In this paper we develop a general representation theory for MV-algebras. We furnish the appropriate categorical background to study this problem. Our guide line is the theory of classifying topoi of coherent extensions of universal algebra theories. Our main result corresponds, in the case of MV-algebras and MV-chains, to the representation of commutative rings with unit as rings of global sections of sheaves of local rings. We prove that any MV-algebra is isomorphic to the MV-algebra of all global sections of (...) a sheaf of MV-chains on a compact topological space. This result is intimately related to McNaughton’s theorem, and we explain why our representation theorem can be viewed as a vast generalization of McNaughton’s theorem. In spite of the language used in this abstract, we have written this paper in the hope that it can be read by experts in MV-algebras but not in sheaf theory, and conversely. (shrink)

In this paper we develop a general representation theory for MV-algebras. We furnish the appropriate categorical background to study this problem. Our guide line is the theory of classifying topoi of coherent extensions of universal algebra theories. Our main result corresponds, in the case of MV-algebras and MV-chains, to the representation of commutative rings with unit as rings of global sections of sheaves of local rings. We prove that any MV-algebra is isomorphic to the MV-algebra of all global sections of (...) a sheaf of MV-chains on a compact topological space. This result is intimately related to McNaughton’s theorem, and we explain why our representation theorem can be viewed as a vast generalization of McNaughton’s theorem. In spite of the language used in this abstract, we have written this paper in the hope that it can be read by experts in MV-algebras but not in sheaf theory, and conversely. (shrink)

In “A new proof of the completeness of the Lukasiewicz axioms” Chang proved that any totally ordered MV-algebra A was isomorphic to the segment \}\) of a totally ordered l-group with strong unit A *. This was done by the simple intuitive idea of putting denumerable copies of A on top of each other. Moreover, he also show that any such group G can be recovered from its segment since \^*}\), establishing an equivalence of categories. In “Interpretation of AF C (...) *-algebras in Lukasiewicz sentential calculus” Mundici extended this result to arbitrary MV-algebras and l-groups with strong unit. He takes the representation of A as a sub-direct product of chains A i, and observes that \ where \. Then he let A * be the l-subgroup generated by A inside \. He proves that this idea works, and establish an equivalence of categories in a rather elaborate way by means of his concept of good sequences and its complicated arithmetics. In this note, essentially self-contained except for Chang’s result, we give a simple proof of this equivalence taking advantage directly of the arithmetics of the the product l-group \, avoiding entirely the notion of good sequence. (shrink)

We show the intimate relationship between McNaughton Theorem and the Chinese Remaindner Theorem for MV-algebras. We develop a very short and simple proof of McNaughton Theorem. The arguing is elementary and right out of the definitions. We exhibit the theorem as just an instance of the Chinese theorem. Since the variety of MV-algebras is arithmetic, the Chinese theorem holds for MV-algebras. However, to make this paper self-contained and entirely elementary, we include a simple proof of this theorem inspired in Ferraioli (...) and Lettieri (Math Logic Q 1:27–43, 2011). (shrink)

Im Hinblick auf den Herbrand'schen Satz für die Prädikatenlogik der ersten Stufe und auf die Lehre vom Beweisverfahren mit Rechenautomaten, die daraus folgt, wird ein Beweis als komputazional synthetisch bezeichnet, wenn er sich auf Objekte bezieht, die im erwiesenen Satz nicht erwähnt sind. Die mathematischen Beweise sind aber auch synthetisch in einem begrifflichen Sinne: die Kontrolle oder die Begrenzung der angewandten Begriffe — die sogenannte Methodenreinheit — ist im allgemeinen unerreichbar.

Im Hinblick auf den Herbrand'schen Satz für die Prädikatenlogik der ersten Stufe und auf die Lehre vom Beweisverfahren mit Rechenautomaten, die daraus folgt, wird ein Beweis als komputazional synthetisch bezeichnet, wenn er sich auf Objekte bezieht, die im erwiesenen Satz nicht erwähnt sind. Die mathematischen Beweise sind aber auch synthetisch in einem begrifflichen Sinne: die Kontrolle oder die Begrenzung der angewandten Begriffe — die sogenannte Methodenreinheit — ist im allgemeinen unerreichbar.

