Ce colloque interacadémique a été organisé en partenariat entre le Bureau des Innovations de la Direction de l’Enseignement Scolaire et les coordonnateurs académiques des académies de Montpellier, Caen et Créteil. L’Inspection Générale de Philosophie a tenu à assister à ses travaux et à y intervenir, à partir du moment où les promoteurs de cette innovation revendiquent le qualificatif de « philosophie ». C’est un moment important de la réflexion collective sur une innovation française récente : des pratiques nouvelles d’échanges qui (...) se réclament de la philosophie à l’école primaire et au collège. Et cela propose certains enjeux. Par enjeu, nous entendons ce qui se joue d’important et d’urgent, à différents niveaux et pour divers acteurs, dans une activité humaine. Il y a au moins six enjeux selon moi dans les nouvelles pratiques à visée philosophique à l’école primaire et au collège qui font que rôle du maître devient plus complexe: Un enjeu langagier: c’est sur l’oral que repose fondamentalement ces pratiques. Un enjeu psychologique: L’enjeu de la construction identitaire, la confiance en sa propre possibilité de pensée doit être périodiquement réasssurée. Un enjeu politique L’école républicaine se donne explicitement comme mission de préparer par son enseignement le futur citoyen. Un enjeu éthique développer en classe la pratique éducative d’une éthique discussionnelle fondée sur le respect d’autrui. Un enjeu cognitif, d’ordre réflexif: leur finalité est d’apprendre aux enfants à « penser par eux-mêmes ». Et, enfin, un enjeu pour la philosophie elle-même et son enseignement. Ces pratiques posent enfin des questions à la philosophie elle-même, et à sa didactique. C’est bien la visée philosophique de ces pratiques qui fait leur spécificité. Innovation parce que la philosophie n’est au programme qu’en classe terminale de lycée, et que d’en parler dès l’école maternelle est une rupture profonde avec la tradition de l’enseignement philosophique français. (shrink)

The author discusses in detail the basic issues related to the practice of philosophical discussions with children. He identifies and problematizes the different methods or modalities for doing philosophy with children currently practised throughout the world. He presents a series of pedagogic and didactic issues and puts forward some proposals and directions for the future that might allow us to facilitate philosophy-oriented discussions with children.

Philosopher à l'école maternelle, primaire, en collège, en lycée professionnel, dans des médiathèques, des maisons des jeunes, des foyers de jeunes travailleurs..., ou philosopher dans un café philo, banquet philo, ciné philo, théâtre philo; au cours d'une rando philo, avec une BD philo, par une consultation philo privée ou en entreprise..., ou philosopher en prison, en maison de retraite, à l'hôpital, etc. Dans chaque cas, de Nouvelles pratiques philosophiques (NPP) se mettent place. Cet ouvrage vise, pour un public très large, (...) à : décrire et analyser l'émergence de ces pratiques philosophiques sociales et scolaires souvent inédites ; dresser un panorama de la diversité des publics, des lieux d'exercices et des méthodes utilisées ; inventorier les genres qui se cherchent puis se stabilisent, autour des tenants et aboutissants philosophiques ; préciser les objectifs et les présupposés philosophiques, politiques ou didactiques impliqués, les méthodologies, dispositifs et supports privilégiés ; exposer quelques-unes des controverses souvent passionnées soulevées par ces nouvelles pratiques philosophiques. (shrink)

La 4e de couv. indique: "Dans un contexte de massification des élèves et de réforme de l'enseignement philosophique en France, cet ouvrage, qui s'adresse aux étudiants et professeurs de philosophie, à leurs formateurs et plus généralement à tous eux qui s'intéressent aux Nouvelles Pratiques Philosophiques (NPP), voudrait rendre compte des recherches menées ces trente dernières années sur la question de la didactique de la philosophie, et proposer un certain nombre de pistes pratiques pour développer l'apprentissage du philosopher tant chez les (...) élèves que chez les adultes.". (shrink)

This book addresses central issues in the philosophy and metaphysics of science, namely the nature of scientific theories, their partial truth, and the necessity of scientific laws within a moderate realist and empiricist perspective. Accordingly, good arguments in favour of the existence of unobservable entities postulated by our best theories, such as electrons, must be inductively grounded on perceptual experience and not their explanatory power as most defenders of scientific realism claim. Similarly, belief in the reality of dispositions such as (...) causal powers which ground the natural necessity of scientific laws must be based on experience. Hence, this book offers a synthetic presentation of an original metaphysics of science, namely a metaphysics of properties, both categorical and dispositional, while at the same time opposing strong versions of necessitarism according to which laws are true in all possible worlds. The main theses and arguments are clearly presented in a non-technical way. Thus, on top of being of interest to the specialists of the topics discussed, it is also useful as a textbook in courses for third year and more advanced university students. (shrink)

This volume is a wonderful introduction to Foucault and a testimony to the deep humanity of the man himself.

