Henri Lefebvre has considerable claims to be the greatest living philosopher. His work spans some sixty years and includes original work on a diverse range of subjects, from dialectical materialism to architecture, urbanism and the experience of everyday life. The Production of Space is his major philosophical work and its translation has been long awaited by scholars in many different fields. The book is a search for a reconciliation between mental space and real space. In the course of his (...) exploration, Henri Lefebvre moves from metaphysical and ideological considerations of the meaning of space to its experience in the everyday life of home and city. He seeks, in other words, to bridge the gap between the realms of theory and practice, between the mental and the social, and between philosophy and reality. In doing so, he ranges through art, literature, architecture and economics, and further provides a powerful antidote to the sterile and obfuscatory methods and theories characteristic of much recent continental philosophy. This is a work of great vision and incisiveness. It is also characterized by its author's wit and by anecdote, as well as by a deftness of style which Donald Nicholson-Smith's sensitive translation precisely captures. (shrink)

BackgroundSince 2006, the genetic testing company 23andMe has collected biological samples, self-reported information, and consent documents for biobanking and research from more than 1,000,000 individuals, through a direct-to-consumer online genetic-testing service providing a genetic ancestry report and a genetic health report. However, on November 22, 2013, the Food and Drug Administration halted the sale of genetic health testing, on the grounds that 23andMe was not acting in accordance with federal law, by selling tests of undemonstrated reliability as predictive tests for (...) medical risk factors. Consumers could still obtain the genetic ancestry report, but they no longer had access to the genetic health report in the United States. However, this did not prevent the company from continuing its health research, with previously obtained and future samples, provided that consent had been obtained from the consumers concerned, or with health reports for individuals from other countries. Furthermore, 23andMe was granted FDA authorization on February 19, 2015, first to provide reports about Bloom syndrome carrier status, and, more recently, to provide consumers with “carrier status” information for 35 genes known to cause disease.DiscussionIn this Debate, we highlight the likelihood that the primary objective of the company was probably two-fold: promoting itself within the market for predictive testing for human genetic diseases and ancestry at a low cost to consumers, and establishing a high-value database/biobank for research and personal information).SummaryBy dint of this marketing approach, a two-sided market has been established between the consumer and the research laboratories, involving the establishment of a database/DNA biobank for scientific and financial gain. We describe here the profound ethical issues raised by this setup. (shrink)

" Vivid . . . immense clarity . . . the product of a brilliant and extremely forceful intellect." — Journal of the Royal Naval Scientific Service "Still a sheer joy to read." — Mathematical Gazette "Should be read by any student, teacher or researcher in mathematics." — Mathematics Teacher The originator of algebraic topology and of the theory of analytic functions of several complex variables, Henri Poincare (1854–1912) excelled at explaining the complexities of scientific and mathematical ideas to (...) lay readers. Science and Method, written in 1908, has been appreciated by a wide audience of nonprofessionals and translated into many languages. It defines the basic methodology and psychology of scientific discovery, particularly in regard to mathematics and mathematical physics. Drawing on examples from many fields, it explains how scientists analyze and choose their working facts, and it explores the nature of experimentation, theory, and the mind. 1914 edition. Translated by Francis Maitland. (shrink)

" Vivid . . . immense clarity . . . the product of a brilliant and extremely forceful intellect." — Journal of the Royal Naval Scientific Service "Still a sheer joy to read." — Mathematical Gazette "Should be read by any student, teacher or researcher in mathematics." — Mathematics Teacher The originator of algebraic topology and of the theory of analytic functions of several complex variables, Henri Poincare (1854–1912) excelled at explaining the complexities of scientific and mathematical ideas to (...) lay readers. Science and Method, written in 1908, has been appreciated by a wide audience of nonprofessionals and translated into many languages. It defines the basic methodology and psychology of scientific discovery, particularly in regard to mathematics and mathematical physics. Drawing on examples from many fields, it explains how scientists analyze and choose their working facts, and it explores the nature of experimentation, theory, and the mind. 1914 edition. Translated by Francis Maitland. (shrink)

First published in 2002. Routledge is an imprint of Taylor & Francis, an informa company.

