueness is semantic, leads ineluctably to the view that no sentences containing vague expressions (henceforth ‘vague sentences’) are truth-evaluable. This runs counter to much of the literature on vagueness, which commonly assumes that, though some applications of vague predicates to objects fail to be truth-evaluable, in clear positive and negative cases vague sentences are unproblematically true or false. It is clarity on this, and related points, that removes the puzzles associated with vagueness, and helps us to a satisfying diagnosis of why the sorites arguments both seem compelling and yet so obviously a bit of trickery. We give a proof that semantically vague predicates neither apply nor fail-to-apply to anything, and that consequently it is a mistake to diagnose sorites arguments, as is commonly done, by attempting to locate in them a false premise. Sorites arguments are not sound, but not unsound either. We offer an explanation of their appeal, and defend our position against a variety of worries that might arise about it. The plan of the paper is as follows. We first introduce an important distinction in terms of which we characterize what has gone wrong with vague predicates. We characterize what we believe to be our natural starting point in thinking about the phenomenon of vagueness, from which only a powerful argument should move us, and then trace out the consequences of accepting this starting point. We consider the charge that among the consequences of semantic vagueness are that we must give up classical logic and the principle of bivalence, which has figured prominently in arguments for epistemicism. We argue there are no such consequences of our view: neither the view that the logic of natural languages is classical, nor any plausible principle of bivalence, need be given up. Next, we offer a diagnosis of what has gone wrong in sorites arguments on the basis of our account. We then present an argument to show that our account must be accepted on pain of embracing (in one way or another) the epistemic view of “vagueness”, i.e., of denying that there are any semantically vague terms at all. Next, we discuss some worries that may arise about the intelligibility of our linguistic practices if our account is correct. We argue none of these worries should force us from our intuitive starting point. Finally, we cast a quick glance at other forms of semantic incompleteness. (shrink)

Since the dawn of philosophy, the paradoxical interconnection between the continuous and the discrete plays a central rôle in attempts to understand the ontology of the world, while defying all attempts at consistent formulation. I investigate the relation between (classical) logic and concepts of “space” and “time” in physical and metaphysical theories, starting with the Greeks. An important part of my research consists in exploring the strong connections between paradoxes as they appear and are dealt with in ancient philosophy, (...) and their re-appearance in early modern natural philosophy, as well as in the foundations of contemporary science and mathematics. The way paradoxes are dealt with sheds light on a theory’s hidden metaphysical assumptions, especially with respect to matter, space, time and causation, it defines its ontological signature. This conclusion led me to the in-depth study of early modern natural philosophy, the origin of natural science, especially the influences ancient thinkers had on the new conceptions of space, time and causation developed by Newton, Huygens and Leibniz. (shrink)

ABSTRACT: This paper discusses ancient versions of paradoxes today classified as paradoxes of presupposition and how their ancient solutions compare with contemporary ones. Sections 1-4 air ancient evidence for the Fallacy of Complex Question and suggested solutions, introduce the Horn Paradox, consider its authorship and contemporary solutions. Section 5 reconstructs the Stoic solution, suggesting the Stoics produced a Russellian-type solution based on a hidden scope ambiguity of negation. The difference to Russell's explanation of definite descriptions is (...) that in the Horn Paradox the Stoics uncovered a hidden conjunction rather than a hidden existential sentence. Sections 6 and 7 investigate hidden ambiguities in 'to have' and 'to lose' (including inalienable and alienable possession) and ambiguities of quantification based on substitution of indefinite plural expressions for indefinite or anaphoric pronouns, and Stoic awareness of these. Section 8 considers metaphorical readings and allusions that add further spice to the paradox. (shrink)

Philosophers of education often view the role of religion in education with suspicion, claiming it to be impossible, indoctrinatory or controversial unless reduced to secular premises and aims. The ‘post-secular’ and ‘decolonial’ turns of the new millennium have, however, afforded opportunities to revaluate this predilection. In a social and intellectual context where the arguments of previous generations of philosophers may be challenged on account of positivist assumptions, there may be an opening for the reconsideration of alternative but traditional religious epistemologies. (...) In this article, we pursue one such line of thought by revisiting a classic question in the philosophy of education, Meno’s Paradox of inquiry. We do this to revitalise understanding and justification for religious education. Our argument is not altogether new, but in our view, is in need of restatement: liturgy is at the heart of education and it is so because it is a locus of knowledge. We make this argument by exploring St Augustine’s response to Meno’s Paradox, and his radical claim that only Christ can be called ‘teacher’. Though ancient, this view of the relationship of the teacher and student to knowledge may seem surprisingly contemporary because of its emphasis on the independence of the learner. Although our argument is grounded in classic texts of the Western tradition, we suggest that arguments could be made by drawing on similar resources in other religious traditions, such as Islam, that also draw upon the Platonic tradition and similarly emphasise the importance of communal and personal acts of worship. (shrink)

The article undertakes a phenomenological interpretation of the description of contingency in two late-antique models of the relationship of time and eternity — in the theory of Plotinus, and in the eschatology of Paul on the basis of the First Epistle to the Thessalonians. Contingency as a possible property not of time, but of eternity, the presence of the supertemporal in the physical world — this hypothesis promotes a new view of the relationship between time and eternity and a new (...) view of the properties of time. Time remains as immeasurable as eternity, inheriting its character as a phenomenon of consciousness. The article also compares the ideas of H. Bergson and E. Husserl on duration and memory, on the coincidence of moments and the measurability of the movement of time. A turn to Ptolemaic cosmology proposed by Q. Meillassoux seems relevant, an appeal to ancient mathematics and ontology through the optics of post-metaphysical criticism. The search for a new correlationism is significant for the philosophy of time, and contingency, like any coincidence of thought and object, the world and the subject, the signifier and the signified, leads to new forms of manifestation, new phenomena of presence, a new fullness of being in history. (shrink)

An analysis of the Third Man Argument, especially in light of Constance Meinwald's book Plato's Parmenides. I argue that her solution to the TMA fails. Then I present my own theory as to what Plato's solution was.

Review of Gail Fine, The Possibility of Inquiry (OUP 2014).

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.

