We argue that on logical grounds the constructivist algorithms mentioned by Quartz & Sejnowski (Q&S) do not resolve the learning paradox. In contrast, a neural network might acquire a more powerful structure by means of phase transitions. The latter kind of developmental mechanism can be in agreement with the constructivist manifesto.

Children acquire complex concepts like DOG earlier than simple concepts like BROWN, even though our best neuroscientific theories suggest that learning the former is harder than learning the latter and, thus, should take more time (Werning 2010). This is the Complex- First Paradox. We present a novel solution to the Complex-First Paradox. Our solution builds on a generalization of Xu and Tenenbaum’s (2007) Bayesian model of word learning. By focusing on a rational theory of concept (...) learning, we show that it is easier to infer the meaning of complex concepts than that of simple concepts. (shrink)

This paper examines the paradoxical transparency involved in training machine-learning models. Existing literature typically critiques the opacity of machine-learning models such as neural networks or collaborative filtering, a type of critique that parallels the black-box critique in technology studies. Accordingly, people in power may leverage the models’ opacity to justify a biased result without subjecting the technical operations to public scrutiny, in what Dan McQuillan metaphorically depicts as an “algorithmic state of exception”. This paper attempts to differentiate the (...) black-box abstraction that wraps around complex computational systems from the opacity of machine-learning models. It contends that the degree of asymmetry in knowledge is greater in the former than the latter. In the case of software systems, software codes are difficult to understand as only software experts with sufficient domain knowledge are equipped to formulate a sound critique. In contrast, the meanings of trained parameters in a machine-learning model are obscure even to the data scientists who configure and train the model. Hence, the asymmetry of knowledge lies only in how data examples are collected, the choice and configuration of machine-learning models, and the specification of features in model design. Under the trend of algorithmic decision-making proliferating with machine-learning heuristics, the paper contends that the more symmetric distribution of knowledge in machine learning could lead to a more transparent production process if proper policies are in place. (shrink)

George Francis FitzGerald is well known to have proposed in 1889, three years before Lorentz, the (physical) contraction of bodies moving in the hypothetical ether, as an “explanation” the null result of the Michelson and Morley experiment. Less known is his proposal of an ether-drift experiment based on an electrostatic system. A simple charged condenser suspended by a wire would be subject to a torque due to the earth’s motion. The experiment was done by his pupil Trouton, with Noble, with (...) null result. It was an important independent confirmation of the relativity principle, but it was substantially forgotten. It came back, under the form of a paradox, in the second half of the past century, usefully triggering an in-depth discussion on the electromagnetic energy and momentum flow in stationary systems, in which intuitively one thinks momentum should be zero, but it is not. The solution of the Trouton–Noble paradox, and similar ones, has led to a better understanding of the interplay between electromagnetic field and matter and to develop relevant examples for the university courses. (shrink)

There is no shortage of pedagogical theories from the tradition formal methods of instruction to the free-play methods of unschooling. A sharp shift in education and instruction models took place with the introduction of critical pedagogy. The focus was no longer on the authority of the teacher and the submissive, passive approach taken by the learner, but rather on the engagement between the two. Still, even when critical pedagogy is utilized in a formal model of education something is missing from (...) the system—experiential learning. Although the unschooling method has been criticized it does provide the benefit of experiential learning. This paper explores the nature of education and evaluates models and theories of pedagogy with the conclusion that a paradoxical approach in which there is a merger between the formal guidelines set by traditional educational models and the experiential learning methods of unschooling approach best prepares learners for the world and to be engaged citizens. Although what, precisely, this paradoxical system would entail is not discussed in this paper, it opens the door for further discussion on the topic and for consideration of the theories which have attempted to do exactly this and improve upon them going forward. (shrink)