Les sciences cognitives poursuivent un objectif fort ancien, qui consiste, sommairement dit, à décrire et à expliquer les comportements intelligents. Elles appliquent à cet effet des principes méthodologiques moins traditionnels, dont l'adoption définit ce qu'il est convenu d'appeler le "tournant cognitif". Je me propose ici d'exposer brièvement ces principes, de les illustrer par des exemples appropriés et d’en discuter la signification philosophique. Pour l’essentiel, j’ai mis en avant un domaine qui me semble particulièrement pertinent pour les philosophes: l'analyse de la (...) catégorisation, c'est-à-dire du processus par lequel un ensemble d'entités (stimuli sonores ou visuels, objets concrets ou abstraits) en vient à être classifié en catégories séparées, qui peuvent être de type perceptif (phonèmes, couleurs) ou conceptuel (espèces naturelles, types d'événements, catégories esthétiques et morales). (shrink)

An explicit categorical equivalence is defined between a proper subvariety of the class of \-algebras, as defined by Di Nola and Dvurečenskij, to be called \-algebras, and the category of semi-low \-rings. This categorical representation is done using the prime spectrum of the \-algebras, through the equivalence between \-algebras and \-groups established by Mundici, from the perspective of the Dubuc–Poveda approach, that extends the construction defined by Chang on chains. As a particular case, semi-low \-rings associated to Boolean algebras are (...) characterized. (shrink)

An explicit categorical equivalence is defined between a proper subvariety of the class of \-algebras, as defined by Di Nola and Dvurečenskij, to be called \-algebras, and the category of semi-low \-rings. This categorical representation is done using the prime spectrum of the \-algebras, through the equivalence between \-algebras and \-groups established by Mundici, from the perspective of the Dubuc–Poveda approach, that extends the construction defined by Chang on chains. As a particular case, semi-low \-rings associated to Boolean algebras are (...) characterized. (shrink)

Book Review: Dubucs, J., & Bourdeau, M.. Constructivity and Computability in Historical and Philosophical Perspective. Springer Netherlands, XI. 214, pp. ISBN: 978-94-017-9216-5 978-94-017-9217-2, €83.29.

Book Review: Dubucs, J., & Bourdeau, M.. Constructivity and Computability in Historical and Philosophical Perspective. Springer Netherlands, XI. 214, pp. ISBN: 978-94-017-9216-5 978-94-017-9217-2, €83.29.

Information can be public among a group. Whether or not information is public matters, for example, for accounts of interdependent rational choice, of communication, and of joint intention. A standard analysis of public information identifies it with (some variant of) common belief. The latter notion is stipulatively defined as an infinite conjunction: for p to be commonly believed is for it to believed by all members of a group, for all members to believe that all members believe it, and so (...) forth. This analysis is often presupposed without much argument in philosophy. Theoretical entrenchment or intuitions about cases might give some traction on the question, but give little insight about why the identification holds, if it does. The strategy of this paper is to characterize a practical-normative role for information being public, and show that the only things that play that role are (variants of) common belief as stipulatively characterized. In more detail: a functional role for “taking a proposition for granted” in non-isolated decision making is characterized. I then present some minimal conditions under which such an attitude is correctly held. The key assumption links this attitude to beliefs about what is public. From minimal a priori principles, we can argue that a proposition being public among a group entails common commitment to believe among that group. Later sections explore partial converses to this result, the factivity of publicity and publicity from the perspective of outsiders to the group, and objections to the aprioricity of the result deriving from a posteriori existential presuppositions. (shrink)

Should we regard Jennifer Lackey’s ‘Creationist Teacher’ as understanding evolution, even though she does not, given her religious convictions, believe its central claims? We think this question raises a range of important and unexplored questions about the relationship between understanding, factivity and belief. Our aim will be to diagnose this case in a principled way, and in doing so, to make some progress toward appreciating what objectual understanding—i.e., understanding a subject matter or body of information—demands of us. Here is the (...) plan. After some ground clearing in §1, §2 outlines and motivates a plausible working model—moderate factivity—for characterising the sense in which objectual understanding should be regarded as factive. §3 shows how the datum that we can understand false theories can, despite initial suggestions to the contrary, be assimilated straightforwardly within the moderate factivity model. §4 highlights how the inverse kind of case to that explored in §3—viz., a variant of Lackey’s creationist teacher case—poses special problems for moderate factivity. With reference to recent work on moral understanding by Hills, §5 proposes a solution to the problem, and §6 attempts to diagnose why it is that we might originally have been led to draw the wrong conclusion. (shrink)

Financing innovative and costly treatments in various therapeutic fields entails a number of problems in countries where costs are covered by public services. Providing these drugs is forcing actors to define the maximum sums of money society is willing to spend for given health improvements. This raises the question of whether maximum financing should vary according individuals’ circumstances, such as the rareness of a disease, lifestyles, social inequalities experienced over a life time, etc. This article examines a particular priority, namely (...) that given to the youngest patients, such prioritising usually refers to the “fair innings argument”. We question what could justify such a prioritization criterion. Three arguments are considered. At first we consider that FIA could be justified by the objective of equalizing the opportunities of well-being. Next, we proposed justifying the fair innings argument with the aim of equalizing the time provided to individuals to achieve their plan of life, in accordance with Rawls’s theory of justice as fairness. Finally, we proposed considering the FIA as being justified because of the goal of equalizing the time provided to individuals to accept death. These three arguments, of course, have many limitations, some of which we have highlighted. This article doesn’t aim to convince about the superiority of one argument over the other ones. We seek to contribute to the discussions which could happen on prioritization criteria regarding health care, by making explicit what could justify one specific criterion: the age criterion. (shrink)

The paper is a defense of a strict form of anti-realism, competing the "in principle" form defended by Michael Dummett. It proposes to ground anti-realism on the basis of two principles ("immanence" and "implicitness") and to develop the consequences of these principles in the light of sub-structural logics.