(The Kindle book can be ordered for $3.21 from Amazon) -/- Thinking is a fundamental activity of our species – those that give names to other creatures and call themselves humans. Textbooks tell us that there is about 1.2 kg of matter called the brain inside the human body. It sounds small but actually is proportionally the biggest among all animals on Earth. -/- I became more aware of thinking at around 5th grade upon hearing about an ancient (...) class='Hi'>paradox. It can be summarized as follows. -/- ¤ -/- Once upon a time, there was a stupid king. In his kingdom lived a sage who was highly respected for his intelligence. The King did not appreciate this fact. Maybe the Sage made fun of the King’s intellect, but I am not so sure. Anyway, one day, the King summoned the Sage, intending to kill him. -/- The King said, “Wise man, I heard you earn a living by thinking and arguing. Now I give you two options to die.” -/- The Sage said, “Please tell me the choices, Your Majesty.” -/- The King continued, “You live by your tongue, so I will let you say one sentence before you die. If what you say is true, you will die by hanging. If what you say is false, you will die by beheading.” -/- Little did the King know that this was a stupid order. After a short while, the Sage confidently spoke his “last words”, which actually were what saved his life: -/- “Your Majesty, I am about to be beheaded!” -/- ¤ -/- As a “wild animal” going out into life from a young age, my brain spent a lot of time and energy looking for food. Now that I have become older, my body no longer needs so much sustenance. However, my mind craves a different type of nourishment: food for thought. -/- Food for thought can directly lead to food (on the table). My main job as a scientist exemplifies what I have just stated. Maybe we were wrong. Maybe it has been “thought for food” all along, like in such a sequence as TFFTTTFTFFTTFFFT... -/- In the hyper-chaotic infosphere today, we are surrounded by the noises of information, not only as wavy shores or waterfalls but also mega-tsunamis, through Twitter, Facebook, Tiktok, Instagram, Youtube, etc. More than ever, tranquility and calmness are necessary. Like what you have seen in wilderness video clips, predators such as lions, bears, and alligators act lightning-fast when catching prey. But when food is served, the natural world returns to its peaceful, soothing silence. -/- This short book is in its own tidy infosphere, where each little story is also brief and self-contained. Despite this small appearance, I hope the content inside carries the value of tranquility and life observation. The book is petite, but pretty sure not malnourished. A not-too-small detail is that the way the content was shaped and distilled reflects some innovations of mine and my research team: the mindsponge theory, a new theory of serendipity, the bayesvl R package, the BMF analytics, as well as other experiences from working in the field of science. After all, scientific works were my main source of food (before this book sells well – if it does). -/- Welcome to the priceless sober moments – with a chicken-burger price tag! -/- I hope this book will bring readers some moments of calmness, peaceful smiles, and maybe a couple of good laughs too. -/- ~~~ -/- *This update: December 12, 2023 (Third edition, with additions). (shrink)

The article deals with the question of correct reconstruction of and solutions to the ancient paradoxes. Analyzing one contemporary example of a reconstruction of the so-called Crocodile Paradox, taken from Sorensen’s A Brief History of Paradox, the author shows how the original pattern of paradox could have been incorrectly transformed in its meaning by overlooking its adequate historical background. Sorensen’s quoting of Aphthonius, as the author of a certain solution to the paradox, seems to be (...) a systematic failure since the time of Politiano’s erroneous attributing it to Aphthonius. In the conclusion, the author claims that neglecting the historical background of the ancient paradoxes into account, we are neither able to evaluate their modern interpretations as adequate nor their solutions as successful. (shrink)

Heraclitus uses paradoxical language to present the relationship between opposites in his worldview. This mode of expression has generated much controversy. Some take the paradoxes as evidence of a contradictory identity of opposites (Barnes), while others propose a dynamic union through transformation without identity that avoids the contradiction (Graham). By examining B88 and B62, I seek to identify the stronger and weaker points of such readings. The contradictory identity reading thwarts the transformation between opposites. The dynamic reading offers a plausible (...) alternative. However, it skips a characterization of how Heraclitus conceives of the transformation between opposites in physical terms. To fill this gap, I consider Heraclitus’ use of what I call the anti-cognate internal object in B62. I argue that ‘living the death and dying the life’ is a case of change as mixture, a popular conception among the early Presocratics. Upon closer examination, the anti-cognate internal object suggests that real contradictions belong to Heraclitus conception of change. The details reveal a philosophically compelling view. (shrink)

The ancient puzzle of Dion and Theon has given rise to a surprising array of apparently implausible views. For example, in order to solve the puzzle, several philosophers have been led to deny the existence of their own feet, others have denied that objects can gain and lose parts, and large numbers of philosophers have embraced the thesis that distinct objects can occupy the same space, having all their material parts in common. In this paper, I argue for an (...) alternative approach: I claim that human beings have ordinary parts—hands, heads, feet, and so on—but no extraordinary parts, such as ‘foot-complements’, the existence of which is essential to the puzzle. I rebut three objections to this approach: an objection that it is unacceptably metaphysically arbitrary, an objection that the view is incompatible with versions of the puzzle involving decapitation, and an objection concerning masses of matter. If we can believe that there are such things as hands and feet without involving ourselves in paradox, and without accepting large numbers of co-located material objects that share all their material parts, then that is what we should do. My view is the only known alternative which allows this. (shrink)

Though ancient Pyrrhonian skepticism is apparently based on disagreement, this aspect of skepticism has been widely neglected in contemporary discussion on skepticism. The paper provides a rational reconstruction of the skeptical argument from disagreement that can be found in the books of Sextus Empiricus. It is argued that this argument forms a genuine skeptical paradox that has no fully satisfactory resolution. All attempts to resolve it make knowledge or justified belief either intuitively too easy or impossible.

There was a time in my school years when I have learned about Achilles and Tortoise “paradox” originated from Zeno. It was then clear that the ancient Greeks were arguing about this problem but contemporary science has clarified the issue. Yet to my surprise the problem is still debated over and over, despite the fact there exist mathematical proofs. I feel like reminding myself why this is not a paradox beyond reasonable doubt. This is a draft to (...) a section of a future publication. (shrink)

In ancient philosophy, there is no discipline called “logic” in the contemporary sense of “the study of formally valid arguments.” Rather, once a subfield of philosophy comes to be called “logic,” namely in Hellenistic philosophy, the field includes (among other things) epistemology, normative epistemology, philosophy of language, the theory of truth, and what we call logic today. This entry aims to examine ancient theorizing that makes contact with the contemporary conception. Thus, we will here emphasize the theories of (...) the “syllogism” in the Aristotelian and Stoic traditions. However, because the context in which these theories were developed and discussed were deeply epistemological in nature, we will also include references to the areas of epistemological theorizing that bear directly on theories of the syllogism, particularly concerning “demonstration.” Similarly, we will include literature that discusses the principles governing logic and the components that make up arguments, which are topics that might now fall under the headings of philosophy of logic or non-classical logic. This includes discussions of problems and paradoxes that connect to contemporary logic and which historically spurred developments of logical method. For example, there is great interest among ancient philosophers in the question of whether all statements have truth-values. Relevant themes here include future contingents, paradoxes of vagueness, and semantic paradoxes like the liar. We also include discussion of the paradoxes of the infinite for similar reasons, since solutions have introduced sophisticated tools of logical analysis and there are a range of related, modern philosophical concerns about the application of some logical principles in infinite domains. Our criterion excludes, however, many of the themes that Hellenistic philosophers consider part of logic, in particular, it excludes epistemology and metaphysical questions about truth. Ancient philosophers do not write treatises “On Logic,” where the topic would be what today counts as logic. Instead, arguments and theories that count as “logic” by our criterion are found in a wide range of texts. For the most part, our entry follows chronology, tracing ancient logic from its beginnings to Late Antiquity. However, some themes are discussed in several eras of ancient logic; ancient logicians engage closely with each other’s views. Accordingly, relevant publications address several authors and periods in conjunction. These contributions are listed in three thematic sections at the end of our entry. (shrink)