"Next to Sartre's Search for a Method and in direct opposition to it, Foucault's work is the most noteworthy effort at a theory of history in the last 50 years." -- Library Journal.

Whether the prefrontal cortex is part of the neural substrates of consciousness is currently debated. Against prefrontal theories of consciousness, many have argued that neural activity in the prefrontal cortex does not correlate with consciousness but with subjective reports. We defend prefrontal theories of consciousness against this argument. We surmise that the requirement for reports is not a satisfying explanation of the difference in neural activity between conscious and unconscious trials, and that prefrontal theories of consciousness come out of this (...) debate unscathed. (shrink)

In his influential article ‘Essence and Modality’, Fine proposes a definition of necessity in terms of the primitive essentialist notion ‘true in virtue of the nature of’. Fine’s proposal is suggestive, but it admits of different interpretations, leaving it unsettled what the precise formulation of an Essentialist definition of necessity should be. In this paper, four different versions of the definition are discussed: a singular, a plural reading, and an existential variant of Fine’s original suggestion and an alternative version proposed (...) by Correia which is not based on Fine’s primitive essentialist notion. The first main point of the paper is that the singular reading is untenable. The second that given plausible background assumptions, the remaining three definitions are extensionally equivalent. The third is that, this equivalence notwithstanding, Essentialists should adopt Correia’s version of the definition, since both the existential variant, which has de facto been adopted as the standard version of the definition in the literature, and the plural reading suffer from problems connected to Fine’s primitive essentialist notion. (shrink)

It is widely agreed that fiction is necessarily incomplete, but some recent work postulates the existence of universal fictions—stories according to which everything is true. Building such a story is supposedly straightforward: authors can either assert that everything is true in their story, define a complement function that does the assertoric work for them, or, most compellingly, write a story combining a contradiction with the principle of explosion. The case for universal fictions thus turns on the intuitive priority we assign (...) to the law of non-contradiction. My goal in this paper is to show that our critical and reflective literary practices set constraints on story-telling which preclude universal fictions. I will raise four stumbling blocks for universal fictionalists: the gap between saying and making true, our actual interpretive reactions to story-level contradictions, the criteria we accept for what counts as a story in our literary practices, and the undesirability of the universal fictionalist’s closure principles. (shrink)

The premise that every work belongs to an art-kind has recently inspired a kind-centred approach to theories of art. Kind-centred analyses posit that we should abandon the project of giving a general theory of art and focus instead on giving theories of the arts. The main difficulty, however, is to explain what makes a given kind an art-kind in the first place. Kind-centred theorists have passed this buck on to appreciative practices, but this move proves unsatisfactory. I argue that the (...) root of this dissatisfaction stems not from the act of kicking the can down the road, but from not kicking it far enough. The missing ingredient, I argue, is a notion of convention which does the work of marking the difference between art and non-art for a given physical medium. (shrink)

La contribution de Michel Troper à la théorie générale du droit et à la théorie constitutionnelle est aujourd'hui reconnue et célébrée un peu partout dans le monde. Un talent d'architecte se tient à l'origine de cette audience rarement égalée dans la sphère francophone : celui qu'il faut pour accommoder toutes les exigences, quel que soit l'ordre de valeur dans lequel on les trouve : originalité, rigueur, souci de la fonction, esthétisme, solidité, adaptation, intelligence, inquiétude, esprit critique, renoncement, réalisme... A (...) ces mérites, on ajoutera une curiosité insatiable, un goût prononcé pour l'échange et le débat, un refus distingué de l'académisme, un sens exigeant de l'amitié et une méfiance profônde pour les adjectifs... C'est cet édifice de qualités que les élèves, collègues et amis de Michel Troper sont heureux de célébrer en lui offrant ces Mélanges. (shrink)