THE VALUE OF SCIENCE INTRODUCTION The search for truth should be the goal of our activities; it is the sole end worthy of them. Doubtless we should first bend our efforts to assuage human suffering, but why ? Not to suffer is a negative ...

First published in 2002. Routledge is an imprint of Taylor & Francis, an informa company.

"With its signal distinction between 'intuition' and 'analysis' and its exploration of the different levels of Duration, _An Introduction to Metaphysics_ has had a significant impact on subsequent twentieth century thought. The arts, from post-impressionist painting to the stream of consciousness novel, and philosophies as diverse as pragmatism, process philosophy, and existentialism bear its imprint. Consigned for a while to the margins of philosophy, Bergson’s thought is making its way back to the mainstream. The reissue of this important work comes (...) at an opportune time, and will be welcomed by teachers and scholars alike." --Peter A. Y. Gunter, University of North Texas. (shrink)

Bergson's central contention is that time is not measurable by any objective standard; in Duration and Simultaneity, that position is tried out against the major movement in physics of the day - Relativity. Bergson argues that Relativity fails to live up to the promise of a truly relative physics, and counter to its own spirit retains some of the objectivist assumptions of previous world views. Duration and Simultaneity was conceived in the desire to make good the new paradigm to which (...) Relativity was bound to lay claim; in the desire to be more Einsteinian than Einstein. (shrink)

Democracy is increasingly being challenged, by disengagement and by anti-pluralist movements (Levitsky and Ziblatt in How Democracies Die: What History Reveals About Our Future, Viking, New York, 2018; Wikforss in _Därför demokrati. Om kunskapen och folkstyret_ [Because of this, democracy. On knowledge and people’s rule] Fri Tanke, 2021; Svolik et al. in J Democr 34(1):5–20, 2023). This article draws upon a theoretical discussion about democracy, pluralism, and threats to democracy. Departing from Dewey, Laclau, Mouffe, Young and Allen, we address democracy (...) as an ideology that centers around pluralism, or an ever-increasing inclusion of voices from the margins as its goal. We argue that perceiving democracy pedagogically as a pluralistic ideology would support students’ democratic citizenship and equip them for a world where threats to democracy are being reported. Employing a case study on Finnish social studies textbooks, we analyze how democracy as well as threats to democracy are discursively portrayed. Our study shows that the textbooks present democracy as predominantly institutional and static. We also find that while disengagement is portrayed as a problem for democracy, anti-pluralist movements are generally not referred to as a threat. Additionally, we examine a discourse in the textbooks that connects freedom of speech with democracy in a way that favors a multitude of opinions, even antidemocratic ones, over creating space for marginalized voices. Drawing on the theoretical discussion and the results of the analysis, we argue that a focus on pluralism as the core of democracy makes the opposition between restricting hate speech and advocating for democracy redundant. (shrink)

Bergson's famous study of the philosophical implications of biological evolutionary theory, presenting the idea of a creative life force shaping both the world and itself.

This work has been selected by scholars as being culturally important, and is part of the knowledge base of civilization as we know it. This work was reproduced from the original artifact, and remains as true to the original work as possible. Therefore, you will see the original copyright references, library stamps (as most of these works have been housed in our most important libraries around the world), and other notations in the work.This work is in the public domain in (...) the United States of America, and possibly other nations. Within the United States, you may freely copy and distribute this work, as no entity (individual or corporate) has a copyright on the body of the work.As a reproduction of a historical artifact, this work may contain missing or blurred pages, poor pictures, errant marks, etc. Scholars believe, and we concur, that this work is important enough to be preserved, reproduced, and made generally available to the public. We appreciate your support of the preservation process, and thank you for being an important part of keeping this knowledge alive and relevant. (shrink)

"Science et méthode" de Henri Poincaré. Mathématicien, physicien et philosophe français (1854-1912).