Protagoras, of all the ancient philosophers, has perhaps attracted the most interest in modern times. His saying ‘Man is the measure of all things’ caused Schiller to adopt him as the patron of the Oxford pragmatists, and has generally earned him the title of the first humanist. Yet the exact delineation of his philosophcal position remains a baffling task. Neumann, writing on Die Problematik des ‘Homo-mensura’ Satzes in 1938,2 concludes that no certainty whatever can be reached on the meaning of (...) the dictum, since ‘man’, ‘measure’, and ‘things’ are all ambiguous, nor can we tell which of the three is the predicate. The time is past when it was believed that a man's philosophy could be understood apart from the events of his life and the circumstances of his age: yet in the case of Protagoras the historical method of approach has hardly been attempted, although the impact of environment was perhaps more decisive in the formation of philosophical concepts in the Greek world than anywhere else. The reality about which the Greek philosopher spoke had three aspects: it was either the one universe of physics, or the political unity, or God. For example, the book of Heracleitus Περ φσεως was divided into three chapters or logoi, About the Whole, a political, and a theological. Neither physics nor theology supplies from its own subject-matter the form in which this reality was described. (shrink)

Logic and psychology overlap in judgment, inference and proof. The problems raised by this commonality are notoriously difficult, both from a historical and from a philosophical point of view. Sundholm has for a long time addressed these issues. His beautiful piece of work [A Century of Inference: 1837-1936] begins by summarizing the main difficulty in the usual provocative manner of the author: one can start, he says, by the act of knowledge to go to the object, as the Idealist does; (...) one can also start by the object to go to the act, in the Realist mood; never the two shall meet. He is himself inclined to accept the first perspective as the right one and he has eventually developed an original version of antirealism which starts, not from considerations about the publicity of meaning, in the manner of Dummett, but from an epistemic standpoint, trying to search in a non-Fregean tradition of analysis of judgement and cognate notions a way of founding constructivist semantics. The present paper ploughes the same field. We concentrate on the significance, for Sundholm’s program, of the perspective that has been opened by Twardowski in his important essay on acts and products (1912. (shrink)

Standard epistemic logic actually formalizes folk-psychology. The problem of logical omniscience shows that this logic is not adequate in a cognitivist setting. In order to describe realistic information-processing believers, we need both an ontology of particulars and a hyper-intensional taxonomy of representations. From this point of view, sub-structural logics, which do not overlook the syntaxic details of the processing of information, are an interesting alternative to possible worlds semantics.

According to the realist, the meaning of a declarative, non-indexical sentence is the condition under which it is true and the truth-condition of an undecidable sentence can obtain or fail to obtain independently of our capacity, even in principle, to recognize that it obtains or that fails to do so.1 In a series of papers, beginning with “Truth” in 1959, Michael Dummett challenged the position that the classical notion of truth-condition occupied as the central notion of a theory of meaning, (...) and proposed that it should be replaced by the anti-realist (and intuitionistic) notion of assertability-condition. Taken together with normalization results obtained by Dag Prawitz, Dummett’s work truly opened up the anti-realist challenge at the level of proof-theoretical semantics.2 There has been since numerous rejoinders from partisans of classical logic, which were at times met with by attempts at watering down the anti-realist challenge, e.g., by arguing that anti-realism does not necessarily entail the adoption of intuitionistic logic. Only a few anti-realists, such as Crispin Wright and Neil Tennant, tried to look instead in the other direction, towards a more radical version of anti-realism which would entail deeper revisions of classical logic than those recommended by intuitionists.3 In this paper, which is largely programmatic, we shall also argue in favour of a radical anti-realism which would be a genuine alternative to the traditional anti-realism of Dummett and Prawitz. The debate about anti-realism has by now more or less run out of breath and we wish to provide it with a new lease on life, by taking into account the profound changes that took place in proof theory during the intervening years. We have in mind in particular the considerable development within Gentzen-style proof theory of non-classical, substructural logics other than intuitionistic logic, which seriously opens up the possibility that anti-realism, when properly understood, might end up justifying another logic, and the development of closer links between proof theory and computational complexity theory that has renewed interest in a radical form of anti-realism, namely strict finitism. (shrink)