Argumentations are at the heart of the deductive and the hypothetico-deductive methods, which are involved in attempts to reduce currently open problems to problems already solved. These two methods span the entire spectrum of problem-oriented reasoning from the simplest and most practical to the most complex and most theoretical, thereby uniting all objective thought whether ancient or contemporary, whether humanistic or scientific, whether normative or descriptive, whether concrete or abstract. Analysis, synthesis, evaluation, and function of argumentations are described. Perennial (...) philosophic problems, epistemic and ontic, related to argumentations are put in perspective. So much of what has been regarded as logic is seen to be involved in the study of argumentations that logic may be usefully defined as the systematic study of argumentations, which is virtually identical to the quest of objective understanding of objectivity. -/- KEY WORDS: hypothesis, theorem, argumentation, proof, deduction, premise-conclusion argument, valid, inference, implication, epistemic, ontic, cogent, fallacious, paradox, formal, validation. (shrink)

Hegel's most interesting and controversial claims about nonconceptual knowledge arise in contexts of value. This paper examines the relation between nonconceptual and conceptual knowledge in Hegel's Phenomenology, specifically in connection with early Greek aesthetics. I take up Hegel's claim that the ancient Greeks expressed in their myths, religious narratives, sculpture, and artistic materials certain high powered philosophical truths which they shouldn't express in words. I raise a paradox about his claims and show how his claims about ineffable knowledge (...) clash with his general propositional criterion of knowledge, namely, that for something to count as knowledge it must be expressible in words. However I argue that Hegel's thoughts about the matter were coherent and I solve the paradox. (shrink)

Stoic philosophers had to face the accusation of incoherence, self-contradiction and Paradoxes since ancient times. Plutarch in his Moralia writes against them; Cicero devotes a separate work on stoic paradoxes. Even in contemporary Literature there are still discussions on the possibility of such an incoherence and existence of paradoxes in the stoic theory. At first glance, stoic Cosmology gives the impression to both accept a kind of Determinism, and at the same time it undoubtedly argues for the moral agent’s (...) freedom of the Will. In pre-stoic or even other contemporary to Stoicism Philosophical Traditions, the definitions that these two terms/concepts are given, fairly accuse as incoherent any Theory that does not set them as “contraries”. Under these types of accusations, the stoic Cosmology and Theory of the Freedom of the Will is often to be included. This phenomenal self-contradiction inside the Principles of Stoicism becomes even more obvious in Epictetus, a philosopher of the Late Stoa. He is interested in practical ethics, thus the phenomenal contradiction gets more lucid. This would have augmented the criticism of the Stoic philosophy for incoherence, if Epictetus had not made his main philosophical aim/target : the clarification of how an agent’s Will can be Free inside a Universe ruled by Fate/Destiny ; namely, a Universe merely Determined by Nature’s/God’s Will. Epictetus’ originality appears in the way he interrelates the concept of Freedom of the Will with the concept of Destiny and Determinism, in order to accomplish their simultaneous co-existence. This approach guards him against being easily accused for incoherence and self-contradiction. Through the unique way he understands and defines the Moral Agency, which is the agent’s internal state/condition/disposition, he steers towards an integrated, accomplished, strong and coherent line of argument. This sturdy declaration is able to support the weight of the Consent to a Free Will, and thus a certain kind Freedom of the moral agent. The excellence of this line of argument is that it can bear also the burden of the Consent to the phenomenally contrary concept of Determinism and Destiny. The elements used to the construction of this argument, which is stretched throughout the whole epictetean corpus can be summarised to a few key concepts, which are: the things which are in our power and the things which are not in our power, the concept of Freedom. These concepts work towards his philosophical targeting, because of the special definition he gives them. Axiomatically Epictetus states that in order for man to be free, it is necessary to be liberated from what the body forces him to do. Desires, passions and beliefs are considered as elements which are external to the moral agent. The moral agent “shrinks” into the Will. Thus man has the capability to free himself from anything external to his Will and therefore to harmonise his own Will to the Will of Nature/God; namely, to will what Nature/God wills and thus never conflict to the external facts. Consequently, Epictetus’ solution, is to include in the category of τά οὐκ ἐφ' ἡμῖν anything that he defines as external to the prohairesis: the desires, beliefs, passions and in general anything the body entails, the external facts. Thus the prohairesis, remains unhindered and it is completely depended on man’s power ; as characteristically Epictetus writes, “not even Zeus himself can overpower” the prohairesis. -/- Dissertation for the MSc Ancient Philosophy (2008-2009) at The University of Edinburgh, supervised by Inna Kupreeva. (shrink)

The primary interpretative challenge for understanding Parmenides’ poem revolves around explaining both the meaning of, and the relationship between, its two primary sections: a) the positively endorsed metaphysical arguments which describe some unified, unchanging, motionless, and eternal “reality”, and b) the ensuing cosmology, which incorporates the very principles explicitly denied in Aletheia. I will refer to this problem as the “A-D Paradox.” I advocate resolving this paradoxical relationship by reading Parmenides’ poem as a ring-composition, and incorporating a modified version (...) of Palmer’s modal interpretation of Aletheia. On my interpretation, Parmenides’ thesis in Aletheia is not a counter-intuitive description of how all the world must truly be, but rather a radical rethinking of divine nature. Understanding Aletheia in this way, the ensuing “cosmology” can be straightforwardly rejected as an exposition of how traditional, mythopoetic accounts have misled mortals in their understanding of divinity. Not only does this interpretative view provide a resolution to the A-D Paradox, it offers a more holistic account of the poem by making the opening lines of introduction integral to understanding Parmenides’ message. By setting forth its own unacceptable fiction, paralleling the elements of the Doxa in a ring-composition, the Proem simultaneously establishes the scope of the ensuing inquiry, and its target. Maintaining Parmenides’ historical position as the “father of metaphysics,” the narrative that he advanced a strictly secular account of all reality is challenged. Instead, Parmenides is best understood as further advancing Xenophanes’ criticisms of traditional religion, an intellectual relationship which the ancient testimonia strongly supports. (shrink)

