I discuss the "theory of recollection" in Plato's Meno (81a–86c). Socrates' comments on the "geometry lesson" (85b8–86c3) are used to support the claim that, in a Socratic dialogue, we ought to differentiate between between non-committal and committal questions (= those implying a commitment of the questioner). It is then argued that the "theory of recollection" is no Platonic doctrine: Socrates uses Pythagorean material against Meno who is acquainted with the Pythagorean tradition and whose eristical argument against the possibility (...) of learning is meant to be refuted by the paradoxical consequences about the slave-boy's learning Meno is made to admit. (shrink)

This paper discusses passages in Plato’s Phaedo which seem to contradict each other: at Phaedo 65a-d and at 66e-67a Plato seems to rule out that sense perception can be of any help in the acquisition of knowledge, whereas at Phaedo 74b-75a it is claimed that we get our knowledge of (the form of) equality only via the perception of equal things. I argue that the incompatibility of these passages is only apparent since in the first group of texts (all taken (...) from Socrates’ so-called apology) Socrates is made to represent the ‚true philosophers‘ (probably the Pythagoreans), whereas in the latter passages (from the recollection argument) he speaks in propria persona. I then discuss the question why Plato did insert in his dialogue a position which he does not share, and I finally argue that Plato did not believe in the recollection of the form of equality. (shrink)

I hope to show how Plato’s doctrines in these dialogues are meant to resolve questions in moral theory, by contrasting the theory of recollection, and the theory of desire, with Socratic theories of moral knowledge and motivation. These views of Socrates are parts of his general conception of virtue and moral knowledge as a craft ; I will outline the doctrines which belong to this general conception, and suggest some reasons why one of these doctrines leads Socrates (...) to another. First I will point to an important conflict between the theory of recollection in the Meno and Socratic views on moral knowledge, and to a further conflict between the account of desire in the Symposium and Socratic views on motivation. We will find that these two points of conflict are connected, and that Plato connects them in the Phaedrus. My aim is to present a plausible way of understanding certain Platonic doctrines; in the space available here I cannot argue for all the claims I make, but I hope the general picture will seem interesting enough to deserve more detailed defense or refutation. (shrink)

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Recent research suggests that the subjective feeling of conscious recollection is uniquely characterized by joint memory for several context features while merely familiar memories lack this property . In the present research we took the novel approach of extending the dual task paradigm to the simultaneous study of subjective retrieval experience and joint memory for two orthogonal context features. While dual task load during encoding lead to reductions in the frequency of the subjective experience of conscious recollection and reductions in (...) overall context memory, joint context memory was not affected. Furthermore, the relation of higher overall context memory for consciously recollected items than for familiar items was preserved even under dual task load. These results have import implications for theories of long-term feature binding and the processes involved in producing the experience of conscious recollection. (shrink)

This chapter first considers the estimates of how great the contribution of the Pythagoreans was to Plato's philosophy and how these views diverge substantially, and which vary across the range from ‘decisive’ to ‘insignificant’. It shows that Platonists were characterized by a benevolent attitude to Pythagoras and the Pythagoreans and an interest in their scientific, philosophical, and religious theories. Number doctrine is found in the testimonies of all three Platonists, but there is in them no picture of a Pythagorean philosophy (...) even remotely reminiscent of number doctrine. The Platonists reacted, not to a common Pythagorean doctrine, but to various theories of Pythagoras and his successors: Philolaus, Archytas, Ecphantus and Hicetas, et al. The chapter then considers Aristotle's reports on the Pythagoreans in his surviving works. (shrink)

Problem 2 at the 56th International Mathematical Olympiad asks for all triples of positive integers for which ab−c, bc−a, and ca−b are all powers of 2. We show that this problem requires only a primitive form of arithmetic, going back to the Pythagoreans, which is the arithmetic of the even and the odd.