Conceptual development requires learning. It requires learning to make discriminations that were previously unavailable to the subject. Notwithstanding the descriptions of learning available in the psychological and educational literature, there is no account available that shows that it is so much as possible. There can be no such account unless there is an answer to Jerry Fodor’s paradox of learning. On our current understanding of concept acquisition, there is no such thing as learning. In (...) this paper I explore a way of avoiding this conclusion. The enquiry is foundational, an enquiry into the very possibility of learning and development. The account of learning that I sketch has, however, clear consequences for our basic ideas about education. (shrink)

Conceptual development requires learning. It requires learning to make discriminations that were previously unavailable to the subject. Notwithstanding the descriptions of learning available in the psychological and educational literature, there is no account available that shows that it is so much as possible. There can be no such account unless there is an answer to Jerry Fodor's paradox of learning. On our current understanding of concept acquisition, there is no such thing as learning. In (...) this paper I explore a way of avoiding this conclusion. The enquiry is foundational, an enquiry into the very possibility of learning and development. The account of learning that I sketch has, however, clear consequences for our basic ideas about education. (shrink)

A notable feature of paradox is recognition that seemingly contradictory terms are inextricably intertwined and interrelated—holding out the hope that something new can be learned from the cognitive tension contained within. Aram has characterized the central concern of the business and society field as the paradox of interdependent relations. Our study argues that this and related paradoxes can be addressed by engaging with others and trying to gain shared insight via an interactive, developmental, exploratory sensemaking process that can (...) inform the governance of stakeholder networks. We advocate multistakeholder learning dialogues (MSLDs) as a means for both scholars and practitioners to construct meanings that can guide joint efforts to cope with messy problems that help shape complex, paradoxical relationships within stakeholder networks. (shrink)

In his later lectures, published as The Hermeneutics of the Subject, Michel Foucault surveys different modalities of obtaining ‘truth’ about one's self and the world: from Socrates to the Cynics, Stoics, Epicureans and early church writers. Genealogically tracing this opposition between knowing self and world, he occasionally invites phenomenological enquiry into how this epistemic couplet bears on education. Drawing on three vignettes familiar to educators, my investigation explores modes of discovering self and world through counselling, distributed governance in the classroom (...) and the arts of writing. In each case we confront a paradox of freedom, in that agency is needed, already, to liberate the self from the world. An exegetical task is to show how Foucault worked through this philosophical problem, of relevance to many situations in education, by re-reading Kant, Nietzsche and Heidegger. (shrink)

The intuitionistic conception of truth defended by Dummett, Martin Löf and Prawitz, according to which the notion of proof is conceptually prior1 to the notion of truth, is a particular version of the epistemic conception of truth. The paradox of knowability (first published by Frederic Fitch in 1963) has been described by many authors2 as an argument which threatens the epistemic, and the intuitionistic, conception of truth. In order to establish whether this is really so, one has to understand (...) what the epistemic conception of truth really is. So I shall start inpart I with a description of the matter at issue between theepistemic conception of truth and the opposite position, therealistic conception of truth. Inpart II I shall very briefly describe the paradox. Inpart III I shall try to answer the question which appears in the title of this paper: What can we learn from the paradox of knowability?. My conclusion will be that the paradox of knowability is not a refutation of the epistemic conception of truth, but helps us to better formulate (and understand) such a view. (shrink)

This article outlines the context in which General National Vocational Qualifications (GNVQs) have been developed with particular reference to the independent learning dimension of their principles and practice. It provides an overview of the problems associated with the GNVQ approach from the literature and from a study by the authors of twelve post-16 institutions in the process of implementing Advanced GNVQ programmes. It analyses the dimensions of independent learning and argues that GNVQs provide a hybrid learner experience in (...) which autonomy in the organisation of the individual learning process is mediated by a heavily prescribed GNVQ framework. The article concludes by locating this paradox in four central dilemmas characterising post-16 curricular policy in the UK. (shrink)

