Cauchy’s contribution to the foundations of analysis is often viewed through the lens of developments that occurred some decades later, namely the formalisation of analysis on the basis of the epsilon-delta doctrine in the context of an Archimedean continuum. What does one see if one refrains from viewing Cauchy as if he had read Weierstrass already? One sees, with Felix Klein, a parallel thread for the development of analysis, in the context of an infinitesimal-enriched continuum. One sees, with Emile Borel, (...) the seeds of the theory of rates of growth of functions as developed by Paul du Bois-Reymond. One sees, with E. G. Björling, an infinitesimal definition of the criterion of uniform convergence. Cauchy’s foundational stance is hereby reconsidered. (shrink)

A construction of the real number system based on almost homomorphisms of the integers $\mathbb {Z}$ was proposed by Schanuel, Arthan, and others. We combine such a construction with the ultrapower or limit ultrapower construction to construct the hyperreals out of integers. In fact, any hyperreal field, whose universe is a set, can be obtained by such a one-step construction directly out of integers. Even the maximal (i.e., On -saturated) hyperreal number system described by Kanovei and Reeken (2004) and independently (...) by Ehrlich (2012) can be obtained in this fashion, albeit not in NBG . In NBG , it can be obtained via a one-step construction by means of a definable ultrapower (modulo a suitable definable class ultrafilter). (shrink)

The Schur-Zassenhaus Theorem is one of the fundamental theorems of finite group theory. Here is its statement:Fact1.1 (Schur-Zassenhaus Theorem). Let G be a finite group and let N be a normal subgroup of G. Assume that the order ∣N∣ is relatively prime to the index [G:N]. Then N has a complement in G and any two complements of N are conjugate in G.The proof can be found in most standard books in group theory, e.g., in [S, Chapter 2, Theorem 8.10]. (...) The original statement stipulated one ofNorG/Nto be solvable. Since then, the Feit-Thompson theorem [FT] has been proved and it forces eitherNorG/Nto be solvable. (The analogous Feit-Thompson theorem for groups of finite Morley rank is a long standing open problem).The literal translation of the Schur-Zassenhaus theorem to the finite Morley rank context would state that in a groupGof finite Morley rank a normal π-Hall subgroup (if it exists at all) has a complement and all the complements are conjugate to each other. (Recall that a groupHis called aπ-group, where π is a set of prime numbers, if elements ofHhave finite orders whose prime divisors are from π. Maximal π-subgroups of a groupGare called π-Hall subgroups. They exist by Zorn's lemma. Since a normal π-subgroup ofGis in all the π-Hall subgroups, if a group has a normal π-Hall subgroup then this subgroup is unique.)The second assertion of the Schur-Zassenhaus theorem about the conjugacy of complements is false in general. As a counterexample, consider the multiplicative group ℂ* of the complex number field ℂ and consider thep-Sylow for any primep, or even the torsion part of ℂ*. LetHbe this subgroup.Hhas a complement, but this complement is found by Zorn's Lemma (consider a maximal subgroup that intersectsHtrivially) and the use of Zorn's Lemma is essential. In fact, by Zorn's Lemma, any subgroup that has a trivial intersection withHcan be extended to a complement ofH. Since ℂ* is abelian, these complements cannot be conjugated to each other. (shrink)

One of the purposes of this paper is to prove a partial Schur-Zassenhaus Theorem for groups of finite Morley rank.Theorem 2.Let G be a solvable group of finite Morley rank. Let π be a set of primes, and let H ⊲ G a normal π-Hall subgroup. Then H has a complement in G.This result has been proved in [1] with the additional assumption thatGis connected, and thought to be generalized in [2] by the authors of the present article. Unfortunately in (...) the last section of the latter paper there is an irrepairable mistake. Here we give a new proof of the Schur-Zassenhaus Theorem using the results of [2] up to the last section and a new result that we are going to state below.The second author has shown in [11] that a nilpotentω-stable group is the central product of a divisible subgroup and a subgroup of bounded exponent, generalizing a well-known result of Angus Macintyre about abelian groups [8]. One could ask a similar question for solvable groups: are they a product of two subgroups, one divisible, one of bounded exponent? One is allowed to be hopeful because of the well-known decomposition of the connected solvable algebraic groups over algebraically closed fields as the product of the unipotent radical and a torus. (shrink)

We classify irreducible actions of connected groups of finite Morley rank on abelian groups of Morley rank 3.