: Some of the great physicists' belief in the existence of a connection between the aesthetical features of a theory (such as beauty and simplicity) and its truth is still one of the most intriguing issues in the aesthetics of science. In this paper I explore the philosophical credibility of a version of this thesis, focusing on the connection between the mathematical beauty and simplicity of a theory and its truth. I discuss a heuristic interpretation of this thesis, (...) attempting to clarify where the appeal of this Pythagorean view comes from and what are the arguments favoring its acceptance or rejection. Along the way, I sketch the historical context in which this heuristic interpretation gained credibility (the quantum crisis in physics in the 1920s), as well as the more general implications of this thesis for physicists' metaphysical outlook. (shrink)

The paper offers a running commentary on ps-Archytas’ On Intellect and Sense Perception (composed ca. 80 BCE), with the aim to provide a clear description of Hellenistic/post-Hellenistic Pythagorean epistemology. Through an analysis of the process of knowledge and of the faculties that this involves, ps-Archytas presents an original epistemological theory which, although grounded in Aristotelian and Platonic theories, results in a peculiar Pythagorean criteriology that accounts for the acquisition and production of knowledge, as well as for the specific competences (...) of each cognitive faculty. (shrink)

Who were the true forerunners of the seventeenth-century theorists of innate ideas? Credit should go, not to Plato, despite the common label Platonist, but to the Stoics—or so this challenging new study claims. Plato’s celebrated doctrine of knowledge as recollection differed from these others’ theories not merely in its extravagant postulate of a prenatal knowing state but in many hitherto unrecognized ways, Scott argues. Among those who shared the belief that all men are endowed at birth with considerable epistemological resources, (...) Plato alone is a pessimist both about how few of us make any use of these—only those who make philosophical progress—and about the difficulty of unearthing these resources. Contrary to a prevalent view, Scott holds that Plato invokes recollection to explain not “ordinary learning,” the acquisition or application of everyday concepts such as equality or beauty, but “higher learning”—the province of the philosopher. (shrink)

Interpretations of recollection in the "Phaedo" are divided between ordinary interpretations, on which recollection explains a kind of learning accomplished by all, and sophisticated interpretations, which restrict recollection to philosophers. A sophisticated interpretation is supported by the prominence of philosophical understanding and reflection in the argument. Recollection is supposed to explain the advanced understanding displayed by Socrates and Simmias (74b2-4). Furthermore, it seems to be a necessary condition on recollection that one who recollects also perform a comparison of sensible particulars (...) to Forms (74a5-7). I provide a new ordinary interpretation which explains these features of the argument. First, we must clearly distinguish the philosophical reflection which constitutes the argument for the Theory of Recollection from the ordinary learning which is its subject. The comparison of sensibles to Forms is the reasoning by which we see, as philosophers, that we must recollect. At the same time, we must also appreciate the continuity of ordinary and philosophical learning. Plato wants to explain the capacity for ordinary discourse, but with an eye to its role as the origin of philosophical reflection and learning. In the "Phaedo", recollection has ordinary learning as its immediate explanandum, and philosophical learning as its ultimate explanandum. (shrink)

This chapter discusses how all the Pythagorean theories of the soul known to us are different. Only Simmias and Echecrates, the pupils of Philolaus, held identical views. The similarity among some of these theories can sometimes be explained by direct influence, but most often by the fact that many Pythagoreans shared the interpretation of the soul as the source of motion, which was the most widespread view amongst the Presocratics. It is also shown that there is neither a clear formulation (...) of number doctrine, nor tangible examples of it, in ancient Pythagoreanism. It transpires that the theory which was taken to be the essence of Pythagorean philosophy, a theory backed by the authority of Aristotle as the source and as a historian of philosophy, is, like many other elements of the ancient tradition about the Pythagoreans, a retrospective projection. (shrink)

Starohelenska etika nosila je u svom predanju protivrjecan odnos u razumjevanju vrline kao kljucnog pojma na kojem se zasniva polis i politika. Na izostravanju i objelodanjavanju ove protivrjecnosti umnogome je doprinjela sofistika koja je mjerilom racionalnosti uocavala ona filosofski nedovoljno razjasnjena mjesta u starohelenskoj slici svijeta. Da bi razrjesio protivrjecnost nastalu iz nacelnog tradicionalnog stava da se vrlina ne moze nauciti i stava da je vrlina povezana sa znanjem, Platon uvodi u razmatranje pojam sjecanja. Sjecanje postaje sredisnja tacka u Platonovom (...) prevazilazenju navedene protivrjecnosti. Razmatraju se dva oblika sjecanja, ono koje je univerzalno ali i time samo potencijalno dato, i ono koje je djelatno i koje vodi do teorije ideja koja odredjuje sta jeste vrlina. PR Projekat Ministarstva nauke Republike Srbije, br. 179049. (shrink)

In a unique rethinking of political transformation, Drucilla Cornell argues for the crucial role of psychoanalysis in social theory in voicing connection between our constitution as gendered subjects and social and political change.