This article analyzes three approaches to resolving the classical Meno paradox, or its variant, the learning paradox, emphasizing Charles S. Peirce’s notion of abduction. Abduction provides a way of dissecting those processes where something new, or conceptually more complex than before, is discovered or learned. In its basic form, abduction is a “weak” form of inference, i.e., it gives only tentative suggestions for further investigation. But it is not too weak if various sources of clues and restrictions (...) on the abductive search are taken into account. We present three, complementary versions of abduction: as a sort of guessing instinct or expert-like intuition, where unconscious clues are important; as a form of inference, where a strategic point of view is essential; and as a part of distributed cognition and mediated activity, where the interaction with the material, social, and cultural environment is emphasized. Our starting point is Peirce’s own notion of abduction, but we broaden the perspective, especially to the direction of distributed cognition. (shrink)

In describing the foundations of our pedagogical approaches to service-learning, we seek to go beyond the navel-gazing—at times, paralyzing—paradoxes of neoliberal forces, which can do “good” for students and their communities, yet which also call students into further calculative frameworks for understanding the “value” of pre-health humanities education and social engagement. We discuss methods to create quiet forms of subversion that call for a moral imagination in extending an ethics of care to students as well as to the communities (...) with which they engage. While we recognize the partiality and limitations of our attempts, framing mentored service-learning in unexpected ways can help students and practitioners to understand their role within broader social, historical, cultural, and emotional contexts and encourage them to act intentionally toward the communities they seek to serve in response to this new self-knowledge. To that end, we outline an academically rigorous service-learning intervention at one of our universities. (shrink)

Name der Zeitschrift: Semiotica Jahrgang: 2016 Heft: 212 Seiten: 199-217.

In 2012, a U.S. Institute of Medicine report called for a different approach to health care: “Left unchanged, health care will continue to underperform; cause unnecessary harm; and strain national, state, and family budgets.” The answer, they suggested, would be a “continuously learning” health system. Ethicists and researchers urged the creation of “learning health organizations” that would integrate knowledge from patient‐care data to continuously improve the quality of care. Our experience with an ongoing research study on atrial fibrillation—a (...) trial known as IMPACT‐AFib—gave us some insight into one of the challenges that will have to be dealt with in creating these organizations. Although the proposed educational intervention study placed no restrictions on what providers and health plans could do, the oversight team argued that the ethical principle of beneficence did not allow the researchers to be “bystanders” in relation to a control group receiving suboptimal care. In response, the researchers designed a “workaround” that allowed the project to go forward. We believe the experience suggests that what we call “bystander ethics” will create challenges for the kinds of quality improvement research that LHOs are designed to do. (shrink)

Paradoxes are poems of science and philosophy that collectively allow us to address broad multidisciplinary issues within a microcosm. A true paradox is a source of creativity and a concise expression that delivers a profound idea and provokes a wild and endless imagination. The study of paradoxes leads to ultimate clarity and, at the same time, indisputably challenges your mind. Paradoxes in Scientific Inference analyzes paradoxes from many different perspectives: statistics, mathematics, philosophy, science, artificial intelligence, and more. The book (...) elaborates on findings and reaches new and exciting conclusions. It challenges your knowledge, intuition, and conventional wisdom, compelling you to adjust your way of thinking. Ultimately, you will learn effective scientific inference through studying the paradoxes. (shrink)

This thesis will argue that Plato's influential philosophical puzzle known as the Meno Paradox and the related Problem of False Belief are a more serious threat to Plato's philosophical programme than many interpreters recognize. Furthermore, Plato's most obvious candidate for a solution to these problems, the Theory of Recollection, is not sufficient to explain how the Paradox misunderstands the epistemic processes of learning which it treats. ;This failure of Plato's account motivates a close consideration of Aristotle's sophisticated (...) attempt to resolve the difficulties Plato raises. I will argue that a proper understanding of Aristotle's philosophy of mind and the forms of cognition through which he thinks humans progress yields the key to a powerful and heretofore unrecognized Aristotelian solution to the Meno Paradox and the Problem of False Belief. (shrink)