We examine Paul Halmos’ comments on category theory, Dedekind cuts, devil worship, logic, and Robinson’s infinitesimals. Halmos’ scepticism about category theory derives from his philosophical position of naive set-theoretic realism. In the words of an MAA biography, Halmos thought that mathematics is “certainty” and “architecture” yet 20th century logic teaches us is that mathematics is full of uncertainty or more precisely incompleteness. If the term architecture meant to imply that mathematics is one great solid castle, then modern logic tends to (...) teach us the opposite lesson, namely that the castle is floating in midair. Halmos’ realism tends to color his judgment of purely scientific aspects of logic and the way it is practiced and applied. He often expressed distaste for nonstandard models, and made a sustained effort to eliminate first-order logic, the logicians’ concept of interpretation, and the syntactic vs semantic distinction. He felt that these were vague, and sought to replace them all by his polyadic algebra. Halmos claimed that Robinson’s framework is “unnecessary” but Henson and Keisler argue that Robinson’s framework allows one to dig deeper into set-theoretic resources than is common in Archimedean mathematics. This can potentially prove theorems not accessible by standard methods, undermining Halmos’ criticisms. (shrink)

Cauchy's sum theorem is a prototype of what is today a basic result on the convergence of a series of functions in undergraduate analysis. We seek to interpret Cauchy’s proof, and discuss the related epistemological questions involved in comparing distinct interpretive paradigms. Cauchy’s proof is often interpreted in the modern framework of a Weierstrassian paradigm. We analyze Cauchy’s proof closely and show that it finds closer proxies in a different modern framework.

One of the twentieth century’s most brilliant and unconventional thinkers, Alexandre Kojève was a Russian émigré to France whose lectures on Hegel in the 1930s galvanized a generation of French intellectuals. Although Kojève wrote a great deal, he published very little in his lifetime, and so the ongoing rediscovery of his work continues to present new challenges to philosophy and political theory. Written in 1931 but left unfinished, Atheism is an erudite and open-ended exploration of profound questions of estrangement, (...) death, suicide, and the infinite that demonstrates the range and the provocative power of Kojève’s thought. Ranging across Heidegger, Buddhism, Christianity, German idealism, Russian literature, and mathematics, Kojève advances a novel argument about freedom and authority. He investigates the possibility that there is not any vantage point or source of authority—including philosophy, science, or God—that is outside or beyond politics and the world as we experience it. The question becomes whether atheism—or theism—is even a meaningful position since both affirmation and denial of God’s existence imply a knowledge that seems clearly outside our capacities. Masterfully translated by Jeff Love, this book offers a striking new perspective on Kojève’s work and its implications for theism, atheism, politics, and freedom. (shrink)

Depersonalization consists in a deep modification of the way things appear to a subject, leading him to feel estranged from his body, his actions, his thoughts, and his mind, and even from himself. Even though, when it was discovered at the end of the 19th century, this psychiatric condition was widely used to probe certain aspects of bodily awareness, and more specifically the sense of bodily ownership (SBO), it has been strangely neglected in contemporary debates. In this chapter, I argue (...) that because of three specific features, depersonalization raises some important challenges for current theories of the SBO. The first feature — call it “generality” — is that depersonalization does not only affect the sense of bodily ownership but also, typically, the sense of ``mental ownership’’ (SMO), the sense of agency or ``action ownership’’ (SOA), and the subject’s core sense of herself (CSS), that is, her awareness of herself as an I. The second feature is that except for the symptoms of depersonalization, depersonalized patients are hard to distinguish, psychologically, from normal subjects. This makes it hard to find psychological features that might explain their condition. The last feature, call it “fundamentality” is that the psychological features that do seem abnormal among depersonalized patients seem more likely to be explained by depersonalization than to explain it. These three features raise three challenges — the centrality challenge, the dissociation challenge, and the grounding challenge. Taken together, I will argue, these challenges suggest that the SBO depends on a form of phenomenal “mineness” that would mark my mental states as mine and that cannot be accounted for in sensorimotor, cognitive, or even affective terms. A phenomenal mineness that indeed seems to be psychologically primitive, and only accountable in neurophysiological terms. (shrink)

(2013). Does consciousness entail subjectivity? The puzzle of thought insertion. Philosophical Psychology: Vol. 26, No. 2, pp. 291-314. doi: 10.1080/09515089.2011.625117.