This chapter contains sections titled: Recollection in the Meno Recollection in the Phaedo Recollection in the Phaedrus The Place of Recollection in Plato's General Theory of Knowledge.

The paper considers a generalization of Peano arithmetic, Hilbert arithmetic as the basis of the world in a Pythagorean manner. Hilbert arithmetic unifies the foundations of mathematics (Peano arithmetic and set theory), foundations of physics (quantum mechanics and information), and philosophical transcendentalism (Husserl’s phenomenology) into a formal theory and mathematical structure literally following Husserl’s tracе of “philosophy as a rigorous science”. In the pathway to that objective, Hilbert arithmetic identifies by itself information related to finite sets and series (...) and quantum information referring to infinite one as both appearing in three “hypostases”: correspondingly, mathematical, physical and ontological, each of which is able to generate a relevant science and area of cognition. Scientific transcendentalism is a falsifiable counterpart of philosophical transcendentalism. The underlying concept of the totality can be interpreted accordingly also mathematically, as consistent completeness, and physically, as the universe defined not empirically or experimentally, but as that ultimate wholeness containing its externality into itself. (shrink)

The paradox in Inquiry in Plato's Meno raises the fundamental epistemological problem of how one can come to know the basic and primary criteria of philosophical reasoning. Two key tenets of the Socratic search for definitions underlie the paradox. First, Socrates argues in both the Euthyphro and Hippias Major, that knowledge of particular instances of a given Form presupposes knowledge of the universal Form. Secondly, Socrates insists in the Meno that knowledge of essence logically preceeds knowledge of a Form's other (...) properties. Taken together, these two principles entail that one cannot gain knowledge of essence either by inductive or by deductive reasoning. Thus when Socrates seeks to determine the correct definition of the essence of virtue, he faces the apparently insuperable problem of having no rational method for establishing the proper definition. The paradox of inquiry states in effect that Socratic elenchus is absurd because it posits an essence both as the goal and the necessary starting point of rational argumentation. ;It is in the face of this serious skeptical dilemma that Plato articulates a profoundly original conception of reasoning. According to Plato, the solution to the paradox is that reasoning toward a definition of essences involves raising to explicit consciousness one's implicit knowledge of the very essence being sought. The description of this process as a recalling of knowledge actually acquired in an earlier life is intended only as a metaphor: it illuminates the process of bringing to full awareness what one already implicitly knows. Both the problem and the solution presented in the Meno exhibit the characteristic Platonic interrelationship of metaphysicis and epistemology. When Socrates asks for a definition of virtue in the Meno, he means to uncover the nature of a Form which exists separately from its examples. Socratic definition is neither a form of conceptual analysis nor an analysis of immanent characteristics in particulars. The failure of many commentators to appreciate the recollection theory often derives from a failure to comprehend these metaphysical dimensions of Plato's solution. (shrink)

This book explores the persistence of Pythagorean ideas in theoretical physics. It shows that the Pythagorean position is both philosophically deep and scientifically interesting. However, it does not endorse pure Pythagoreanism; rather, it defends the thesis that mind and mathematical structure are the grounds of reality. The book begins by examining Wigner's paper on the unreasonable effectiveness of mathematics in the natural sciences. It argues that, whilst many issues surrounding the applicability of mathematics disappear upon examination, there are some core (...) issues to do with the effectiveness of mathematics in fundamental physics which remain. The core issues are the existence of the laws of nature and our minds ability to fathom them, the use of formal mathematics in discovering things about the quantum world, the fact that deep mathematics is needed to describe fundamental physics, and the asymptotic nature of the quest for knowledge. These issues are the focus of the book. The author seeks to explain them within a metaphysical framework that takes mind and mathematical structure as its fundamental principles. The framework - called quantum monadology - combines ideas from Leibnizian monadology, set theory, and consistent histories quantum theory. (shrink)