For anyone approaching the Encheiridion of Epictetus for the first time, this book provides a comprehensive guide to understanding a complex philosophical text. Including a full translation and clear explanatory commentaries, Epictetus's 'Encheiridion' introduces readers to a hugely influential work of Stoic philosophy. Scott Aikin and William O. Stephens unravel the core themes of Stoic ethics found within this ancient handbook. Focusing on the core themes of self-control, seeing things as they are, living according to nature, owning one's roles (...) and fulfilling the responsibilities that those roles entail, the authors elucidate the extremely challenging ideas in Epictetus's brisk chapters. Divided into five distinct parts, this book provides readers with: -/- - A new translation of the Encheiridion by William O. Stephens. - A new introduction to ancient Stoicism, its system of concepts, and the ancient figures who shaped it. - A fresh treatment of the notorious and counter-intuitive 'Stoic paradoxes'. - An accessible overview of the origin and historical context of the Encheiridion. - Detailed commentaries on each chapter of the Encheiridion that clarify its recurring themes and highlight their interconnections. - Careful attention to the presentation of the arguments embedded in Epictetus's aphoristic style. - A thoughtful discussion of serious criticisms of Epictetus's Stoicism and replies to these objections. -/- Written with clarity and authority, Epictetus's 'Encheiridion' provides a foundation from which readers can understand this important text and engage with the fundamental questions of Stoic philosophy and ethics. This guide will aid teachers of Epictetus, students encountering Stoicism for the first time, and readers seeking a greater understanding of Stoic ethics. (shrink)

We now have a paradoxical situation where the place and status of stories is in decline within the humanities, while scientists are increasingly recognizing their importance. Here the attitude towards narratives of these scientists is defended. It is argued that stories play a primordial role in human self-creation, underpinning more abstract discourses such as mathematics, logic and science. To uphold the consistency of this claim, this thesis is defended by telling a story of the evolution of European culture from (...) class='Hi'>Ancient Greece to the present, including an account of the rise of the notion of culture and its relation to the development of history, thereby showing how stories function to justify beliefs, situate people as agents within history and orient them to create the future. (shrink)

Vlastos, G. Introduction: the paradox of Socrates.--Lacey, A. R. Our knowledge of Socrates.--Dover, K. J. Socrates in the Clouds.--Robinson, R. Elenchus.--Robinson, R. Elenchus, direct and indirect.--Robinson, R. Socratic definition.--Nakhnikian, G. Elenctic definitions.--Cohen, S. M. Socrates on the definition of piety: Euthyphro 10A-11B.--Santas, G. Socrates at work on virtue and knowledge in Plato's Laches.--Burnyeat, M. F. Virtues in action.--Walsh, J. J. The Socratic denial of Akrasia.--Santas, G. Plato's Protagoras and explanations of weakness.--Woozley, A. D. Socrates on disobeying the law.--Allen, R. (...) E. Plato's earlier theory of forms. (shrink)

This paper is about the relevance of the ineffable and the singular to hermeneutics. I respond to standard criticisms of Friedrich Schleiermacher by Karl Barth and Hans-Georg Gadamer in order to clarify his understanding of language, interpretation, and religion. Schleiermacher’s “indicative hermeneutics” is developed in the context of the ethical significance of communication and the ineffable. The notion of trace is employed in order to interpret the paradox of speaking about that which cannot be spoken. The trace is not (...) a brute singularity but bears a fundamental relationship to the word—and ultimately the word of God—for Schleiermacher. (shrink)

The thesis I should like to advance in this essay is that Plato cannot and, in fact, does not adhere consistently to the doctrine that to know the good is to do the good. First, in order to display the paradoxes in the Platonic ethical system, I shall discuss the concept of the homogeneity of the good which Plato explicitly endorses. Second, by referring to Plato's practice, I shall endeavor to demonstrate that he treats the good as heterogeneous although this (...) treatment is inconsistent with his equation of knowledge with virtue. I shall use the descriptive phrase 'homogeneity of the good' to stand for that conception of the good which identifies the good exclusively with the moral good. I shall use the descriptive phrase 'heterogeneity of the good' to stand for that conception of the good which includes in the definition of good mixed pleasures or the natural good. Our understanding of the good as heterogeneous allows us to clarify many of the paradoxes present in Platonic ethics and affords us a deeper understanding of Plato. (shrink)

As with so many mystics, Alexis karpouzos intuitively know the oneness of cosmic creation and historic humanity as part of all that is and all there isn't. So, the originality of Alexis Karpouzos thought is that it crosses the most diverse fields, the most opposing philosophies, to unite them into an often contradictory and broken whole. Marx and Heidegger, Nietzsche, Freud and Heraclitus, poets and political theorists all come together in the same distance and the same unusual proximity. Alexis karpouzos (...) use Pre-Socratics philosophy and generally the ancient Greek philosophy, as well as the pre-philosophical thinking of The Upanishads, the Vedas and Buddhism in India, of Lao Tzu, of Zen Buddhism and the Taoist tradition in China, of the Arab mystics and poets, with their metaphysical religiosity as the metaphysical basis for the interpretation and understanding of the world and existence. At the same time the ancient metaphysics is connect with Hegel’s dialectical ontology and with the modern thinking of Marx, Nietzsche, Freud, Heidegger, and others as the interpretive context for understanding the central problems of the technical and scientific world during his time. Novalis, Hölderlin, Rimbaud, Whitman, Eliot and others show the dreamy nature of existence, the transcendence of the Cosmos, welcome the infinity. For Alexis karpouzos the combination of ancient and modern thought creates the holistic experience of universal space-time and the consciousness of the unity. The poetic thought of Alexis karpouzos is a expressions of soul's inner experiences, expression of universality. The inspiring visual images and the symbolic use of language offer a description of elevating experiences of consciousness, a glimpse of higher worlds. The philosophy of Alexis karpouzos speak to the human experience from a universal perspective, transcending all religions, cultural and national boundaries. Using vivid images and a direct language that speaks to the heart, his philosophy evokes a sense of deep communication with the collective unconscious, a sense of connection to all the creatures of the world, compassion for others, admiration for the beauty of nature, reverence for all life, and an abiding faith in the invisible touch of world. Alexis karpouzos thoughts are often terse and paradoxical, challenging us to to break out of the box of limiting beliefs and see things from a new perspective. Above all, Alexis karpouzos continually calls to us to wake up and explore the mysteries within our own selves, i.e the mysteries of universe. (shrink)

The main aim of our paper is to identify the potential limits of Socratic dialogue in moral education. These limits will be identified using a) the original ancient writings preserving several versions of Socrates’ dialogue, and b) modern writing on the Socrates’ dialogue in moral education. We will determine whether these limits are to be found in the writing of Plato or Xenophon, or rather in the problems and paradoxes of this type of education. We assume that a historical (...) exploration of the original Socratic philosophy will help us to more easily identify the limits and problems in moral education. However, our intention is not to reject the Socratic dialogue as such, but merely to point out some of the potentially controversial aspects of its use in moral education. (shrink)