-- v. 3. From modernity to modernism (towards a metaphilosophy of daily life).

One of the requirements in the Dutch regulation for euthanasia and assisted suicide is that the doctor must be satisfied ‘that the patient's suffering is unbearable, and that there is no prospect of improvement.’ In the notorious Chabot case, a psychiatrist assisted a 50 year old woman in suicide, although she did not suffer from any somatic disease, nor strictly speaking from any psychiatric condition. In Seduced by Death, Herbert Hendin concluded that apparently the Dutch regulation now allows physicians to (...) assist anyone in suicide simply because he or she is unhappy.In this paper, I reject Hendin's conclusion and in particular his description of Mrs Boomsma as someone who was ‘simply unhappy.’ After a detailed narration of her lifestory, I turn to the American philosopher Harry Frankfurt's account of volitional incapacity and love for a more accurate characterization of her suffering. Having been through what she had, she could only go on living as another person than the one she had been when she was a happy mother. That would have violated her integrity, and that she could not bring herself to do. (shrink)

"Dernières pensées" de Henri Poincaré. Mathématicien, physicien et philosophe français (1854-1912).

Introduction: Myth and reality, by H. and H. A. Frankfort.--Egypt: The nature of the universe. The function of the state. The values of life. By J. A. Wilson.--Mesopotamia: The cosmos as a state. The function of the state. The good life. By Thorkild Jacobsen.--The Hebrews: God. Man. Man in the world. Nation, society, and politics. By W. A. Irwin. Conclusion: The emancipation of thought from myth, by H. and H. A. Frankfort.

Self-organization -- Organisms, finalisms, programs, machines -- Spinoza -- Judaism, determinism, and rationalities -- Fabricating the living -- Ethics.

This edition contains a new introduction by Stefan Kipfer, explaining the book’s contemporary ramifications in the ever-expanding reach of the urban in the ...

The history of western metaphysics from Plato onwards is dominated by the dualism of being and appearance. What something really is is believed to be hidden behind the 'mere appearances' through which it manifests. Twentieth-century European thinkers radically overturned this way of thinking. 'Appearance' began to be taken seriously, with the observer participating in the dynamic event of perception.In this important book, Henri Bortoft guides us through this dynamic way of seeing, exploring issues including how we distinguish things, how (...) we find meaning, and the relationship between thought and words. Expanding the scope of his previous book, The Wholeness of Nature, Bortoft shows how Goethean insights combine with this dynamic way of seeing in continental philosophy, to offer an actively experienced 'life of meaning'. This book will be of interest to anyone who wants to understand the contribution and wider implications of modern European thought in the world today. (shrink)

Considers the problem of stylistic change in art, arguing that art is not reducible to external political, social, or economic determinants.

Fulfilling consumer expectations of corporate social responsibility can bring strategic advantage to firms. However, research on the topic is fragmented across disparate disciplines, and a comprehensive framework to connect CSR supply and demand is missing. As a result, firms often supply CSR that does not attract demand, as signified by pessimism about ethical consumerism in recent years and the inconclusive link between corporate financial and social performance. In this study, we propose a framework of strategic CSR management to define how (...) a company’s supply of CSR could meet consumer demand for ethical products by aligning managerial and consumer perspectives. We then investigate empirically whether such a strategic approach, which integrates potential demand in CSR management, would influence consumer choice of products with CSR components. Our hybrid choice modeling allows the inclusion of psychological biases caused by social desirability and cynicism to increase result validity. The findings support the explanatory power of the framework and reveal that consumers prefer some CSR elements while others adversely affect choices. This study advances the understanding of strategic CSR management and its impact on consumer choice and helps managers include the right mix of CSR characteristics in their products to satisfy ethical consumers. (shrink)