In the twenty-fourth aporia of Theophrastus' Metaphysics, there appears an important, if ‘bafflingly elliptical’, ascription to Plato and the ‘Pythagoreans’ of a theory of reduction to the first principles via ‘imitation’. Very little attention has been paid to the idea of Platonic and ‘Pythagorean’ reduction through the operation of ‘imitation’ as presented by Theophrastus in his Metaphysics. This article interrogates the concepts of ‘reduction’ and ‘imitation’ as described in the extant fragments of Theophrastus’ writings – with special attention to (...) his Metaphysics – in an attempt to make sense of how, precisely, Theophrastus characterizes the metaphysical systems of Plato and the ‘Pythagoreans’. A fuller examination of Aporia 24 produces important new understandings of the nature of the Early Academy in the mid fourth century B.C.E. Specifically, by ascribing the concept of reduction via ‘imitation’ to Plato and the ‘Pythagoreans’, Theophrastus is actually describing theories about the structure of the universe held by an important Platonist competitor and the contemporary head of the Academy in Athens, Xenocrates of Chalcedon (396/5–314/13 B.C.E.), who (a) took it upon himself to establish a Platonic doctrine that could be associated with his master’s writings and (b) coordinated that doctrine with the philosophical precepts of the Pythagoreans. As a consequence, we are prompted to question Aristotle’s famous ascription of a theory of ‘imitation’ to the metaphysics of the genuine contemporary or recently deceased Pythagoreans (such as Philolaus of Croton or Archytas of Tarentum) and consider how Xenocrates’ writings on Plato and the ‘Pythagoreans’ might be informing both Theophrastus’ and Aristotle’s descriptions of the Platonic and Pythagorean philosophical system(s). (shrink)

In the light of Glucker's claim to have found in "De Divinatione" 1.115 a separate, unnamed Pythagorean-Platonic influence on Cicero, I examine the passage again with special reference to early Platonic interpretation. I find that the "Meno's" influence is wider than had been suspected, suggesting (i) the correspondence between the two types of 'natural' divination, dreams and ecstatic prophecy, and (ii) the kinship of souls. Posidonius' influence on the underlying interpretation of Platonic psychology is to be detected, insofar as he (...) would have read "Meno" 81d as a statement about all souls (together) having all available knowledge. However, Cratippus, Cicero's other main source, can be held to have directly borrowed from "Meno" 81d2-3 for his crowning argument ("De Div." 1.71), and it is likely that other material that uses 81d would also stem from Cratippus. A little is known elsewhere of early interpretation of the "Meno." Comparison with other early 'Platonist' material suggests strongly that we must look to Antiochus' school for this view that dreams regularly contain substantial truth explicable in terms of the nature of soul. This would lead once again to Cratippus, and nothing prevents our detecting his hand behind 1.115. Indeed 1.70, which Glucker uses to argue that Cratippus' dream-divining soul would literally have to leave the body, only makes good sense when understood metaphorically. (shrink)

Philosophers are generally somewhat wary of the hints of number mysticism in the reports about the beliefs and doctrines of the so-called Pythagoreans. It's not clear how much Pythagoras himself (as opposed to his later followers) indulged in speculation about numbers, or in more serious mathematics. But the Pythagoreans whom Aristotle discusses in the Metaphysics had some elaborate stories to tell about how the universe could be explained in terms of numbers—not just its physics but perhaps morality too. Was this (...) just fanciful speculation? Is it muddled as a theory of causality, as Aristotle suggests? I shall try to rehabilitate the passion for numbers by linking it with the notions of harmony and proportion in other thinkers who have a higher credibility factor in the philosophical stakes, and by showing that the desire to reduce quality to quantity, and to discover an exact science that can explain human life and meaning, is a serious philosophical passion that doesn't easily go away. And, after all, why should it? (shrink)

We re-examine the geometry lesson in the Meno, focusing on the interaction between interlocutors in the practice of recollection. We appeal to an analogy with interactive memory to suggest how Plato could think that inquiry could be successful even when participants have no awareness of what would satisfy their inquiry. This exposes a feature of recollection that needs no metaphysical assumptions, and which emphasises interaction. This feature, which has escaped the notice of philosophers, is more fundamental to the Meno than (...) a theory of innate ideas. Such a theory may be superimposed on the view about interactive memory we describe for the Meno, but to focus on Plato’s epistemological theory without first understanding what he has to say about the social dimensions of memory is putting the cart before the horse. (shrink)

Spinoza’s account of memory has not received enough attention, even though it is relevant for his theory of consciousness. Recent literature has studied the “pancreas problem.” This paper argues that there is an analogous problem for memories: if memories are in the mind, why is the mind not conscious of them? I argue that Spinoza’s account of memory can be better reconstructed in the context of Descartes’s account to show that Spinoza responded to these views. Descartes accounted for the (...) preservation of memories by holding that they are brain states without corresponding mental states, and that the mind is able to interpret perception either as new experience or as memory. Spinoza has none of these conceptual resources because of his substance monism. Spinoza accounts for memories as the mind’s ability to generate ideas according to the order of images. This ability consists in the connection of ideas, which is not an actual property, but only a dispositional one and thus not conscious. It is, however, grounded in the actual property of parts of the body, of which ideas are conscious. (shrink)