Definida como beleza lógica e forma do paradoxo, a ironia romântica de Friedrich Schlegel (1772-1829) assimila a antiga ironia socrática e a reinterpreta, inserindo-a como elemento central de sua teorização crítico-literária. O presente artigo analisa a ironia romântica, buscando situar sua alteração e abrangência no final do século XVIII, quando o conceito passa a significar metacrítica, reflexão filosófica, ruptura ficcional, distância estética e forma de exposição da arte literária. Defined as logical beauty and form of paradox, Friedrich Schlegel's (1772-1829) (...) romantic irony incorporates ancient Socratic irony and reinterprets it, inserting it as a nuclear element of his theorization on literary criticism. The current paper analyses the concept of romantic irony seeking to situate its alterations at the end of 18th century, when it changed its meaning for metacritics, philosophical reflexion, fictional rupture, aesthetical distance and form of art exposition. (shrink)

Phenomenology, as propounded by Edmond Husserl, is an important movements in the modern western philosophy, while sÅÙkhya and its application yoga are the ancient Indian philosophical disciplines or dar±ana. This is a comparative study of phenomenology with sÅÙkhya and yoga. As per my present understanding this project is now completed. I have organized the outcome of my study in the following four papers preceded by prolegomena: Prolegomena to the comparative study of Phenomenology and SaÙkhya 1, Consciousness in Phenomenology and (...) SÅÙkhya 2. ‘Nature’ (ontology) in Phenomenology and SÅÙkhya 3. Structures (cosmology) in Phenomenology and SÅÙkhya 4. ‘Terminal Transcendental Teleological Cause’ in Phenomenology and SÅÙkhya -/- The parallelism between the philosophical disciplines, so far removed historically, geographically and culturally from each other, which this study brought out, was not only fascinating but also extensive. Certain differences also have been critically brought out. Viewing phenomenology through the grid of sÅÙkhya, I found, elucidates phenomenology. In being viewed from the perspective of a philosophical school, as modern as that of phenomenology, the ancient Indian disciplines also stand to benefit. The comparative study can hope to introduce sÅÙkhya to those acquainted with phenomenology and vice versa. This presentation is an attempt to share the flavor of my findings. (shrink)

Mereological nihilism is the philosophical position that there are no items that have parts. If there are no items with parts then the only items that exist are partless fundamental particles, such as the true atoms (also called philosophical atoms) theorized to exist by some ancient philosophers, some contemporary physicists, and some contemporary philosophers. With several novel arguments I show that mereological nihilism is the correct theory of reality. I will also discuss strong similarities that mereological nihilism has with (...) empirical results in quantum physics. And I will discuss how mereological nihilism vindicates a few other theories, such as a very specific theory of philosophical atomism, which I will call quantum abstract atomism. I will show that mereological nihilism also is an interpretation of quantum mechanics that avoids the problems of other interpretations, such as the widely known, metaphysically generated, quantum paradoxes of quantum physics, which ironically are typically accepted as facts about reality. I will also show why it is very surprising that mereological nihilism is not a widely held theory, and not the premier theory in philosophy. (shrink)

This paper contends that Stoic logic (i.e. Stoic analysis) deserves more attention from contemporary logicians. It sets out how, compared with contemporary propositional calculi, Stoic analysis is closest to methods of backward proof search for Gentzen-inspired substructural sequent logics, as they have been developed in logic programming and structural proof theory, and produces its proof search calculus in tree form. It shows how multiple similarities to Gentzen sequent systems combine with intriguing dissimilarities that may enrich contemporary discussion. Much of Stoic (...) logic appears surprisingly modern: a recursively formulated syntax with some truth-functional propositional operators; analogues to cut rules, axiom schemata and Gentzen’s negation-introduction rules; an implicit variable-sharing principle and deliberate rejection of Thinning and avoidance of paradoxes of implication. These latter features mark the system out as a relevance logic, where the absence of duals for its left and right introduction rules puts it in the vicinity of McCall’s connexive logic. Methodologically, the choice of meticulously formulated meta-logical rules in lieu of axiom and inference schemata absorbs some structural rules and results in an economical, precise and elegant system that values decidability over completeness. (shrink)

It is known that the Big Bang theory was based on the concept of creation ex nihilo, after ancient Greek philosophers. In this paper, we will make few remark on the concept of creatio ex nihilo (as a commentary to a recent paper by Kalachanis, Athanasios Anastasiou, Ioannis Kostikas, Efstratios Theodossious and Мilan S. Dimitrijevi), as well as two other approaches, i.e. Intelligent Design and Emergence Theory by Clayton/Yong. As continuation of our recent paper to appear in forthcoming issue (...) of J. Asia Mathematika, we argue that beside the above three approaches, a new concept called creatio ex-rotatione offers a resolution to the long standing disputes between beginning and eternity of the Universe. In other words, in this respect we agree with Vaas, i.e. it can be shown: “how a conceptual and perhaps physical solution of the temporal aspect of Immanuel Kant’s „first antinomy of pure reason“ is possible, i.e. how our universe in some respect could have both a beginning and an eternal existence. Therefore, paradoxically, there might have been a time before time or a beginning of time in time.” By the help of computational simulation, we also show how a model of early Universe with rotation can fit this new picture. (shrink)