This paper offers an overview of the prospects and ethics of using AI to achieve human enhancement, and more broadly what we call intellectual augmentation (IA). After explaining the central notions of human enhancement, IA, and AI, we discuss the state of the art in terms of the main technologies for IA, with or without brain-computer interfaces. Given this picture, we discuss potential ethical problems, namely inadequate performance, safety, coercion and manipulation, privacy, cognitive liberty, authenticity, and fairness in more detail. (...) We conclude that while there are very significant technical hurdles to real human enhancement through AI, and significant ethical problems, there are also significant benefits that may realistically be achieved in ways that are consonant with a rights-based ethics as well. We also highlight the specific concerns that apply particularly to applications of AI for "sheer" IA (more realistic in the near term), and to enhancement applications, respectively. (shrink)

This paper considers the medium of videogames from a goodmanian standpoint. After some preliminary clarifications and definitions, I examine the ontological status of videogames. Against several existing accounts, I hold that what grounds their identity qua work types is code. The rest of the paper is dedicated to the epistemology of videogaming. Drawing on Nelson Goodman and Catherine Elgin's works, I suggest that the best model to defend videogame cognitivism appeals to the notion of understanding.

This is a commentary on Andrea Lavazza and Murilo Vilaça's article "Human Extinction and AI: What We Can Learn from the Ultimate Threat" (Lavazza & Vilaça, 2024). I discuss the potential concern that their proposal to create artificial successors to "insure" against the tragedy of human extinction might mean being too quick to accept that catastrophic prospect as inevitable, rather than single-mindedly focusing on avoiding it. I also consider the question of the value that we might reasonably assign to such (...) a future of artificial successors under the assumption that they do not enjoy phenomenal consciousness. (shrink)

According to what we will call subjectivity theories of consciousness, there is a constitutive connection between phenomenal consciousness and subjectivity: there is something it is like for a subject to have mental state M only if M is characterized by a certain mine-ness or for-me-ness. Such theories appear to face certain psychopathological counterexamples: patients appear to report conscious experiences that lack this subjective element. A subsidiary goal of this chapter is to articulate with greater precision both subjectivity theories and the (...) psychopathological challenge they face. The chapter’s central goal is to present two new approaches to defending subjectivity theories in the face of this challenge. What distinguishes these two approaches is that they go to great lengths to interpret patients’ reports at face value – greater length, at any rate, than more widespread approaches in the extant literature. (shrink)

Henri Bergson is primarily known for his work on time, memory, and creativity. His equally innovative interventions into politics and religion have, however, been neglected or dismissed until now. In the first book in English dedicated to Bergson as a political thinker, leading Bergson scholars illuminate his positions on core concerns within political philosophy: the significance of emotion in moral judgment, the relationship between biology and society, and the entanglement of politics and religion. Ranging across Bergson's writings but drawing mainly (...) on his last book, _The Two Sources of Morality and Religion_, the contributors consider Bergson's relevance to contemporary discussions of human rights, democratic pluralism, and environmental ethics. _Contributors._ Keith Ansell-Pearson, G. William Barnard, Claire Colebrook, Hisashi Fujita, Suzanne Guerlac, Vladimir Jankélévitch, Frédéric Keck, Leonard Lawlor, Alexandre Lefebvre, Paola Marrati, John Mullarkey, Paulina Ochoa Espejo, Carl Power, Philippe Soulez, Jim Urpeth, Melanie White, Frédéric Worms. (shrink)

Too many somersaults -- The strange creature that I am -- Giving meaning to reality -- The sincerity of true kindness -- Embracing our condition -- Drawing strength from our weakness -- Pity anesthetizes -- The other's gaze -- The joy of being alive -- They talked and analyzed -- Culture shock -- Conditional happiness -- A man of God -- A craving for learning -- Genuine friends -- Marginal.