In lieu of an abstract, here is a brief excerpt of the content:Reviewed by:Logos and Alogon: Thinkable and Unthinkable in Mathematics, from the Pythagoreans to the Moderns by Arkady PlotnitskyNoam CohenPLOTNITSKY, Arkady. Logos and Alogon: Thinkable and Unthinkable in Mathematics, from the Pythagoreans to the Moderns. Cham: Springer, 2023. xvi + 294 pp. Cloth, $109.99The limits of thought in its relations to reality have defined Western philosophical inquiry from its very beginnings. The shocking discovery of the incommensurables in Greek mathematics (...) not only reintroduced these limits with greater force but also instigated two different forms of coping with the unthinkable in Western philosophy, mathematics, and science. As Arkady Plotnitsky sets forth, in response to the incommensurability crisis in the ancient Greek intellectual world, there appeared two different attitudes toward the alogon, that is, the unthinkable or irrational. Plato and his followers sought to overcome the unthinkable, of which the incommensurables in mathematics are only an example, through philosophy. In contrast, the Pythagoreans continued to hold on to mathematics as the primary means of knowing the world, but put a larger emphasis on geometry. Plotnitsky [End Page 359] claims that by not putting aside the primacy of mathematics, the Pythagorean shift from arithmetic to geometry established in Western thought a certain tolerance toward the unthinkable within the realm of the thinkable, “a possibility of the alogon in the logos.” Until modern times this remained no more than a possibility. However, in modern mathematics and mathematical physics Plotnitsky identifies a certain fulfillment of this potential, a “radical Pythagorean mathematics.” In his comprehensive and thought-provoking study, Plotnitsky recounts the development of such radical modern Pythagoreanism, not only to tell its history but also to suggest that the unthinkable is a condition of possibility for thought, and that a proper recognition of this role it plays is crucial for the advancement of mathematical thinking and thinking in general.Plotnitsky begins by portraying in broad strokes the two defining characteristics of radical Pythagorean mathematics: the presence of the unthinkable within mathematical thought itself, and the interplay of algebra and geometry. Relying on an extensive knowledge of the history of modern mathematics and physics, in the first two chapters of the book Plotnitsky gradually demonstrates the key role that the alogon plays in some theories of modern mathematical thought, such as Gödel’s incompleteness theorems and quantum mechanics. He also presents and clarifies his own conception of the history of Western thought as a creative process of concept-forming. By creating rather than discovering concepts, great mathematicians break new ground for thinking. The book as a whole argues in length for these two main theses.In chapter 3, the author addresses the thought of Bernhard Riemann to make the case that Riemann’s mathematical thought puts an emphasis on creative conceptual thinking and is not defined merely by calculations or logic. Such thinking is problem-posing rather than axiomatic. Riemann’s central innovation in this respect is the concept of manifold (Mannigfaltigkeit), which enabled him to think anew space and geometry in a radical non-Euclidean fashion, implying an infinite number of possible geometries. Plotnitsky argues—borrowing Deleuze and Guattari’s terminology—that this opened up a “plane of immanence,” which is to say that Riemann created a concept-generating movement of thought. However, we cannot grasp the generation of concepts in modern mathematics without giving proper attention to the interplay of algebra and geometry that defines it. Chapter 4 demonstrates this interweaving of the two fields by recounting the history of the idea of the curve in modernity, from the analytic geometry and calculus of Fermat and Descartes to its modification in the concept of a Riemann surface, up to its more recent developments in the algebraic geometry of Weil and Grothendieck. It gives a historical account of the algebraization of the curve that at the same time brings into relief the irreducible geometrical aspect, continuity, of all modern mathematical conceptualizations of the curve.The next two chapters provide further case studies. Chapter 5 expands and solidifies the argument of chapter 2. It discusses three examples of mathematical practice, each displayed by a pair of important [End Page 360] mathematicians: Abel and Galois, Lobachevsky and Riemann, Weil and Grothendieck. Each case... (shrink)