Introduction Reza Davari Ardakni, the Iranian contemporary philosopher, distinguishes development from Western modernity; in that it considers modernity as natural and organic changes that Europe has gone through, but sees development as a planned design for implementing modernity in other countries. As a result, the closedness of development concerns only the developing countries, not Western modern ones. Davari emphasizes that the Western modernity has a universality that pertains to a unique reason and a unified world. The only way of thinking (...) in this world is a philosophical thought based on human self-centered reason, and given the pervasiveness of Western civilization. Therefore, Davari does not consider Westernization as mere imitation of Western customs and methods, but rather as a way of existence in the world. Westernization is a subjective view of the world and beings. Westernization is not optional, enabling non-Western people to avoid it. According to the Westernization scenario, the world today is entirely Westernized, and Davari considers Westernization as the inevitable fate of the people of this era, seeing two alternatives for them, both of which ultimately lead to the same destination, which is to embrace development; either they seize the power of science and technology and join the process of global modernization and participate in it, or they become subdued by this process and accept it without participation. Davari regards the first type of Westernization as active and the second type as passive. Problematique Therefore, underdevelopment is not a concept of the ancient world, nor even of a world between the ancient and the modern, or on the threshold of modernization. Underdevelopment is a condition of suspension and timelessness and being exposed to modernization. To escape the paradox of underdevelopment, which is the inevitable historical fate of non-modernized societies, Davari sees no way out other than embracing development. In other words, Westernized societies, which have become confused due to modernization, have no escape route other than turning to development. Therefore, some critics of Davari accuse the theory of Westernization of being a theoretical rupture. M. T. Tabatabaei, by rejecting the theoretical rupture in the theory of Westernization, believes that in the argument of Davari, we are only faced with a shift from a philosophical to an intellectual level. Tabatabaei, by avoiding providing a philosophical response to the critics of the theoretical rupture, believes that the introduction of active Westernization and collaboration in science and technology as a solution to escape from underdevelopment conditions, is only a shift from a philosophical level to an intellectual level and does not involve a rupture. Therefore, it seems that the philosophical issue of how or the possibility of escaping from underdevelopment conditions is still an open non answered problem. In this study, seeking a philosophical answer to this problem, an attempt has been made to summarize Davari's definitions of development, underdevelopment, participation in the world of science, and the role of humanities and social sciences in development, using his writings and speeches. It is proposed that a way to escape from the clesedness of development based on Davari's views, is to make use of analytical method with emphasizing on concepts and theories of the philosophy and metaphysics of science. Argument According to Davari, the social and human sciences that are responsible for development planning in underdeveloped societies must consider the characteristics of underdevelopment in order to facilitate the transition to more favorable conditions. Davari identifies the following conditions for successful development: 1) replacing tradition with science as the organizing and coordinating principle in society, 2) recognizing the universality of philosophy and science of the Western modernity and the impossibility of blindly imitation and adopting it, 3) inevitability of actively engaging and interacting with development, 4) recognizing the internal dynamics of scientific progress and avoiding authoritarian control, and 5) promoting free participation in the scientific paradigms. Therefore, Davari suggests the following steps towards development: 1) recognizing and understanding the problems of society and the local ecosystem, 2) understanding the philosophical and cultural foundations of Western civilization, 3) understanding the historical context and paradigms of science, 4) understanding the philosophical and metaphysical foundations of science, 5) recognizing the intellectual and philosophical capacities of our own community, and 6) reflecting our own philosophical and metaphysical assumptions in the scientific world in a way that is compatible with scientific methods. Given the motivations for change in science at both the global and national levels, including the emergence of heterodox or indigenous sciences, and the inevitable nature of development, Davari points to the possibility of a path between absolute rejecting or accepting the mainstream social and human sciences. However, this path is challenging and contingent upon the aforementioned conditions and steps of transition. Conclusion It is necessary to seek this path within the realm of the philosophy and metaphysics of science, particularly in the origins and foundations of the social and human sciences. Research in the metaphysics and philosophy of the social sciences provides the opportunity for active scientific engagement in the scientific paradigms and a reconsideration of the foundations of science, allowing for different philosophical foundations while are compatible with scientific methods. Successfully finding a path between absolute rejecting or accepting the existing social sciences will lead to an internal transformation within the field of science and, in fact, will advance the boundaries of knowledge. Therefore, it is possible, while adhering to the conditions of transition and actively participating in the world of science and technology, and accepting the unity of modernity and avoiding selectivity and imitation, to search for a way to overcome the closedness of development through a reconsideration of the philosophical and metaphysical foundations of science, while recognizing our own intellectual heritage and critically assessing Western science and technology. (shrink)

Diogenes Laertius (8.63-6) preserves a fascinating account of the Presocratic philosopher Empedocles' life. There, drawing on evidence from Aristotle, Xanthus, and Timaeus of Tauromenium, the biographer provides several anecdotes which are meant to demonstrate how Empedocles had, contrary to expectation, been a democratic philosopher - a paradox of itself in Ancient Greece. This article unpacks the complex web woven by Diogenes and argues that there is no good reason to assume that Empedocles was indeed a democratic philosopher, and (...) moreover, that neither Xanthus nor Aristotle thought him so. Indeed, what Diogenes actually preserves for us is the Hellenistic biographer Timaeus' critical dialectical engagement with the versions Aristotle and Xanthus, in his anachronistic bid to render Empedocles a democratic hero. (shrink)

In this paper I argue that we can solve the interpretation problem of quantum mechanics and the question of ontology of Quantum Field Theory on the basis of simple metaphysical position: The connection of the phase space with the ancient Theory of Logi of Beings, which is, by giving ontological meaning to the entities which "live" at the phase space, the Hamiltonian or Lagrangian formalism. There is a physical subject of such functions and it is the logos of a (...) being. Therefore we can refer to the logical space as the total sum of logi of being. The result of this position is that we can attribute to the wave function a physical meaning, a special case of logos of a being and also give an ontological meaning at a quantum field. The developed metaphysical scheme can interpret the quantum paradoxes, by using the commonly accepted mathematical formalism. It can also interpret certain issues of Quantum Field Theory, although further study of this topic is necessary. (shrink)

‘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)

In the times where the predominant description of the world has become that of the so-called “post-truth” reality, all the questions on the possibilities of leading a fulfilled life, the life of εὐδαιμονία, seem to have become irrelevant, if not unattainable. This is due to the reason that εὐδαιμονία, as such, intrinsically involves a connection with the truth and the universal. On the other hand, the concept of a fulfilled life should not exclude subjective happiness. The latter has always been (...) intertwined with the concept of pleasure. Nonetheless, what the contemporary world-view has to offer is not at all the compound of pleasure and truth, the dialectics of particular and the universal. Instead, it is a paradigm of life led by undifferentiated particular pleasures, to be desired and pursued for the sole purpose of their being pleasurable. Paradoxical as it may seem, the issue is not a new one. The first aim of this paper is to critically assess the Epicurean concept of pleasure. Rather than taking an a priori moralistic stance, I intent to point out that the concept in question is intrinsically, i.e., theoretically problematic. My second aim is to critically analyze the hedonistic world-view as such assessing it primarily as a political attitude. In addition, I hope to show that in contrast to ancient hedonism, which I regard as a type of unintentional individual escapism, contemporary hedonism has transformed into a systematically induced and politically desired ideology of activism prevention. Phrased in the context of Platonic terminology, it has become the discourse of the Cave. Thus, beginning with the sources analysis, the paper is mainly conceived as a critique of an idea targeting both its early and its ultimate manifestations. (shrink)

The tragic death in Tolstoy's writings has helped both Max Weber and György Lukács in characterizing the modern pathos as a tragic contemplation of the emptiness of life. Through Tolstoy's readings, Weber and Lukács found an interesting source of denying arts and modern sciences autonomy, considering, from the aesthetics sphere, the meaningless of this new immanent reality. Both has assumed Tolstoy main theme from the same perspective, contrasting ancient and modern worldviews. Max Weber presented this theme in his disenchantment (...) of world theory and Lukács, in a very similar way, following the paradox of religious needing as a mainline. -/- O tema da morte trágica, presente nos escritos de Liev Tolstói, auxiliou tanto a Max Weber como a György Lukács a caracterizarem o pathos moderno de pressentimento da morte como uma contemplação do vazio. Weber e Lukács encontraram, através das leituras de Tolstói, uma interessante maneira de questionar a autonomia da arte e da ciência moderna, considerando pela esfera estética, como se mostra sem sentido a recente realidade imanente. Ambos assumiram o tema central das obras de Tolstói segundo uma mesma imagem, derivada do contraste entre o mundo antigo e o moderno. Max Weber adequou esse tema a sua teoria do desencantamento do mundo e Lukács, de modo muito semelhante, seguindo seu conceito do paradoxo da necessidade religiosa. (shrink)