Given a 4-tuple of Boolean variables (a, b, c, d), logical proportions are modeled by a pair of equivalences relating similarity indicators ( \({a \wedge b}\) and \({\overline{a} \wedge \overline{b}}\) ), or dissimilarity indicators ( \({a \wedge \overline{b}}\) and \({\overline{a} \wedge b}\) ) pertaining to the pair (a, b), to the ones associated with the pair (c, d). There are 120 semantically distinct logical proportions. One of them models the analogical proportion which corresponds to a statement of the form “a (...) is to b as c is to d”. The paper inventories the whole set of logical proportions by dividing it into five subfamilies according to what they express, and then identifies the proportions that satisfy noticeable properties such as full identity (the pair of equivalences defining the proportion hold as true for the 4-tuple (a, a, a, a)), symmetry (if the proportion holds for (a, b, c, d), it also holds for (c, d, a, b)), or code independency (if the proportion holds for (a, b, c, d), it also holds for their negations \({{(\overline{a},\overline{b}, \overline{c}, \overline{d})}}\) ). It appears that only four proportions (including analogical proportion) are homogeneous in the sense that they use only one type of indicator (either similarity or dissimilarity) in their definition. Due to their specific patterns, they have a particular cognitive appeal, and as such are studied in greater details. Finally, the paper provides a discussion of the other existing works on analogical proportions. (shrink)

This is a partial translation by Wade Baskin of the original French work Ecrits et Paroles (a 3 volume set, 665 pages) published between 1957 and 1959 by Henri Bergson. It includes the translation from Bergson’s introduction to a French ed. of De rerum natura, by Lucretius published in 1884 under the title: Extraits de Lucre`ce.

This volume brings together generous selections from his major texts: Time and Free Will, Matter and Memory, Creative Evolution, Mind-Energy, The Creative Mind, The Two Sources of Morality and Religion and Laughter. In addition it features material from the Melanges never before translated in English, such as the correspondence between Bergson and William James. The volume will be an excellent textbook for pedagogic purposes and a helpful source book for philosophers working across the analytic/continental divide.

RésuméNous introduisons la notion de structure algébrique dynamique, inspirée de l'évaluation dynamique et de la théorie des modèles. Nous montrons comment cette notion constructive permet une relecture de la théorie d'Artin-Schreier, avec la modification capitale que le résultat final est alors établi de manière constructive. Nous pensons que ce que nous avons réalisé ici sur un cas d'école peut être généralisé à des parties significatives de l'algèbre classique, et est donc une contribution à la réalisation du programme de Hilbert pour (...) l'algèbre classique.We introduce the notion of “Dynamic Algebraic Structure” inspired by Dynamic Evaluation and Model Theory. We show that this constructive notion allows a rereading of the Artin-Schreier-Robinson solution for the 17th Hilbert Problem. So, once we know how to reread the proofs, this kind of abstract theory contains an algorithm which computes the concrete result . Our method gives a constructive semantic for certain parts of abstract classical mathematics.The idea is the following: replace the classical algebraic structures “constructed” by Choice and Principle of Third Excluded Middle , by DAS and dynamic evaluations of these DAS. Then TEM is replaced by construction of branching in the trees of dynamic evaluation of the DAS. If Choice is used in the form of Godel completeness theorem, it is not really necessary to use it for obtaining concrete results: in DAS, Choice is simply replaced by … nothing!. This is because the classical proof is by contradiction: “if there were not a sum of squares then some formal theory would admit a pathological model”. The constructive reasoning is more direct: since the pathological theory proves 0 = 1 we know how to construct the sum of squares … and classical models have disappeared in the proof. They are replaced by dynamic evaluations of DAS. We think that we have given, for an academic example, a new method, realizing a kind of Hilbert Program for significant parts of classical algebra. (shrink)