The second volume in an unprecedented publishing event: the complete College de France lectures of one of the most influential thinkers of the last century Michel Foucault remains among the towering intellectual figures of postmodern philosophy. His works on sexuality, madness, the prison, and medicine are classics his example continues to challenge and inspire. From 1971 until his death in 1984, Foucault gave public lectures at the world-famous College de France. These lectures were seminal events. Attended by thousands, they (...) created benchmarks for contemporary critical inquiry. The lectures comprising Abnormal begin by examining the role of psychiatry in modern criminal justice, and its method of categorizing individuals who "resemble their crime before they commit it." Building on the themes of societal self-defense in the first volume of this series, Foucault shows how and why defining "abnormality" and "normality" were prerogatives of power in the nineteenth century, shaping the institutions--from the prison system to the family--meant to deal in particular with “monstrosity,” whether sexual, phsyical, or spiritual. The College de France lectures add immeasurably to our appreciation of Foucault's thought, and offer a unique window on his singular worldview. (shrink)

This paper examines two influential theoretical frameworks, set forth by Russell Barkley (1997) and Thomas Brown (2005), and argues that important headway in understanding attention deficit hyperactivity disorder can be made if we acknowledge the way in which human cognition and action are essentially embodied and enactive. The way in which we actively make sense of the world is structured by our bodily dynamics and our sensorimotor engagement with our surroundings. These bodily dynamics are linked to an individual's concerns and (...) felt needs, so that what she attends to in perception, decision-making, and action is partially constituted by her cares and concerns. What I call ?affective framing? engages the whole living body, and ordinarily contributes to attentional focusing, working memory, goal-formulation, and action-monitoring. However, due to affective framing deficits, subjects with ADHD find it difficult to focus their attention, kindle their motivation, and systematically simplify cognitive procedures according to considerations of relevance, salience, and context. Thus, what is impaired in ADHD is not simply a set of executive brain functions, but rather a range of bodily dynamics through which subjects engage with their world. For this reason, intensive behavioral intervention that engages the whole living body may be the most effective, lasting treatment for ADHD. (shrink)

Local theories of consciousness state that one is conscious of a feature if it is adequately represented and processed in sensory brain areas, given some background conditions. We challenge the core prediction of local theories based on long-lasting postdictive effects demonstrating that features can be represented for hundreds of milliseconds in perceptual areas without being consciously perceived. Unlike previous empirical data aimed against local theories, localists cannot explain these effects away by conjecturing that subjects are phenomenally conscious of features that (...) they cannot report. We also discuss alternative explanations that localists could offer. (shrink)

Michelle Kosch examines the conceptions of free will and the foundations of ethics in the work of Kant, Schelling, and Kierkegaard. She seeks to understand the history of German idealism better by looking at it through the lens of these issues, and to understand Kierkegaard better by placing his thought in this context. Kosch argues for a new interpretation of Kierkegaard's theory of agency, that Schelling was a major influence and Kant a major target of criticism, and that both the (...) theory and the criticisms are highly relevant to contemporary debates. (shrink)

Politics, Philosophy, Culture contains a rich selection of interviews and other writings by the late Michel Foucault. Drawing upon his revolutionary concept of power as well as his critique of the institutions that organize social life, Foucault discusses literature, music, and the power of art while also examining concrete issues such as the Left in contemporary France, the social security system, the penal system, homosexuality, madness, and the Iranian Revolution.

Gideon Rosen has recently sketched an argument which aims to establish that the notion of metaphysical modality is systematically ambiguous. His argument contains a crucial sub-argument which has been used to argue for Metaphysical Contingentism, the view that some claims of fundamental metaphysics are metaphysically contingent rather than necessary. In this paper, Rosen’s argument is explicated in detail and it is argued that the most straight-forward reconstruction fails to support its intended conclusion. Two possible ways to save the argument are (...) rebutted and it is furthermore argued that the crucial sub-argument only supports a rather particular variant of Metaphysical Contingentism. (shrink)

Phillips argues that blindsight is due to response criterion artefacts under degraded conscious vision. His view provides alternative explanations for some studies, but may not work well when one considers several key findings in conjunction. Empirically, not all criterion effects are decidedly non-perceptual. Awareness is not completely abolished for some stimuli, in some patients. But in other cases, it was clearly impaired relative to the corresponding visual sensitivity. This relative dissociation is what makes blindsight so important and interesting.