Eighteenth-century art historian Johann Joachim Winckelmann (1717-1768) shared with Hegel a profound admiration for the art and culture of ancient Greece. Both viewed ancient Greece as, in some sense, an ideal to which the modern world might aspire—a pinnacle of spiritual perfection and originality that contemporary civilization might, through an understanding of ancient Greek culture, one day equal or surpass. This rather competitive form of nostalgia suggests a paradoxical demand to produce an original and higher state of (...) culture through the imitation of another. In Hegel’s writings, this paradox goes beyond the relation of the modern world to the ancient world—he exposes the same paradox in ancient Greece’s relation to its own predecessors. The solution to the latter paradox—the possibility of the realization of ancient Greece as an original and self-contained civilization despite its cultural debts—would also, then, be the key to repeating the success of the ancient world in the modern, the overcoming of modern Europe’s cultural debt to the ancient world. The present essay examines how this paradox is revealed and resolved in the writings of Winckelmann and Hegel, and shows how this strategy of culture production—as imputed to the ancient world and aspired to in the modern—simultaneously attempts to justify and conceal a self-deceptive practice of cultural and political conquest. My focus will be on the two writers’ interpretations of ancient Greek art since, as I will suggest, their solution to the paradox of culture production turns out to be modeled upon the role of ancient Greek art in the invention and actualization of a cultural ideal of beauty, unity, and self-containment. (shrink)

Chrysippus often talks as if there is a third option when we might expect that two options in response to a question are exhaustive. Things are true, false or neither; equal, unequal, or neither; the same, different, or neither.. and so on. There seems to be a general pattern here that calls for a general explanation. This paper offers a general explanation of this pattern, preserving Stoic commitments to excluded middle and bivalence, arguing that Chrysippus employs this trichotomy move when (...) he wishes to argue that apparent contradictories are only contraries, and wishes to endorse a third option. This general explanation of the pattern of trichotomies sheds light on a number of interpretive puzzles, including on Chrysippus's response to the paradox of the cone. The purpose of these trichotomies is also discussed, and it is suggested that they originate from the dialectical context in which philosophical problems were posed. (shrink)

The theme of essential futility, absurdity, utter incomprehensibility of life and death is stressed in almost allthe writings of Albert Camus. Like Buddha he was shocked by the sight of human misery and mortality. Yet, paradoxically was attracted to the essential desirability of it. Although completely ruffled by the consciousness of an ambiguous and silent God, he was not unaware of “that strange joy that comes from a tranquil conscience”, a perfect inner harmony one experiences on attaining true knowledge. Upanishads (...) are a search for this very reality underlying the flux of things. Malraux, Sartre, and others had already developed this line of thought before Camus. What is essential and original in him is, firstly, that the world’s absurdity not a cause for despair, but on the contrary, a spur to happiness. And secondly, that , mortality and suffering actually enhance the value of life: they invite men to live more intensely. In addition to absurdity another subject the Upanishads insistently deal with is ethics, the purity of human conduct. Very much in the manner of the Existentialists, the Upanishads, aeons before, hold man himself responsible for his actions. Dr. Radhakrishnan, very aptly says that Existentialism is a new name for an ancient method. In Albert Camus and India Sharad Chandra has put forward a convincing comparative study of the two philosophies as expounded in their respective literatures. Her argument is that the parallel ideas found in the two views are not mere fortuitous conclusions but, either the result of seminal influence, or emanation of a common, deeper vision. Reading of the book will help the reader to form a firm opinion. Camus had read the Gita and had attended the lectures given by Swami Shraddhananda of the Ramakrishna Mission in Paris. (shrink)

ABSTRACT: Recently a bold and admirable interpretation of Chrysippus’ position on the Sorites has been presented, suggesting that Chrysippus offered a solution to the Sorites by (i) taking an epistemicist position1 which (ii) made allowances for higher-order vagueness. In this paper I argue (i) that Chrysippus did not take an epistemicist position, but − if any − a non-epistemic one which denies truth-values to some cases in a Sorites-series, and (ii) that it is uncertain whether and how he made allowances (...) for higher-order vagueness, but if he did, this was not grounded on an epistemicist position. (shrink)

A Fortiori Logic: Innovations, History and Assessments is a wide-ranging and in-depth study of a fortiori reasoning, comprising a great many new theoretical insights into such argument, a history of its use and discussion from antiquity to the present day, and critical analyses of the main attempts at its elucidation. Its purpose is nothing less than to lay the foundations for a new branch of logic and greatly develop it; and thus to once and for all dispel the many fallacious (...) ideas circulating regarding the nature of a fortiori reasoning. -/- The work is divided into three parts. The first part, Formalities, presents the author’s largely original theory of a fortiori argument, in all its forms and varieties. Its four (or eight) principal moods are analyzed in great detail and formally validated, and secondary moods are derived from them. A crescendo argument is distinguished from purely a fortiori argument, and similarly analyzed and validated. These argument forms are clearly distinguished from the pro rata and analogical forms of argument. Moreover, we examine the wide range of a fortiori argument; the possibilities of quantifying it; the formal interrelationships of its various moods; and their relationships to syllogistic and analogical reasoning. Although a fortiori argument is shown to be deductive, inductive forms of it are acknowledged and explained. Although a fortiori argument is essentially ontical in character, more specifically logical-epistemic and ethical-legal variants of it are acknowledged. -/- The second part of the work, Ancient and Medieval History, looks into use and discussion of a fortiori argument in Greece and Rome, in the Talmud, among post-Talmudic rabbis, and in Christian, Moslem, Chinese and Indian sources. Aristotle’s approach to a fortiori argument is described and evaluated. There is a thorough analysis of the Mishnaic qal vachomer argument, and a reassessment of the dayo principle relating to it, as well as of the Gemara’s later take on these topics. The valuable contribution, much later, by Moshe Chaim Luzzatto is duly acknowledged. Lists are drawn up of the use of a fortiori argument in the Jewish Bible, the Mishna, the works of Plato and Aristotle, the Christian Bible and the Koran; and the specific moods used are identified. Moreover, there is a pilot study of the use of a fortiori argument in the Gemara, with reference to Rodkinson’s partial edition of the Babylonian Talmud, setting detailed methodological guidelines for a fuller study. There is also a novel, detailed study of logic in general in the Torah. -/- The third part of the present work, Modern and Contemporary Authors, describes and evaluates the work of numerous (some thirty) recent contributors to a fortiori logic, as well as the articles on the subject in certain lexicons. Here, we discover that whereas a few authors in the last century or so made some significant contributions to the field, most of them shot woefully off-target in various ways. The work of each author, whether famous or unknown, is examined in detail in a dedicated chapter, or at least in a section; and his ideas on the subject are carefully weighed. The variety of theories that have been proposed is impressive, and stands witness to the complexity and elusiveness of the subject, and to the crying need for the present critical and integrative study. But whatever the intrinsic value of each work, it must be realized that even errors and lacunae are interesting because they teach us how not to proceed. -/- This book also contains, in a final appendix, some valuable contributions to general logic, including new analyses of symbolization and axiomatization, existential import, the tetralemma, the Liar paradox and the Russell paradox. (shrink)