Recueil des commentaires de Michel Alexandre sur la "Critique de la raison pure" d'après des notes de cours, comme la première édition de 1961. Cependant, on y a ajouté un quatrième chapitre, intitulé "L'ordre", avec des notes sur les deux dernières critiques, "Critique de la raison pratique" et "Critique du jugement". L'ensemble couvre les vingt dernières années d'enseignement de M. Alexandre (1932-1952), dont le commentaire relève du genre "Auslegung" (qu'on pourrait traduire par "exposition") comme celui que firent de (...) Kant un Hegel ou un Heidegger, et qui se caractérise par une certaine manière de questionner les textes. Ce volume est donc aussi un hommage rendu à un maître d'u. (shrink)

Cet ouvrage de philosophie et de sagesse est inséparable de la personnalité de l’auteur. Alexandre Jollien, gravement handicapé à sa naissance, a passé les dix-sept premières années de sa vie dans une institution spécialisée. Grâce à la détermination d’un de ses éducateurs, et après avoir été initié à l’informatique, il a pu entreprendre des études approfondies, notamment en philosophie. Dans un ouvrage publié au Seuil en 2002, il exprimait le point de vue qu’il s’est forgé sur la vie, la (...) souffrance, l’amitié, le rapport au corps que peut entretenir un handicapé. Ce petit livre, Le métier d’homme, a été un best-seller tandis que son auteur, invité par tous les médias, devenait une figure emblématique du handicap assumé et vaincu. Aujourd’hui, Alexandre Jollien aspire très légitimement à être perçu comme philosophe à part entière. Même s’il se réfère encore à l’incroyable et magnifique combat qu’a été sa vie jusqu’à la victoire sur le handicap, il refuse d’être « le philosophe du handicap » ou « le handicapé devenu philosophe ». Il s’oppose donc à ce qu’on fasse mention de son handicap dans les textes promotionnels quels qu’ils soient. Il a raison. Son nouveau livre justifie – et mérite – cette perception et ce respect. Dans ce texte, approfondi et médité, Alexandre Jollien, tout en revenant sur son aventure personnelle, s’exprime en philosophe. Il témoigne, pour l’avoir expérimenté, de l’importance salvatrice de la philosophie. (shrink)

The advent of the Web is one of the defining technological events of the twentieth century, yet its impact on the fundamental questions of philosophy has not yet been explored, much less systematized. The Web, as today implemented on the foundations of the Internet, is broadly construed as the space of all items of interest identified by URIs. Originally a space of linked hypertext documents, today the Web is rapidly evolving as a universal platform for data and computation. Even swifter (...) is the Web‐driven transformation of many previously unquestioned philosophical concepts of privacy, belief, intelligence, cognition, and even embodiment in surprising ways. The ensuing essays in this collection hope to explore the philosophical foundation of the World Wide Web and open the debate on whether or not the changes caused by the Web to technology and society warrant the creation of a philosophy of the Web. (shrink)

Cette préface présente le contexte politique et culturel du fameux discours de Helmholtz prononcé à Heidelberg le 22 novembre 1862, où il défend une certaine idée de l’université et des relations entre les différentes disciplines qu’elle enseigne. L’idée de pluridisciplinarité, tant invoquée aujourd’hui, est au cœur de son propos, ainsi que celle d’une conciliation possible entre philosophie et sciences de la nature, mais en partant du point de vue de ces dernières.

This commentary further explores some of the ethical issues raised by Prof. Peter Singer in his Lanson Lecture “Pandemic Ethics: Five Lessons”. In the first part, I distinguish a prioritarian approach to the allocation of scarce medical resources, from the utilitarian one advocated by Singer. I suggest that the prioritarian view better matches common intuitions about fair distribution, even though it likely needs to be balanced with other principles if it is to have plausibility in contexts like vaccine allocation. In (...) the second part of the commentary, I take a global perspective (as Singer himself does regarding the ethics of lockdowns), and highlight the controversial implications of adopting a fully cosmopolitan ethical outlook when deciding how to distribute Covid-19 vaccines. I also raise justice-related concerns about Singer’s proposal to use well-being as a single metric for evaluating public health policies. (shrink)

"Alexandre Vanautgaerden's research shows that Erasmus never ceased to adapt, depending on each type of text, the layouts of his books to best control their reception. A reversal of the traditional countdown of the exegesis of Erasmus's works, which lends at times a blind faith to his correspondence, this present work focuses on the study of manuscripts and printed books. Erasmus would not settle for just writing his texts, but preoccupied himself, with a growing scrupulousness, with the manner in (...) which they would be read. In addition to this new biography of an Erasmus who we discover riveted to the material existence of his books, the reader will find a great number of unedited documents, in Latin or in translation, as well as a list of the humanist's first editions. This volume offers a new look on the status of authors and readers at the beginning of the 16th century. It will interest historians of books as much as of humanism"--Publisher's website. (shrink)