Meredith Williams is unimpressed by ‘constructive/theoretical’ and ‘resolute/therapeutic’ approaches to the Philosophical Investigations . She takes Wittgenstein’s repudiation of speculation in philosophy seriously but resists interpreting him as engaged in a purely critical endeavour. There is, she holds, ‘a complex interweaving of the diagnostic and positive’ and ‘[a] consequence of the critical diagnostic work is a positive picture’ . Taking the Investigations to be ‘a highly structured argumentative text directed to pursuing a fundamental new problem in philosophy’ , Williams interprets (...) Wittgenstein as resolving ‘the problem of normative similarity’ , i.e. the problem of how meaningful goings-on differ from brute physical happenings. She suggests that ‘Wittgenstein’s diagnostic method is tied to his use of two powerful arguments . By uncovering hidden contradictions and exposing grammatical errors, she argues, Wittgenstein shows that important philosophical theories of language and the mind are ‘self-defeating’ and ‘[i]n removing them, [his] “normative naturalism” can be seen’ . Williams begins by discussing ‘the structure and content of the Investigations . She then examines Wittgenstein’s remarks about word-object relations , rule-governed practice and self-knowledge and sensations . In her view, Wittgenstein recognizes and explains the irreducibility of the normative to the natural in each …. (shrink)

To learn a visual code in an unsupervised manner, one may attempt to capture those features of the stimulus set that would contribute significantly to a statistically efficient representation. Paradoxically, all the candidate features in this approach need to be known before statistics over them can be computed. This paradox may be circumvented by confining the repertoire of candidate features to actual scene fragments, which resemble the “what+where” receptive fields found in the ventral visual stream in primates. We describe (...) a single-layer network that learns such fragments from unsegmented raw images of structured objects. The learning method combines fast imprinting in the feedforward stream with lateral interactions to achieve single-epoch unsupervised acquisition of spatially localized features that can support systematic treatment of structured objects [1]. (shrink)

In 2012, a U.S. Institute of Medicine report called for a different approach to health care: “Left unchanged, health care will continue to underperform; cause unnecessary harm; and strain national, state, and family budgets.” The answer, they suggested, would be a “continuously learning” health system. Ethicists and researchers urged the creation of “learning health organizations” that would integrate knowledge from patient‐care data to continuously improve the quality of care. Our experience with an ongoing research study on atrial fibrillation—a (...) trial known as IMPACT‐AFib—gave us some insight into one of the challenges that will have to be dealt with in creating these organizations. Although the proposed educational intervention study placed no restrictions on what providers and health plans could do, the oversight team argued that the ethical principle of beneficence did not allow the researchers to be “bystanders” in relation to a control group receiving suboptimal care. In response, the researchers designed a “workaround” that allowed the project to go forward. We believe the experience suggests that what we call “bystander ethics” will create challenges for the kinds of quality improvement research that LHOs are designed to do. (shrink)

This article studies the origin and continuity of the identity of the entities inscribed in a distributed ledger. Specifically, it focuses on the differences between the identities of the entities that exist in a distributed ledger and those of the entities that exist outside the ledger but must be represented in the ledger in order to interact with it. It suggests that a distributed ledger that contains representations of entities that exist outside the ledger can yield a continuum of interconnected (...) existing and past identities that is constantly redefined to represent new conceptual entities. This continuum can be understood as a metasortal—or a sortal of sortals—that resembles the mathematical structure of a set of sets. Further, the article presents the dilemma that arises when representing the identities of entities in a distributed ledger, and it draws an analogy between this dilemma and Russell's Paradox. (shrink)