Recollection is an intellectual activity through which fundamental differences of experience, either between a plurality of individuals or within one individual at different stages of development, are comprehended and internally resolved. Together with the process of natural dialectic, recollection is the basis of Hegel’s theory of education and cultural solidification. It would, of course, be quite impossible in a single essay to enter into all the details and ramifications of this theory, and so we shall deal only with (...) the basic concept. Moreover, we shall emphasize the role of the individual, not so much to counter the gross miscomprehensions of Hegel’s thought which result when the activity of cultural enlightenment is generalized and ascribed to conceptually mystified world-historical processes, but simply to provide the proper arena for the functioning of this activity. For it is always the individual who internalizes the elaborated wealth of human spiritual capacities as best he can, and who through so doing is materially empowered to promote the education of others in turn. (shrink)

This book traces the development of Plato's theory in its historical context, from the Socratic conception of virtue, knowledge and moral motivation to the revised Platonic conception, including the Theory of recollection, the Theory of forms, Platonic love, and the divisions of the soul.

This paper argues that Plato’s Meno does not offer evidence for a belief, commonly attributed to Plato, that we when learning something recollect what we learn from previous existences. This “theory of recollection” is a construct based on a reading of the relevant passages in the Meno which does not take into account the dialectical aspect of Socrates’ discussion with his interlocutor. And in one passage (81e3) it is based on a variant reading for which a better and better (...) attested reading is available. The reference to recollection is used to make Meno agree to an absurd position. (shrink)

Reading Hegel retrieves Hegelian speculative experience for literary theory. The relationship between Hegel and literary theory has for a long time been both contested and paradoxical. On the one hand, "theory" is often skeptical of all that Hegel ostensibly stood for: idealism, systematicity, and identity at the expense of difference. Yet, in spite of itself, literary theory is taken to owe a profound debt to Hegel's philosophy. Robert Lucas Scott's book complicates this account and argues that (...) literary theory has made the mistake of abstracting Hegel's thought from its more dynamic presentation in Hegel's writings, reducing "Hegel" to a series of propositions or positions. Literary theory, Scott argues, misses what is perhaps the greatest innovation of Hegel's philosophy: a presentation of experience that begins precisely by setting aside all preconceptions or prior assumptions. It is on this point that Hegel's philosophy itself approaches literature: its content cannot be simply abstracted from the singular experience of reading it. Only through a mode of reading alive to speculative experience can literary theory become truly Hegelian. Scott's exposition of Hegel offers a model of reading with relevance beyond philosophy: one that is critical without pretensions of mastery and detachment and that honors the singularity of the reading experience without succumbing to the subjectivism of the "postcritical." The book also includes engagements with the work of Luther, Kant, Marx, Gillian Rose, Fredric Jameson, Robert Brandom, Catherine Malabou, and more in its recovery of Hegel's thought for a critical understanding of our time. (shrink)

This essay argues for a formative, and not simply abstract, aspect to the philosophy of religion by attending to the practices of writing employed in Søren Kierkegaard’s pseudonymous work Repetition . By locating this text within an ethical tradition that focuses upon the practices that form subjects, rather than simply the formulation of a theory, its seemingly literary performances can be viewed as exercises. In particular, this text deploys and transforms the Stoic practices of self writing, in the form (...) of keeping notebooks and letter writing, so as to cultivate capabilities. This indirect ethical instruction does not, however, lead to the formation of autonomous ethical subjects, but to the cultivation of capabilities that are only possible in the relational space of vulnerability, service and dependence. (shrink)

Carroll Izard’s theoretical and empirical work has played a preeminent role in energizing the renascence in the study of the emotions and emotional development in normality and pathology. A brief historical overview of his career is presented. Izard’s differential emotions theory (DET) has exerted influence in a number of domains and disciplines. Illustrations are provided from research and prevention in developmental psychology and developmental psychopathology. Personal recollections of Cal Izard are provided showing that Izard is not only an influential (...) theoretician and researcher, but also a wonderful emotional being. (shrink)

Based on a new critical edition of Aristotle's "De Memoria" and two interpretive essays, this book challenges current views on Aristotle's theories of memory ...