Ilan Gur-Ze'ev and Education: Pedagogies of Transformation and Peace critically analyses and introduces the main ideas of Ilan Gur-Ze'ev, reflecting on their continuing theoretical and practical relevance for the field of education. This book offers an accessible, higher-level critical discussion on the thought of Ilan Gur-Ze'ev with an impressive breadth and contemporary focus. The book focuses on Gur-Ze'ev's 'counter-pedagogy' project, which brought him much attention and attempts to establish an alternative and non-dogmatic form of education. Gur Ze'ev's views go against (...) 'critical pedagogy' and 'neoliberalism', because while the former advocates achieving an utopia in which there is no oppression, the later defends the idea that 'wants and desires' need to be satisfied through a process of 'marketisation'. This book brings into notice Gur-Ze'ev's concepts of 'counter-education' and 'diasporic education' which seeks to pursue the truth in everyday life, rather than achieving a utopian goal, or the Promised Land. This unique and up-to-date monograph will be of great interest for researchers, academics and postgraduate students in the fields of philosophy of education, theory of education, peace education, Jewish education, neoliberalism, and sociology of education. (shrink)

Computational reproducibility possesses its own dynamics and narratives of crisis. Alongside the difficulties of computing as an ubiquitous yet complex scientific activity, computational reproducibility suffers from a naive expectancy of total reproducibility and a moral imperative to embrace the principles of free software as a non-negotiable epistemic virtue. We argue that the epistemic issues at stake in actual practices of computational reproducibility are best unveiled by focusing on software as a pivotal concept, one that is surprisingly often overlooked in accounts (...) of reproducibility issues. Software is not only about designing and coding but also about maintaining, supporting, distributing, licensing, and governance; it is not only about developers but also about users. We focus on openness debates among computational chemists involved in molecular modeling software packages as empirical grounding for our argument. We then identify and analyse four epistemic characteristics as key to the role of software in computational reproducibility. (shrink)

John Rawls was what we might call a “frenemy” to Stanley Cavell. Time and again, Cavell states his admiration for Rawls's political philosophy but criticizes it for two reasons. First, he believes that Rawls too hastily dismisses a perfectionist tradition that is essential for a flourishing liberal democracy. Second, he attacks certain aspects of Rawls's theory of justice as moralistic and legalistic. The first half of this article examines Cavell's critique of Rawls and argues that the two authors are more (...) closely aligned than suspected. It begins by reconstructing Cavell's critique of Rawls, and using archival materials from Harvard University, presents for the first time Rawls's interpretation of this critique. The second half of the article highlights perfectionist themes in Rawls's A Theory of Justice. The contribution of this article is to reevaluate the relationship between two of the most important moral philosophers of the twentieth century and also to provide a more expansive theory of liberalism that incorporates the psychological depth, moral subtlety and political hopefulness of moral perfectionism. (shrink)

This chapter contains sections titled: A Tale of Two Philosophies: URIs between Proper Names and REST; From References to Referentialization; and Toward Ontological Politics.

Using emotional film clips is one of the most popular and effective methods of emotion elicitation. The main goal of the present study was to develop and test the effectiveness of a new and comprehensive set of emotional film excerpts. Fifty film experts were asked to remember specific film scenes that elicited fear, anger, sadness, disgust, amusement, tenderness, as well as emotionally neutral scenes. For each emotion, the 10 most frequently mentioned scenes were selected and cut into film clips. Next, (...) 364 participants viewed the film clips in individual laboratory sessions and rated each film on multiple dimensions. Results showed that the film clips were effective with regard to several criteria such as emotional discreteness, arousal, positive and negative affect. Finally, ranking scores were computed for 24 classification criteria: Subjective arousal, positive and negative affect (derived from the PANAS; Watson & Tellegen, 1988), a positive and a negative affect scores derived from the Differential Emotions Scale (DES; Izard et al., 1974), six emotional discreteness scores (for anger, disgust, sadness, fear, amusement and tenderness), and 15 “mixed feelings” scores assessing the effectiveness of each film excerpt to produce blends of specific emotions. In addition, a number of emotionally neutral film clips were also validated. The database and editing instructions to construct the film clips have been made freely available in a website. (shrink)