The term "paradox'' signifies a contradiction of some sort. Modern health care appears to be rich in contradictions, and it is claimed to be paradoxical in a number of ways.In particular health care is held to be a paradox itself: it is supposed to do good, but is accused of doing harm. The objective of this article is to investigate whether the concept of paradox can serve as a framework for analysing pressing problems in modern healthcare. To (...) pursue this, three distinctive levels of paradox are identified: resolvable paradoxes, antinomies and aporias. The analysis reveals that when facing the challenges of modern health care the focus of attention should be to resolve the resolvable paradoxes,to acknowledge the antinomies and to learn to live with the aporias. (shrink)

I will use paradox as a guide to metaphysical grounding, a kind of non-causal explanation that has recently shown itself to play a pivotal role in philosophical inquiry. Specifically, I will analyze the grounding structure of the Predestination paradox, the regresses of Carroll and Bradley, Russell's paradox and the Liar, Yablo's paradox, Zeno's paradoxes, and a novel omega plus one variant of Yablo's paradox, and thus find reason for the following: We should continue to characterize (...) grounding as asymmetrical and irreflexive. We should change our understanding of the transitivity of grounding in a certain sense. We should require foundationality in a new, generalized sense, that has well-foundedness as its limit case. Meta-grounding is important. The polarity of grounding can be crucial. Thus we will learn a lot about structural properties of grounding from considering the various paradoxes. On the way, grounding will also turn out to be relevant to the diagnosis (if not the solution) of paradox. All the paradoxes under consideration will turn out to be breaches of some standard requirement on grounding, which makes uniform solutions of large groups of these paradoxes more desirable. In sum, bringing together paradox and grounding will be shown to be of considerable value to philosophy.1. (shrink)

Modern societies depend on a growing production of scientific knowledge, which is based on the functional differentiation of science into still more specialised scientific disciplines and subdisciplines. This is the basis for the paradox of scientific expertise: The growth of science leads to a fragmentation of scientific expertise. To resolve this paradox, the present paper investigates three hypotheses: 1) All scientific knowledge is perspectival. 2) The perspectival structure of science leads to specific forms of knowledge asymmetries. 3) Such (...) perspectival knowledge asymmetries must be handled through second order perspectives. We substantiate these hypotheses on the basis of a perspectivist philosophy of science grounded in Peircean semiotics and autopoietic systems theory. Perspectival knowledge asymmetries are an unavoidable and necessary part of the growth of scientific knowledge, and more awareness of this fact can help avoid blind and futile struggles between scientific perspectives, and direct efforts toward more appropriate ways of handling these fundamental knowledge asymmetries. Concretely, we show how different kinds of scientific knowledge, expertise, disagreement and learning can be correlated to the perspectival structure of science, and propose how polyocular communication based on observations of the observations made by specialised perspectives can be used to handle such perspectival knowledge asymmetries. This can help overcome the observed problems in carrying out cross-disciplinary research and in the collective use of different kinds of scientific expertise, and thereby make society better able to solve complex, real-world problems. (shrink)

This study explored the experiences of the newly-hired faculty in the university to acquire an in-depth and profound understanding of these experiences. It involved eight purposively chosen faculty in a semi-structured interview and focus group discussion documented in voice and video recorders. Using Colaizzi’s seven step-approach to data analysis, results revealed three paradoxical themes: the joys and struggles of teaching, successes and pains of learning, and the privileges and challenges of serving. On the one hand, the joys and struggles (...) of teaching were brought about by their adjustments in instruction. On the other hand, successes and pains of learning centered on professional growth. Finally, the privileges and challenges of serving incorporated the experiences in research, production, and extension. Generally, these teachers have experienced ups and downs in their first two years of teaching at a higher education institution. On the basis of study findings, implications and recommendations are discussed. (shrink)

Parties are back, and many are cheering. Party polarization has voters seeing stark differences between Democrats and Republicans and demonstrating more ideological constraint than previous generations. But these signs of a more “responsible” electorate are an illusion, because the public is no more knowledgeable than ever about the type of “information” it needs if it is to exercise effective control over the public‐policy outcomes it cares the most about. Indeed, polarization has produced a political environment where both voters and policy (...) makers may be less likely to learn about the potential consequences of their governing choices. The result is that holding elected politicians to account for policies treated as divisive ends in themselves has become easier—but that holding them accountable for policies intended as means to the achievement of consensual ends has become harder. (shrink)