A certain number of philosophers are attracted to the idea that knowledge is the epistemic norm of practical reasoning in the sense that it is epistemically appropriate to rely on p in one’s practical reasoning if and only if one knows that p. A well-known objection to the sufficiency direction of that claim is that there are cases in which a subject supposedly knows that p and yet should not rely on p. In light of the distinction between sufficient and (...) insufficient reasons, some philosophers contend that these cases are inconclusive. In this paper, I argue that this insufficient reason manoeuvre is defective because it either misconstrues the relevant cases or is at odds with strong intuitions about how we (should) reason. I then put forward further considerations relative to the instability of some pieces of reasoning and show how they can be explained by a certainty norm for practical reasoning. (shrink)

Introduction: Myth and reality, by H. and H.A. Frankfort.--Egypt: The nature of the universe. The function of the state. The values of life. By J.A. Wilson.--Mesopotamia: The cosmos of the state. The function of the state. The good life. By T. Jacobsen. Conclusion: The emancipation of thought from myth, by H. and H.A. Frankfort.

C'est le parcours de la composition devenue une oeuvre-objet avant d'être une oeuvre-restituée, médiatisée, publique et partagée, que nous propose Henri-Claude Fantapié, chef d'orchestre, compositeur, pédagogue et musicologue, qui n ...

In lieu of an abstract, here is a brief excerpt of the content:Notes and Discussions NOTE SUR G. SEBBA,"A 'NEw' DESCARTESEDITION?"* Puisque le titre du tr~s int~ressant article: "A 'New' Descartes Edition?" contient un point d'interrogation, donnons imm~diatement la r6ponse: non, il ne s'agit pas d'une 6dition vraiment "nouvelle." Le professeur Gregor Sebba a tr~s exactement expos6 les raisons qui justifieraient une "nouvelle ~dition": le projet de la Librairie Vrin pretend simplement ~tre une solution empirique et provisoire. Des professeurs et (...) des chercheurs ont actuellement besoin de l'6dition Adam et Tannery pour pr6parer des cours ou des theses ou des articles: on va leur procurer les onze 1 volumes sous un format plus commode, certains ~tant divis~s en deux tomes; avec le concours de Centre National de la Recherche Scientifique, nous esp6rons que le prix de vente de chaque tome ne sera pas trop 61ev6; enfin, si minutieuse que soit la r6vision, rien n'empdchera une publication rapide. IIne peut &re question de commentaires. Mais, par des cahiers suppl6mentaires ajout6s ~t chaque volume et particuli~rement importants pour les tomes de la Correspondance, le lecteur saura tout ce que l'6rudition contemporaine ajoute, depuis 1913, ~ notre connaissance des textes cartesiens. Bien entendu, on reprendra ce que L6on Roth a apport6 sur la correspondance de Descartes avec Huygens. M. Bernard Rochot fera entrer darts les appendices tousles 616merits actuellement connus de la future 6dition critique que souhaite M. Gregor Sebba. Quant,h cette 6dition critique, elle est une oeuvre de longue haleine. I1 conviendrait, en particulier, de reviser les notices qui pr6sentent chaque lettre, d'op6rer un s6rieux contr61e des dates propos6es, de reprendre l'6dition des textes du t. X comme le demande M. Gregor Sebba. Tousles historiens de Descartes souhaitent qu'un nouvel Adam et un nouveau Tannery se chargent d'un travail aussi utile. Mais ceux que la Librairie Vrin a consuh~s ont pens6 que, en attendant, une r6-6dition de l'"Adam et Tannery," mis "hjour, si l'on peut dire, ~3tait devenue indispensable. HENRI GOUHIER Paris, France 9 Journal o[ the tlistory o[ Philosophy, Vol. I, No. 2 (1963), pp. 231-236. xII n'est pas question de r6-6diter let. XII, c'est.h-dire la Fie de Descartes par Ch. Adam. [71]... (shrink)