Le noyau de cet ouvrage est formé par les notes prises de janvier 1933 à mai 1939 au cours que fit Alexandre Kojève à l'Ecole pratique des Hautes Etudes, sous le titre La philosophie religieuse de Hegel, et qui était en réalité une lecture commentée de la Phénoménologie de l'Esprit. Chaque année de cours est complétée par le résumé publié dans l'Annuaire de l'Ecole des Hautes Etudes. De plus, les trois premières leçons de l'année 1937-1938 et toute l'année 1938-1939 (...) sont données dans leur texte intégral. Enfin, en guise d'introduction, on trouvera la traduction commentée de la section A du chapitre IV de la Phénoménologie de l'Esprit, parue dans Mesures (14 janvier 1939). (shrink)

In a previous article on cosmological arguments, I have put forward a few examples of complete infinite and circular explanations, and argued that complete non-wellfounded explanations such as these might explain the present state of the world better than their well-founded theistic counterparts (Billon, 2021). Although my aim was broader, the examples I gave there implied merely causal explanations. In this article, I would like to do three things: • Specify some general informative conditions for complete and incomplete non-wellfounded causal (...) explanations that can be used to assess candidate explanations and to generate new examples of complete non-wellfounded explanations. • Show that these conditions, which concern chains of causal explanations, easily generalize to chains of metaphysical, grounding explanations and even to chains involving other “determination relations” such as supervenience. • Apply these general conditions to the recent debates against the existence of nonwellfounded chains of grounds and show, with a couple of precise examples, that the latter can be complete, and that just like in the case of causal explanations, non-wellfoundedness can in fact be an aset rather than a liability. (shrink)

Remise en cause de la théorie d’Einstein, de celle de Darwin, créationnisme et fondamentalismes, cosmologies païennes, mouvements technofascistes, idéologies radicales anti-science… Pourquoi des personnes formées à la science en viennent-elles à adopter une attitude en opposition virulente à la science de leur époque? Comment mobilisent-elles leur capacité de raisonnement au service de dogmes et d’idéologies sans rapport avec la science? Peut-on tirer un fil historique entre ces postures depuis la naissance de la science moderne au XVIe siècle? De nos jours, (...) quel est l’impact sur les rapports entre science et société de ces attitudes, diffusées et multipliées par le canal de l’Internet? Rejet de la science contemporaine, de la spécialisation et de l’abstraction mathématique ; appel au bon sens et à une science globale ; vitupération pouvant aller jusqu’à l’invocation de la théorie du complot ; instrumentalisation de la science à des fins idéologiques ou religieuses : voilà les principales caractéristiques des mouvements ou des individus étudiés dans cet ouvrage. Alexandre Moatti, ingénieur en chef des Mines, est chercheur associé en histoire des sciences et des idées à l’université Paris-VII-Denis-Diderot. Il est notamment l’auteur deEinstein, un siècle contre lui (2007). (shrink)

Fundamentally, a ruin is a utilitarian structure which through the ravages of time or through some other circumstance has lost its utility and its function. When a useful object becomes useless, it continues to be present without a true existence, exactly as if it were dead. A torn glove, a bicycle without wheels, do not deserve to be called by their original names. It is difficult, of course, for us to resign ourselves to the fact that objects we have always (...) thought of as useful are no longer useful; we hold on to the illusion of profiting from them as long as possible. We still make use of an abandoned automobile by stripping it of its accessories; we make use of a dilapidated house by salvaging some of its building material. However, the time comes when we must accept the evidence and admit that the object has become a burden. (shrink)

We must begin from the principle that all language is necessarily limited. The art of speaking is a common heritage, even if it is wasted. It has so lost its mystery (more precisely; we are so calm in its possession) that we consider it almost as a gift of nature. Nevertheless, it must be learned; it is, in fact, a product of education, even for those who might believe that they have never received any. Like all acquired disciplines, then, it (...) is the fruit of a long process of restraint. Manuals exist which teach Latin without tears. Learning the first language seems to take place without recourse to handbooks and hickory sticks, but this is because a vast program is available, full time, along with dedicated teachers who do not keep an eye on the clock, and fresh intellects who never think their knowledge is sufficient. Instruction is difficult, in spite of all this, for the task is more challenging than adults imagine it to be. (shrink)