Schopenhauer’s invective is legendary among philosophers, and is unmatched in the historical canon. But these complaints are themselves worthy of careful consideration: they are rooted in Schopenhauer’s philosophy of language, which itself reflects the structure of his metaphysics. This short chapter argues that Schopenhauer’s vitriol rewards philosophical attention; not because it expresses his critical take on Fichte, Hegel, Herbart, Schelling, and Schleiermacher, but because it neatly illustrates his philosophy of language. Schopenhauer’s epithets are not merely spiteful slurs; instead, they reflect (...) deep-seated theoretical and methodological commitments to transparency of exposition. (shrink)

To study consciousness, scientists need to determine when participants are conscious and when they are not. They do so with consciousness detection procedures. A recurring skeptical argument against those procedures is that they cannot be calibrated: there is no way to make sure that detection outcomes are accurate. In this article, I address two main skeptical arguments purporting to show that consciousness scientists cannot calibrate detection procedures. I conclude that there is nothing wrong with calibration in consciousness science.

Dying serves so often within the narratives of Western popular culture, as an exercise in self-improvement both to the individual dying and to those looking on. It enlightens, ennobles and renders exceptional all those affected by it. Though mainstream cinema's “grammar of dying” is mired in similar myths, film has the potential to do dying differently: it can, instead, connect us, ethically, to the vulnerability of others. The aim of this article is to pursue this potential of film. Using the (...) mainstream grammar of dying as a starting point, I will consider how the moving image, and this ethical potential, is harnessed within two hybrid-media pieces about a loved-one's decline and death: George Saxon's art installation, “A Record of Undying” (2014) and photographer Briony Campbell's short film The Dad Project (2009). While these works will be located within the traditions and transformations of moving image practice, the primary concern here is with how such emotionally resonant pieces navigate our relation to, and responsibility for, our own and others' harsh realities. In this way, the question of ethics is grounded not in the solipsistic circuits of affective modes – whether as the catharsis or betterment of mainstream myths, or what Jane Stadler privileges as the ethical effects of empathy – but in something more inherently, more inevitably, political. (shrink)

Within the Neoplatonic tradition, the absolute transcendence of the First Principle—the One-Good, from which the whole reality in its various articulations derives—plays a crucial role. This philosophical perspective implies, particularly in Plotinus and Proclus, some fundamental philosophical consequences, above all the transcendence of the Principle with respect to being and thought as well. This necessarily implies that the One-Good must be conceived of as beyond the intelligible Beauty itself. In this paper I aim to examine the theoretical implications and consequences (...) of this perspective with specific reference to the conception of God’s absolute transcendence outlined within two texts of the Corpus Areopagiticum, overall characterized by the reworking of some fundamental Neoplatonic concepts in the context of Christian theology: the De divinis nominibus and the De mystica theologia. Indeed, in the De divinis nominibus it is shown that the names/predicates attributed to God in the Sacred Scriptures must be understood only in an allegorical-symbolic meaning, because God is above any possible definition. Not even the character of Beauty can be attributed to him, since he radically transcends it: in fact, God constitutes the absolute foundation and the very first source of Beauty itself. Therefore, God must be understood as ἀκαλλής, that is, “devoid of the connotation of Beauty”, precisely because he completely transcends it. In line with this theological and theoretical perspective, in the De mystica theologia a form of radical and absolute apophatism is developed, which in turn must ultimately lead to its own overcoming for the sake of the henosis, the mystical union with God. (shrink)

It is widely believed, among philosophers of literature, that imagining contradictions is as easy as telling or reading a story with contradictory content. Italo Calvino’s The Nonexistent Knight, for instance, concerns a knight who performs many brave deeds, but who does not exist. Anything at all, they argue, can be true in a story, including contradictions and other impossibilia. While most will readily concede that we cannot objectually imagine contradictions, they nevertheless insist that we can propositionally imagine them, and regularly (...) do, simply by entertaining a text which prompts us to do so. I argue that this narrative does not bear scrutiny for two main reasons. First, because propositional imagining is beside the point, where truth in fiction is concerned; evaluating truth in fiction engages the cognitive architecture in ways that prohibit the mobilization of merely propositional imagination to that end. And second, because it is not obvious, given the strategies usually suggested, that we ever propositionally imagine contradictions in the first place—in fact, it seems we go out of our way to avoid directly imagining them. (shrink)