A new form of the Hyperbolic Pythagorean Theorem, which has a striking intuitive appeal and offers a strong contrast to its standard form, is presented. It expresses the square of the hyperbolic length of the hypotenuse of a hyperbolic right-angled triangle as the “Einstein sum” of the squares of the hyperbolic lengths of the other two sides, Fig. 1, thus completing the long path from Pythagoras to Einstein. Following the pioneering work of Varičak it is well known that relativistic velocities (...) are governed by hyperbolic geometry in the same way that prerelativistic velocities are governed by Euclidean geometry. Unlike prerelativistic velocity composition, given by the ordinary vector addition, the composition of relativistic velocities, given by the Einstein addition, is neither commutative nor associative due to the presence of Thomas precession. Following the discovery of the mathematical regularity that Thomas precession stores, it is now possible to extend Thomas precession by abstraction, (i) allowing hyperbolic geometry to be studied by means of analogies that it shares with Euclidean geometry; and, similarly (ii) allowing velocities and accelerations in relativistic mechanics to be studied by means of analogies that they share with velocities and accelerations in classical mechanics. The abstract Thomas precession, called the Thomas gyration, gives rise to gyrovector space theory in which the prefix gyro is used extensively in terms like gyrogroups and gyrovector spaces, gyroassociative and gyrocommutative laws, gyroautomorphisms, gyrotranslations, etc. We demonstrate the superiority of our gyrovector space formalism in capturing analogies by deriving the Hyperbolic Pythagorean Theorem in a form fully analogous to its Euclidean counterpart, thus contrasting it with the standard form in which the Hyperbolic Pythagorean Theorem is known in the literature. The hyperbolic metric, which supports the Hyperbolic Pythagorean Theorem, has a dual metric. We show that the dual metric does not support a Pythagorean theorem but, instead, it supports the π-Theorem according to which the sum of the three dual angles of a hyperbolic triangle is π. (shrink)

This paper discusses an autobiographical approach to Critical Theory, an approach which, as I argue, can be found in Walter Benjamin′s work. The core idea is that remembering one′s own life within a certain culture provides a productive method for a differentiated critique of this culture. In order to explain and defend this I idea, I draw on resources from both analytic philosophy and Benjamin′s work. Along the way, I describe Benjamin′s distinctive mode of ideology critique, a mode of (...) critique that Habermas calls “rettende Kritik.” What is attractive about autobiographical recollection is that it provides precisely the kind of epistemic and evaluative perspective that is suitable for this subtle form of social criticism. Remembering one′s past can allow us to criticize past ideologies while simultaneously acknowledging that they may articulate valid ideals of the good life. (shrink)

This book is an attempt "to give a systematic account of the development of plato's theory of knowledge" (page vii). thus it focuses on the dialogues in which epistemological issues come to the fore. these dialogues are "meno", "phaedo", "symposium", "republic", "cratylus", "theastetus", "phaedrus", "timaeus", "sophist", "politicus", "philebus", and "laws". issues discusssed include the theory of recollection, perception, the difference between belief and knowledge, and mathematical knowledge. (staff).

Unlike Tocqueville's other writing, Recollections, which was never intended for publication, contained the internally contrary, multiple viewpoints characteristic of carnivalesque discourse. Its greater spontaneity may allow'us more easily to see some of the ways in which writing can undermine the intentions of the writer. In following the Recollections' treatment of the February revolution, the writing soberly sets out to embody the story of a deadly struggle between the bourgeoisie and the people over the issue of property but steadily veers off (...) in the direction first of irony, then satire, and finally carnival. Tocqueville's rhetorical ending shows him trying to turn his unruly text back into a cautionary tale of the moralistically ironic type. But the text keeps getting out of hand and dissolves moralism in a bath of satire and burlesque. (shrink)

The field of neutrosophic set theory and its applications has been rapidly expanding, particularly since the introduction of the journal "Neutrosophic Sets and Systems." New theories, techniques, and algorithms are being developed at a very high rate. One of the most notable trends in neutrosophic theory is its hybridization with other set theories such as rough set theory, bipolar set theory, soft set theory, hesitant fuzzy set theory, and more. Various hybrid structures like rough (...) neutrosophic sets, neutrosophic soft set, single valued neutrosophic hesitant fuzzy sets, among others, have been proposed in a short period. Neutrosophic sets have proven to be crucial tools across a wide array of fields including data mining, decision making, e-learning, engineering, medical diagnosis, social sciences, and beyond. -/- The third volume in the series “New Trends in Neutrosophic Theories and Applications” focuses on theories, methods, and algorithms for decision making, as well as applications involving neutrosophic information. Some topics introduce new sets such as the Pythagorean neutrosophic vague soft set, the triangular fuzzy penta-partitioned neutrosophic set, interval-valued neutrosophic b-open sets, and interval-valued neutrosophic b-closed sets. Other topics present applications in medical diagnosis, non-preemptive neutrosophic priority queues with uneven services (labeled as NM/NM/1), AHP in an interval neutrosophic set environment, MAGDM in a triangular fuzzy neutrosophic number environment, MAGDM in a pentapartitioned neutrosophic environment, the entropy-ARAS strategy in a single-valued neutrosophic number environment, and the MABAC strategy in a rough neutrosophic set environment. (shrink)