Almost everything that we know about Zeno of Elea is to be found in the opening pages of Plato's Parmenides. There we learn that Zeno was nearly 40 years old when Socrates was a young man, say 20. Since Socrates was born in 469 BC we can estimate a birth date for Zeno around 490 BC. Beyond this, really all we know is that he was close to Parmenides (Plato reports the gossip that they were lovers when Zeno was young), (...) and that he wrote a book of paradoxes defending Parmenides' philosophy. Sadly this book has not survived, and what we know of his arguments is second-hand, principally through Aristotle and his commentators (here I have drawn particularly on Simplicius, who, though writing a thousand years after Zeno, apparently possessed at least some of his book). There were apparently 40 ‘paradoxes of plurality’, attempting to show that ontological pluralism — a belief in the existence of many things rather than only one — leads to absurd conclusions; of these paradoxes only two definitely survive, though a third argument can probably be attributed to Zeno. Aristotle speaks of a further four arguments against motion (and by extension change generally), all of which he gives and attempts to refute. In addition Aristotle attributes two other paradoxes to Zeno. Sadly again, almost none of these paradoxes are quoted in Zeno's original words by their various commentators, but in paraphrase. (shrink)

‘It is necessary to a Prince to learn how not to be good’. This quotation from Machiavelli’s The Prince has become the mantra of the standard dirty hands thesis. Despite its infamy, it features proudly in most conventional expositions of the dirty hands problem, including Michael Walzer’s original analysis. In this paper, I wish to cast a doubt as to whether the standard conception of the problem of DH—the recognition that, in certain inescapable and tragic circumstances an innocent course of (...) action is unfeasible—fully captures Machiavelli’s message and its terrifying implications. In particular, I argue that the standard DH thesis is inadequately ‘static’: it conceives the conflict between ordinary morality and political morality as a stark, momentary and rare paradox of action—an anomaly disrupting the normality of harmony. As such it misconceives both the extent and the nature of the rupture between morality and politics. In this sense, the argument I shall advance does just involve an exercise in the history of political thought. Rather, I want to suggest that, by virtue of its failure to take Machiavelli’s insights seriously, the standard DH thesis fails to live up to its purported capacity to capture the complexity and fragmentation of our moral cosmos and that, consequently, it is nothing more than a thinly veiled version of the idealism and monism it purports to reject. (shrink)

In an era where autonomous technologies are progressively taking over more complex tasks and decision-making previously done by humans, the mastering of paradox-based skills and effectively reconciling paradoxical situations in everyday life will become increasingly important. This paper asserts that understanding and living with paradox is not only necessary for the future of work but also for human flourishing. While work is the primary means by which humans flourish in the traditional sense, there are deeper and more holistic (...) understandings of human flourishing which requires the acceptance and learning of paradoxical realities. Those who are steeped in the understanding and reality of paradox in everyday life can also be more open to these deeper and more holistic understandings of human flourishing. (shrink)

Extensively classroom-tested, Possibilities and Paradox provides an accessible and carefully structured introduction to modal and many-valued logic. The authors cover the basic formal frameworks, enlivening the discussion of these different systems of logic by considering their philosophical motivations and implications. Easily accessible to students with no background in the subject, the text features innovative learning aids in each chapter, including exercises that provide hands-on experience, examples that demonstrate the application of concepts, and guides to further reading.