A part of the “return to religion” now evident in European philosophy, this book represents the culmination of the career of a leading phenomenological thinker whose earlier works trace a trajectory from Marx through a genealogy of psychoanalysis that interprets Descartes’s “I think, I am” as “I feel myself thinking, I am.” In this book, Henry does not ask whether Christianity is “true” or “false.” Rather, what is in question here is what Christianity considers as truth, what kind of truth (...) it offers to people, what it endeavors to communicate to them, not as a theoretical and indifferent truth, but as the essential truth that by some mysterious affinity is suitable for them, to the point that it alone is capable of ensuring them salvation. In the process, Henry inevitably argues against the concept of truth that dominates modern thought and determines, in its multiple implications, the world in which we live. Henry argues that Christ undoes “the truth of the world,” that He is an access to the infinity of self-love, to a radical subjectivity that admits no outside, to the immanence of affective life found beyond the despair fatally attached to all objectifying thought. The Kingdom of God accomplishes itself in the here and now through the love of Christ in what Henry calls “the auto-affection of Life.” In this condition, he argues, all problems of lack, ambivalence, and false projection are resolved. (shrink)

An examination of the relation between war and politics, by one of the twentieth century’s most influential thinkers From 1971 until 1984 at the College de France, Michel Foucault gave a series of lectures ranging freely and conversationally over the range of his research. In Society Must Be Defended , Foucault deals with the emergence in the early seventeenth century of a new understanding of war as the permanent basis of all institutions of power, a hidden presence within society (...) that could be deciphered by an historical analysis. Tracing this development, Foucault outlines the genealogy of power and knowledge that had become his dominant concern. (shrink)

Bijdragen over uiteenlopende aspecten van leven en werk van de Franse filosoof (1926-1984).

First published: 2010; Previous edition: 2012..

This paper provides an overview of the history of the notion of essence in 20th century analytic philosophy, focusing on views held by influential analytic philosophers who discussed, or relied on essence or cognate notions in their works. It in particular covers Russell and Moore’s different approaches to essence before and after breaking with British idealism, the (pre- and post-)logical positivists’ critique of metaphysics and rejection of essence (Wittgenstein, Carnap, Schlick, Stebbing), the tendency to loosen the notion of logical necessity (...) to accommodate certain metaphysical truths in Wittgenstein and others, Quine’s logical rehabilitation of metaphysics and criticism of de re modality, the modal view of essence promoted by the development of quantified modal logic (C. I. Lewis, Barcan Marcus, Kripke) and direct reference theory (Barcan Marcus, Kripke, Putnam), and the emergence of the notion of metaphysical necessity (Kneale, Kripke), and finally Fine’s re-establishment of a Neo-Aristotelian, hyperintensional notion of essence in contemporary metaphysics. (shrink)

The brain displays both the anatomical features of a vast amount of interconnected topological mappings as well as the functional features of a nonlinear, metastable system at the edge of chaos, equipped with a phase space where mental random walks tend towards lower energetic basins. Nevertheless, with the exception of some advanced neuro-anatomic descriptions and present-day connectomic research, very few studies have been addressing the topological path of a brain embedded or embodied in its external and internal environment. Herein, by (...) using new formal tools derived from algebraic topology, we provide an account of the metastable brain, based on the neuro-scientific model of Operational Architectonics of brain-mind functioning. We introduce a “topodynamic” description that shows how the relationships among the countless intertwined spatio-temporal levels of brain functioning can be assessed in terms of projections and mappings that take place on abstract structures, equipped with different dimensions, curvatures and energetic constraints. Such a topodynamical approach, apart from providing a biologically plausible model of brain function that can be operationalized, is also able to tackle the issue of a long-standing dichotomy: it throws indeed a bridge between the subjective, immediate datum of the naïve complex of sensations and mentations and the objective, quantitative, data extracted from experimental neuro-scientific procedures. Importantly, it opens the door to a series of new predictions and future directions of advancement for neuroscientific research. (shrink)