It is argued that recollection in Plato's "Meno" is used as a metaphor, though not one for a priori knowledge: the point of comparison is the analogy between the processes of learning in the sense of coming to know from an error and recollecting something one has forgotten. Recollecting in this sense as well as correcting an error implies the becoming aware of a lack of knowledge previously unnoticed. It is shown that the geometry lesson (82b9-85b7) is intended to bring (...) out this analogy. It is argued further that the error to be corrected by the staging of the geometry lesson is an error of Meno's concerning the nature of knowledge. It is finally argued that Socrates' speech in 81a5-d5 is a parody of a Gorgian speech and that the learning-is-recollection statement in this passage is an allegorical conceit in the manner of Gorgias and Empedocles. (shrink)

Greek Memories aims to identify and examine the central concepts underlying the theories and practices of memory in the Greek world, from the archaic period to Late Antiquity, across all the main literary genres, and to trace some fundamental changes in these theories and practices. It explores the interaction and development of different 'disciplinary' approaches to memory in Ancient Greece, which will enable a fuller and deeper understanding of the whole phenomenon, and of its specific manifestations. This collection of papers (...) contributes to enriching the current scholarly discussion by refocusing it on the question of how various theories and practices of memory, recollection, and forgetting play themselves out in specific texts and authors from Ancient Greece, within a wide chronological span, and across a broad range of genres and disciplines. (shrink)

In Ancient times, synesthesia was a form of perception sought after, as developed both by Pythagoras and by Aristotle. It was a degree of perception sought after for the perception of the divine. It was part of a definite aesthetics because art was supposed to permit access to synesthesia through very precise rules defined by Aristotle in his Rhetoric. Synesthesia was not an anomalous form of perception experienced by some writers only. It was supposed to be induced by certain masterpieces, (...) thus connecting the reader’s experience of synesthesia with the writer’s. The hypothesis of the present paper is that Nabokov knew those theories and that his knowledge of Ancient sources was not limited to Plato whom he quotes repeatedly in his interviews, but also comprised Aristotle. Not only did Nabokov know about that theory, some interviews, and some of his novels reveal a game with those sources and a quest for the reader’s synesthesia. The present article focuses on the two first pages of The Gift as a skillful implementation of Aristotle’s theory on synesthesia. (shrink)

이 논문은 헤겔이 『철학대계』의 표상 장 중 지능론에서 개진하는 ‘상기’의 개념을 다룬다. 지능, 즉 이론적 정신에 속하는 범주로서의 상기에 대한 헤겔의 이론을 고찰하는 작업이 제대로 이루어지기 위해서는 적어도 두 가지 비교 지점에 대한 선이해가 필요하다. 첫째, 지능의 한 단계로서의 상기는 하나의 미시적 범주로서, 헤겔의 정신철학 및 체계 전체의 변증법적 운동 방향을 특징짓는 거시적 차원의 상기 과정에서 일부분을 차지하는 하위단계를 의미한다. 그리고 이는 미시적 차원의 상기가 거시적 차원의 상기의 완성태에는 아직 이르지 못한다는 것을 동시에 의미한다. 둘째, 헤겔에게서 상기는 ‘기억’과도 범주적으로 구분된다. (...) 기억은 사유의 구성 요소인 ‘기호’를 그 기본 내용으로 하지만, 상기는 감각적대상의 존재와의 직접적 접촉에 의존하는 ‘직관’을 필수적 요소로 전제하기 때문이다. 이러한 체계적 맥락과 개념들 간의 상이성에 의거하여 필자는 1) 상기를 그 첫 번째 형태로 포함하는 ‘표상’에 대한 헤겔의 근본 입장을 ‘직관’과 ‘사유’와의 관계 및 그 비교의 준거틀이 되는, 인식 주체의 자발성의 강도를 염두에 두면서 고찰하고, 2) 지능론적 하위 범주로서의 상기의 세 국면, 즉 ‘심상’, ‘심상의 저장’ 및 ‘직관과 심상의 종합’을 그 내용과 과정을 중심으로 분석한 후, 3) 헤겔의 텍스트에 대해 제기할 수 있는 또 다른 쟁점들을 비판적으로 검토하는 순서로 이 논문을 구성하였다. (shrink)