Learning to perceive is faced with a classical paradox: if understanding is required for perception, how can we learn to perceive something new, something we do not yet understand? According to the sensorimotor approach, perception involves mastery of regular sensorimotor co-variations that depend on the agent and the environment, also known as the “laws” of sensorimotor contingencies (SMCs). In this sense, perception involves enacting relevant sensorimotor skills in each situation. It is important for this proposal that such skills (...) can be learned and refined with experience and yet up to this date, the sensorimotor approach has had no explicit theory of perceptual learning. The situation is made more complex if we acknowledge the open-ended nature of human learning. In this paper we propose Piaget’s theory of equilibration as a potential candidate to fulfill this role. This theory highlights the importance of intrinsic sensorimotor norms, in terms of the closure of sensorimotor schemes. It also explains how the equilibration of a sensorimotor organization faced with novelty or breakdowns proceeds by re-shaping pre-existing structures in coupling with dynamical regularities of the world. This way learning to perceive is guided by the equilibration of emerging forms of skillful coping with the world. We demonstrate the compatibility between Piaget’s theory and the sensorimotor approach by providing a dynamical formalization of equilibration to give an explicit micro-genetic account of sensorimotor learning and, by extension, of how we learn to perceive. This allows us to draw important lessons in the form of general principles for open-ended sensorimotor learning, including the need for an intrinsic normative evaluation by the agent itself. We also explore implications of our micro-genetic account at the personal level. (shrink)

In lieu of an abstract, here is a brief excerpt of the content:The Paradox of Education:A ConversationHumberto R. Maturana and Bernhard PoerksenResponsibility of the TeacherPoerksen: Immanuel Kant writes in his essay Über Pädagogik that the wide field of education is governed by a fundamental paradox. On the one hand, we want free and self-determined individuals to leave our schools; on the other, we impose a syllabus on the future individuals, force them to attend schools, punish their failures, and (...) persecute their noncompliance. There is, if we follow Kant, an inescapable relationship of tension between the goals and the means of educational efforts: They contradict each other. Would you agree?Maturana: No. Education, the commentary of an observer, is the process of transformation resulting from the co-existence with adults. We become the adults we have been living with. This means: If freedom and self-determined thinking are the goals of educational activity, then we have to live together in a way that is supported by the mutual respect for the autonomy of the other. In my view, the paradox formulated by Kant does not exist at all. The way of life, the manner of living together, shapes and transforms people. If you want to teach autonomy and reflection, you cannot use force as a method but must create an open space for communal reflection and action. There must be no contradiction between goals and means.Poerksen: Surely, there must also be constraints? It must be laid down when everybody has to be present, what the task is, who the teacher is, who has authority.Maturana: Compulsion will emerge if the teachers do not succeed in presenting their material in a thrilling way and in making school an attractive place of being together. Their failure will lead to force.Poerksen: The teacher is totally responsible for everything that may happen in school. Is this not an exaggerated claim?Maturana: No. If a teacher behaves respectfully, if he does not intimidate his pupils, if he listens, encourages cooperation and reflection, then a special form of interaction will emerge. The way of living practiced by the teacher, including the goals of teaching, will be the source of profitable learning for the pupils. This also implies that three questions and tasks must be sorted out cooperatively in education. First it seems necessary to me to debate the educational ideal to be chosen—what should the future adults be like when leaving the school one day? Should they be democratically minded and responsibly acting citizens? Or are they to be authoritarian and commandeering hierarchs, lords who feel superior to everyone else? It is then necessary to anchor a way of life in the school that permits acting and thinking according to that ideal. Finally, there is the essential task of preparing the teachers for their job in such a [End Page 25] way as to do justice to the desired goals—to enable them to live what they have to achieve.Poerksen: This would mean that teaching has nothing to do with the stepwise elimination of ignorance, as is commonly thought. The transmission of knowledge is secondary. The primary requirement is a way of life that corresponds with one's ideals, a particular form of living together, out of which the material topics will arise in due course.Maturana: Exactly. The children do not learn mathematics in school; they learn how to live together with a mathematics teacher. Perhaps they will one day carry on this enjoyable and exciting kind of being together independently—and become mathematics teachers or mathematicians themselves. Teachers do not simply transmit some content; they acquaint their pupils with a way of living. In the process, the rules of arithmetic, the laws of physics, or the grammar of a language will be acquired. My claim is: Pupils learn teachers.Poerksen: What about children who systematically refuse to cooperate? What is to be done with them? The classical answer is, of course: bad marks, relegation, exclusion from the winning circles.Maturana: The so-called difficult children about whom teachers keep complaining often only struggle to be seen and accepted, while the whole world expects them to behave in a calculable manner and to adapt to strange demands. Asking... (shrink)