The derivative is a basic concept of differential calculus. However, if we calculate the derivative as change in distance over change in time, the result at any instant is 0/0, which seems meaningless. Hence, Newton and Leibniz used the limit to determine the derivative. Their method is valid in practice, but it is not easy to intuitively accept. Thus, this article describes the novel method of differential calculus based on the double contradiction, which is easier to accept intuitively. Next, the (...) geometrical meaning of the double contradiction is considered as follows. A tangent at a point on a convex curve is iterated. Then, the slope of the tangent at the point is sandwiched by two kinds of lines. The first kind of line crosses the curve at the original point and a point to the right of it. The second kind of line crosses the curve at the original point and a point to the left of it. Then, the double contradiction can be applied, and the slope of the tangent is determined as a single value. Finally, the meaning of this method for the foundation of mathematics is considered. We reflect on Dehaene’s notion that the foundation of mathematics is based on the intuitions, which evolve independently. Hence, there may be gaps between intuitions. In fact, the Ancient Greeks identified inconsistency between arithmetic and geometry. However, Eudoxus developed the theory of proportion, which is equivalent to the Dedekind Cut. This allows the iteration of an irrational number by rational numbers as precisely as desired. Simultaneously, we can define the irrational number by the double contradiction, although its existence is not guaranteed. Further, an area of a curved figure is iterated and defined by rectilinear figures using the double contradiction. (shrink)

When considering the possibility of a vision of God, a paradox seems to appear in John Scot-tus Eriugena’s philosophy. On the one hand, God is said to be invisible, unthinkable, inac-cessible to any creature, be it rational or intellectual, man or angel. On the other hand, a vision of God, a contemplation, is said to be the reward of all nature in paradise, and this very contemplation the condition of all future souls. The solution of this false problem is (...) to be found in the notion of theophany. Its analysis and interpretation are the core of this article. Eriugena finds this ancient greek term, which means literally ‘manifestation of God’, in the corpus of the Pseudo-Dionysus and promptly uses it in a new philosophical way. Four different meanings of theophany may be found in John Scottus’ writing. They are: the manifestation of the first principle, the sensible world, the Christ, and finally human nature deified. This order encompasses Eriugena’s whole philosophical system: everything is a theophany, and the creatures participate in the creation of the creator. A theophany is thus a manifestation of God, as in a manifestation of himself to himself. According to Eriugena, God as principle isn’t yet a being; for God to be, he has to show himself and see himself through humankind. (shrink)

What is so special and mysterious about the Continuum, this ancient, always topical, and alongside the concept of integers, most intuitively transparent and omnipresent conceptual and formal medium for mathematical constructions and the battle field of mathematical inquiries ? And why it resists the century long siege by best mathematical minds of all times committed to penetrate once and for all its set-theoretical enigma ? -/- The double-edged purpose of the present study is to save from the transfinite deadlock (...) of higher set theory the jewel of mathematical Continuum -- this genuine, even if mostly forgotten today raison d'etre of all set-theoretical enterprises to Infinity and beyond, from Georg Cantor to W. Hugh Woodin to Buzz Lightyear, by simultaneously exhibiting the limits and pitfalls of all old and new reductionist foundational approaches to mathematical truth: be it Cantor's or post-Cantorian Idealism, Brouwer's or post-Brouwerian Constructivism, Hilbert's or post-Hilbertian Formalism, Goedel's or post-Goedelian Platonism. -/- In the spirit of Zeno's paradoxes, but with the enormous historical advantage of hindsight, we claim that Cantor's set-theoretical methodology, powerful and reach in proof-theoretic and similar applications as it might be, is inherently limited by its epistemological framework of transfinite local causality, and neither can be held accountable for the properties of the Continuum already acquired through geometrical, analytical, and arithmetical studies, nor can it be used for an adequate, conceptually sensible, operationally workable, and axiomatically sustainable re-creation of the Continuum. -/- From a strictly mathematical point of view, this intrinsic limitation of the constative and explicative power of higher set theory finds its explanation in the identified in this study ultimate phenomenological obstacle to Cantor's transfinite construction, similar to topological obstacles in homotopy theory and theoretical physics: the entanglement capacity of the mathematical Continuum. (shrink)

This book is a PhD dissertation and a very personal book at the same time. It asks the question whether society can and should be a point of orientation ("Bezugspunkt") for the human individual. Please note, that this cannot be a scientific book: If sociology is defined as society observed by society (or by sociologists, who are the agents of society), society observed by a single person (and for the aim of this single person) cannot be scientific. This is also (...) true if the researcher adheres to reason and scientific methodology: observations and understanding created by the human individual for its own private purposes simply are not scientific because they lack universality. "Bezugspunkt Gesellschaft" studies a number of different strains of sociology (and their scientific representatives, e.g. Pierre Bourdieu, Niklas Luhmann, Ralf Dahrendorf, Norbert Elias, Berger/Luckmann) in order to find out what it is that sociology studies? Is sociology the study of a society of human beings? Or is it true that society does not consist of human beings, but, as Luhmann claims, of acts of communication? Or is it true, as Bourdieu claims, that society consists of the instances of freedom abandoned half willingly, half out of habitude, by human individuals like in the case of a coffeehouse waiter who over time has just given up the idea that he could be anything else than a coffeehouse waiter. This book was inspired by a deconstructivist method of analysis in the field of literary theory where researchers state that it is of no interest what the author of a book wanted to say. Instead we should treat the work of literature as if the society of the author's epoch had written it. This theoretical "murder" of the human being in the form of the authors of works of literature in literary theory might have its analogy in sociology: Maybe sociology is also, like literary theory, not about people? However, if sociology is not about people - what can sociology teach us, us people? The book looks at different concepts of society throughout history, starting from the ancient concept that society is community, or that it is a circle of friendships, to more modern and dystopian concepts like that society is some kind of unhuman society. The book ends with the "Balzac machine", representing the incredibly talented and prolific French author Honoré de Balzac as a person who was an expert in the study of society and entirely blind to the phenomenon of society at the same time. The paradox of Balzac manifested itself in the fact that he literally worked himself to death in an attempt to gain society's recognition. (shrink)

The production of sound by the machinery of change is a viral element in the problems of civilization. Conceptual historical paradox involving mind and matter as the recurring source of the problems of civilization is elaborated to expose a space reducing friction residing at the border of conceptual and empirical interpretation involving cause and effect rather than physical form. A visually based mathematical-physical form, is elaborated and discussion, based on a philosophy of motion, volume and processes that is indivisible, (...) unmoved by the willed power of the discourse, is evolved in an analogy to interpreted ancient mathematics of Euclid. (shrink)