The traditional view in epistemology has it that knowledge is insensitive to the practical stakes. More recently, some philosophers have argued that knowledge is sufficient for rational action: if you know p, then p is a reason you have (epistemically speaking). Many epistemologists contend that these two claims stand in tension with one another. In support of this, they ask us to start with a low stakes case where, intuitively, a subject knows that p and appropriately acts on p. Then, (...) they ask us to consider a high stakes version of the case where, intuitively, this subject does not know that p and could not appropriately act on p without double-checking. Finally, they suggest that the best explanation for our shifty intuitions is that p is a reason the subject has in the low stakes case but not in the high stakes case. In short, according to this explanation, having a reason (in the epistemic sense) is sensitive to the stakes. If so, either knowledge is sensitive to the stakes or else you can know that p even if p is not a reason you have (in the epistemic sense). In this paper, I consider more closely the relation between having a reason (in the epistemic sense) and having a reason to check. I argue that the supposition that if one has p as a reason (in the epistemic sense) then one has a reason not to check whether p, or no reason to check whether p, is highly doubtful. On the contrary, I suggest, it is plausible that, given our fallibility, one always has an epistemic reason to check whether p, whether or not p is a reason one has (in the epistemic sense). On the basis of this observation, I show that one can offer a new way of explaining the cases in question, allowing us to reconcile the traditional view about knowledge and the sufficiency of knowledge for rational action. (shrink)

Poetry turns everything into life. It is that form of life that turns everything into language. It does not come to us unless language itself has become a form of life. That is why it is so unquiet. For it does not cease to work on us. To be the dream of which we are the sleep. A listening, awakening that passes through us, the rhythm that knows us and that we do not know. It is the organization in language (...) of what has always been said to escape language: life, the movement no word is supposed to be able to say. And in effect words do not say it. That is why poetry is a meaning of time more than the meaning of words. Even when its course is ample, it is contained in what passes from us through words. It does not have the time of glaciers and ferns. It tells about a time of life. Through everything that it names. Even its haste transforms. Since it is a listening that compels a listening.But traditionally poetry suffers from the effect of the separation between the order of language and the order or disorder of life. It is that the order in which the thought of language is found is an order against chaos. The fabulous is not found in chaos. It is found in order. A mythic thought about language is charged with the maintaining of order. Thus there is an impassable barrier between poetry in terms of life and language in terms of the forms of poetry. Its meters and its rhymes. That is what we have to think about. Through and for poetry, language, life. Against sentimental poetizations of poetry and of life. As much as against formalizations. Henri Meschonnic is professor of linguistics at the University of Paris—VIII at Vincennes. His penultimate book of poems, Voyageurs de la voix , was awarded the Prix Mallarmé. His other books include Critique du rythme, anthropologie historique du langage and Modernité, modernité . Gabriella Bedetti, associate professor of English at Eastern Kentucy University, is completing A Meschonnic Reader. (shrink)

This article addresses the question of the mechanisms of the emergence of structure and meaning in the biological and physical sciences. It proceeds from an examination of the concept of intentionality and proposes a model of intentional behavior on the basis of results of computer simulations of structural and functional self-organization. Current attempts to endow intuitive aspects of meaningful complexity with operational content are analyzed and the metaphor of DNA as a computer program (the `genetic program') is critically examined in (...) relation to an alternative metaphor of DNA as data. It is argued that relatively simple networks of boolean automata can classify and recognize patterns of binary strings on the basis of non-programmed, self-generated criteria, but lack a capacity for self-observation and interpretation. To overcome this problem it is necessary to clarify the relationships between the goals and underlying mechanisms of a process and between a system and its environment. It will be shown that memory devices that record the histories of interactions are essential for models of conscious and unconscious intentional behavior and that the possibility of infinitely sophisticated - and therefore unprogrammable - machines cannot be avoided. It will be argued that the notion of infinite sophistication allows the ideas of self-organization and physical determinism to be reconciled. These models will be used to suggest how the voluntary aspect of decision-making in general can emerge out of functional self-organizing processes. The conclusion will introduce the notion of `underdetermination' of theories, which imposes an intrinsic limitation on models of complex natural systems - a limitation that, at the same time, may be precisely what makes possible mutual understanding and intersubjectivity. (shrink)

In this book, author Henri Parens discusses and documents the core psychodynamics that lead groups to war. Detailing some of the psychodynamics that led from World War I to World War II and their respective aftermath, Parens addresses how major factors that gave rise to these wars must, can, and have been counteracted.