The problem of mortality treats death as posing a paradox for the narrative view of the self. This view, on some interpretations, needs death in order to complete a life in a manner analogous to the ending of a story. But death is inaccessible to the subject herself, and so the analogy fails. Our inability to grasp the event of our own death is thought to undermine the possibility of achieving a meaningful, coherent, or complete life on narrativist terms. (...) Narrativist attempts to solve the problem of mortality often involve exercises in "learning to be dead" in an effort to demonstrate that one's death is not entirely outside one's grasp. But there are different versions of the problem of mortality, which invite disparate solutions. I argue that most versions do not in fact pose a significant conundrum for the narrative view of the self. In order to strike at the narrative view in particular, in a fashion that is significant and a form that is paradoxical, a quite specific type of death must be at issue--one that is sudden and unanticipated. But a suggested solution to this version of the problem of mortality implies that the problem can be dissolved by disavowing certain alleged narrative presuppositions that fuel it. Those suppositions may, in turn, be essential to sustaining a uniquely narrative outlook on life and death. (shrink)

Once upon a time, during a large and international conference of the world's leading philosophers, an angel miraculously appeared and said, "I come to you as a messenger from God. You will be permitted to ask any one question you want - but only one! - and I will answer that question truthfully. What would you like to ask?" The philosophers were understandably excited, and immediately began a discussion of what would be the best question to ask. But it quickly (...) became obvious that they needed more time to discuss the matter, so they asked the angel if he could get back to them. The angel was obliging, and said that he would return at the same time the next day. "But be prepared then," he warned them, "for you will only get this one chance." All of the philosophers gathered at the convention worked at a frenzied pace for the next twenty-four hours, proposing and weighing the merits of various questions. Other philosophers from around the world became involved as well, faxing and emailing their suggestions. Some were in favor of asking the kind of practical question that lots of people might like to know the answer to, such as this one: Q1 Is it better to check your oil when the car is hot or when it is cold? But others said they should not squander this rare opportunity, which gave them a chance to learn something about a truly important and intrinsically interesting topic, and after some discussion it was generally agreed that this was right. (shrink)

The purpose of this note is to present a strong form of the liar paradox. It is strong because the logical resources needed to generate the paradox are weak, in each of two senses. First, few expressive resources required: conjunction, negation, and identity. In particular, this form of the liar does not need to make any use of the conditional. Second, few inferential resources are required. These are: (i) conjunction introduction; (ii) substitution of identicals; and (iii) the inference: (...) From ¬(p ∧ p), infer ¬ p. It is, interestingly enough, also essential to the argument that the ‘strong’ form of the diagonal lemma be used: the one that delivers a term λ such that we can prove: λ = ¬ T(⌈λ⌉); rather than just a sentence Λ for which we can prove: Λ ≡ ¬T(⌈Λ⌉). The truth-theoretic principles used to generate the paradox are these: ¬(S ∧ T(⌈¬S⌉); and ¬(¬S ∧ ¬T(⌈¬S⌉). These are classically equivalent to the two directions of the T-scheme, but they are intuitively weaker. The lesson I would like to draw is: There can be no consistent solution to the Liar paradox that does not involve abandoning truth-theoretic principles that should be every bit as dear to our hearts as the T-scheme. So we shall have to learn to live with the Liar, one way or another. (shrink)