The central dogma of molecular biology dictates that, with only a few exceptions, information proceeds from DNA to protein through an RNA intermediate. Examining the enigmatic steps from prebiotic to biological chemistry, we take another road suggesting that primordial peptides acted as template for the self-assembly of the first nucleic acids polymers. Arguing in favour of a sort of archaic “reverse translation” from proteins to RNA, our basic premise is a Hadean Earth where key biomolecules such as amino acids, polypeptides, (...) purines, pyrimidines, nucleosides and nucleotides were available under different prebiotically plausible conditions, including meteorites delivery, shallow ponds and hydrothermal vents scenarios. Supporting a protein-first scenario alternative to the RNA world hypothesis, we propose the primeval occurrence of short two-dimensional peptides termed “selective amino acid- and nucleotide-matching oligopeptides” (henceforward SANMAOs) that noncovalently bind at the same time the polymerized amino acids and the single nucleotides dispersed in the prebiotic milieu. In this theoretical paper, we describe the chemical features of this hypothetical oligopeptide, its biological plausibility and its virtues from an evolutionary perspective. We provide a theoretical example of SANMAO’s selective pairing between amino acids and nucleosides, simulating a poly-Glycine peptide that acts as a template to build a purinic chain corresponding to the glycine’s extant triplet codon GGG. Further, we discuss how SANMAO might have endorsed the formation of low-fidelity RNA’s polymerized strains, well before the appearance of the accurate genetic material’s transmission ensured by the current translation apparatus. (shrink)

Si l’on connaît aujourd’hui le dialogue fructueux que Paul Ricœur a noué avec les penseurs structuralistes, on ignore largement son positionnement face à la mouvance poststructuraliste. Faut-il opposer la philosophie de Ricœur au poststructuralisme à la française ou au contraire doit-on montrer qu’elle en est une variante singulière? C’est la seconde option qui est ici défendue. Certes, le poststructuralisme ne doit pas être considéré comme une école de pensée mais comme une reconstruction qui relève de l’histoire de la philosophie. Dans (...) la mesure où les horizons de dépassement du structuralisme ont été posés de manière chaque fois particulière, il est préférable de parler de poststructuralismes au pluriel. C’est la raison pour laquelle J. Michel propose des confrontations dyadiques entre Ricœur et certains de ses contemporains que l’on regroupe habituellement dans cette mouvance. (shrink)

This collection of essays on the philosophy of Foucault assesses his various work from a variety of perspectives: his place in the history of philosophy; his style and method of philosophical expression; his notions of political power; his ethical thought; and his attitude to psychoanalysis.

This title considers whether any generalisations can be made about word order in language. The chapters, written by international scholars, draw on data from several 'disharmonic' and typologically distinct languages, including Mandarin Chinese, Basque, French, English, Hixkaryana (a Cariban language), Khalkha Mongolian, Uyghur Turkic, and Afrikaans.

La contribución específica de Hans Kellner a la Nueva Filosofía de la Historia se dirige a dar cuenta del revival de la narrativa a partir de los 80 en términos de un revival de la retórica. Sus relecturas de los textos históricos, metahistóricos, literarios y filosóficos nos invitan a apreciar las estrategias retóricas implicadas en ellos, desplegando aquello que habilitan o imposibilitan decir acerca del pasado. Kellner invita a eludir el planteo fundacionista que se ciñe a la cuestión de la (...) validez epistémica del texto, sin caer por ello en la actitud determinista lingüística que fija las estrategias discursivas en tanto estructuras artificiosas y distorsivas de la realidad. Kellner nos desafía a abandonar la metáfora de la distorsión para caracterizar la relación entre representación y realidad. Si en cuanto filósofxs de la historia nos interesa trazar líneas de continuidad y comunidad en la indagación historiográfica, debemos enfocar en sus fuentes retóricas más que en la evidencia documental o la experiencia del pasado cuyo rasgo manifiesto es la fragmentariedad. Su propuesta promueve que nos focalicemos, por un lado, en las innumerables elecciones tomadas entre las diversas modalidades de conocimiento disponibles. Por el otro, nos advierte de la ansiedad provocada por dicha elección en contra de otras opciones descartadas que podrían habernos hecho pensar las cosas de otra manera. ARK: ark:/s18537960/xdxtang:n. (shrink)

Physical and biological measurements might display range values extending towards infinite. The occurrence of infinity in equations, such as the black hole singularities, is a troublesome issue that causes many theories to break down when assessing extreme events. Different methods, such as re-normalization, have been proposed to avoid detrimental infinity. Here a novel technique is proposed, based on geometrical considerations and the Alexander Horned sphere, that permits to undermine infinity in physical and biophysical equations. In this unconventional approach, a continuous (...) monodimensional line becomes an assembly of countless bidimensional lines that superimpose in quantifiable knots and bifurcations. In other words, we may state that Achilles leaves the straight line and overtakes the turtle. (shrink)