A possible relevant meaning of Hilbert’s program is the following one: “give a constructive semantic for classical mathematics”. More precisely, give a systematic interpretation of classical abstract proofs about abstract objects, as constructive proofs about constructive versions of these objects.If this program is fulfilled we are able “at the end of the tale” to extract constructive proofs of concrete results from classical abstract proofs of these results.Dynamical algebraic structures or geometric theories seem to be a good tool for doing this (...) job. In this setting, classical abstract objects are interpreted through incomplete concrete specifications of these objects.The structure of axioms in geometric theories gives rise in a natural way to distributive lattices and pointfree topological spaces. Abstract objects correspond to classical points of these pointfree spaces.We shall insist on the Zariski spectrum of distributive lattices and commutative rings and give a constructive interpretation of the Krull dimension.We underline the fact that many abstract objects in classical mathematics can be viewed as points of spectral spaces corresponding to distributive lattices whose definition is concrete and natural.Two important facts are to be stressed.First, abstract proofs about points of these pointfree spaces can very often be reread as constructive proofs about constructible subsets of these spaces.Second, function spaces on these pointfree spaces are often explicitly used in elegant abstract theories. The structure of these function spaces is fully constructive: indeed by the compactness theorem, “all is finite”. The constructive rereading of the abstract proofs is in this setting is nothing but the simple constatation that abstract proofs use correctly axioms.RésuméUne manière pertinente de revisiter le Programme de Hilbert serait la suivante: « donner une sémantique constructive pour les mathématiques classiques ». Plus précisément donner une interprétation systématique des preuves classiques abstraites au sujet des objets abstraits, en terme de preuves constructives au sujet de contreparties constructives de ces objets abstraits.Si ce programme est rempli, nous sommes capables « à la fin de l’histoire » d’extraire des preuves constructives de résultats concrets à partir des preuves classiques abstraites de ces résultats.Les structures algébriques dynamiques, ou ce qui revient à peu près au même les théories géométriques, semblent être un bon outil pour réaliser ce travail. Dans cette optique, les objets abstraits des mathématiques classiques sont remplacés par des spécifications incomplètes mais concrètes de ces mêmes objets.La structure des théories géométriques donne naissance de manière naturelle à des treillis distributifs et à des espaces topologiques sans points. Les objets abstraits utilisés par les mathématiques classiques correspondent aux points classiques de ces espaces sans points.Dans cet article, nous illustrerons ce phénomène principalement avec le spectre de Zariski des treillis distributifs et celui des anneaux commutatifs, en indiquant notamment un équivalent constructif de la notion de dimension de Krull.Nous insistons sur le caractère extrêmement général de l’interpétation des objets abstraits idéaux des mathématiques classiques comme des points d’espaces spectraux associés à des treillis distributifs qui sont définis de façon naturelle et concrète.Souligons deux faits d’expérience importants.Tout d’abord, les preuves abstraites au sujet des points de ces espaces sans points peuvent en général être relues comme des preuves concernant les parties constructibles de ces espaces.Enfin, les espaces de fonctions continues sur ces espaces sans points sont souvent utilisés dans d’élégantes théories abstraites. Ces espaces de fonctions sont bien définis constructivement. Cela tient au « théorème de compacité » qui nous dit que dans le cadre en question « tout est fini ». La relecture constructive des preuves abstraites n’est alors rien d’autre que la constatation que les axiomes géométriques sont utilisés de manière correcte. (shrink)