Bolzano was the first to establish an explicit distinction between the deductive methods that allow us to recognise the certainty of a given truth and those that provide its objective ground. His conception of the relation between what we, in this paper, call "subjective consequence", i.e., the relation from epistemic reason to consequence and "objective consequence", i.e., grounding however allows for an interpretation according to which Bolzano advocates an "explicativist" conception of proof: proofs par excellence are those that reflect the (...) objective order of grounding. In this paper, we expose the problems involved by such a conception and argue in favour of a more rigorous demarcation between the ontological and the epistemological concern in the elaboration of a theory of demonstration. (shrink)

The achievements of the textile industry in Roman Britain are often underestimated as a result of the meagreness of our available evidence. The Edict on maximum prices issued by Diocletian in A.D. 301 shows that British capes commanded high prices on the markets of the Empire, and that in the late third century A.D. British rugs were the best in the world. In view of the competition from the traditional centres of rug manufacture in the East, this is an astonishing (...) achievement. (shrink)

The received translation and interpretation of many of the technical terms current in the textile industry of the Roman Empire are inaccurate, because lexicographers have either fought shy of being precise, or have thought that they recognized in the ancient world technical processes which originated at a much later date. The evidence is often equivocal or insufficient, but may still yield details that have been overlooked. The textile expression scutulatus, to take an example, deserves more attention than Blümner has devoted (...) to it. When it refers to the appearance of a garment, Lewis and Short, s.v. scutulatus, translate ‘diamond or lozenge-shaped, checkered’. It seems worth while to attempt a more precise translation, and, if possible, to estimate the significance in context of the goods so designated. (shrink)

This paper can be read as an attempt at providing philosophical foundations to linear logic. The only plausible form of philosophical antirealism deals with practical feasibility rather than with effectivity in principle. The very notion of recognizability is ambiguous, audit has to be considered from a stricter perspective than currently done. The intuitionistic assertability conditions are to be reinforced. This change requires a move towards a frame in which the circumstances of the application of a logical rule can be specified. (...) Gentzen's sequential calculi provide such a frame, when some structural rules have been removed or limited. (shrink)

If the world itself is metaphysically indeterminate in a specified respect, what follows? In this paper, we develop a theory of metaphysical indeterminacy answering this question.

In this article I try to refute the so-called "libertarian" theory of free will, and to examine how our conclusion ought to modify our common attitudes of praise and blame. In attacking the libertarian view, I shall try to show that it cannot be consistently stated. That is, my dscussion will be an "analytic-philosophic" one. I shall neglect what I think is in practice an equally powerful method of attack on the libertarian: a challenge to state his theory in such (...) a way that it will fit in the modern biology and psychology, which are becoming increasingly physicalistic. (shrink)

Ranging from Alan Turing’s seminal 1936 paper to the latest work on Kolmogorov complexity and linear logic, this comprehensive new work clarifies the relationship between computability on the one hand and constructivity on the other. The authors argue that even though constructivists have largely shed Brouwer’s solipsistic attitude to logic, there remain points of disagreement to this day. Focusing on the growing pains computability experienced as it was forced to address the demands of rapidly expanding applications, the content maps the (...) developments following Turing’s ground-breaking linkage of computation and the machine, the resulting birth of complexity theory, the innovations of Kolmogorov complexity and resolving the dissonances between proof theoretical semantics and canonical proof feasibility. Finally, it explores one of the most fundamental questions concerning the interface between constructivity and computability: whether the theory of recursive functions is needed for a rigorous development of constructive mathematics. This volume contributes to the unity of science by overcoming disunities rather than offering an overarching framework. It posits that computability’s adoption of a classical, ontological point of view kept these imperatives separated. In studying the relationship between the two, it is a vital step forward in overcoming the disagreements and misunderstandings which stand in the way of a unifying view of logic. (shrink)

Philosophy of Probability provides a comprehensive introduction to theoretical issues that occupy a central position in disciplines ranging from philosophy of ...

The paper deals with the contributions of Jacques Herbrand to logic and philosophy in historical context.

According to foundationalism, mathematical propositions form a complex objective structure we have to discover and in which each proposition depends for its truth on the propositions that precede and ground it. Proofs that only establish the truth of their conclusions are contrasted with proofs that give also the objective reason of that truth. Foundationalism claims that the cognitive resources required by these proofs are universally available. This paper tries to undermine that claim and to show that foundationalism is a dead (...) end. (shrink)

SABINE CHOQUET. — Est-ce qu’il y a encore une chance pour que le mouvement souverainiste apparaisse comme un mouvement d’avenir ? Et si, pour vous, il n’est pas porteur d’un projet qui permette le développement du Québec, pouvez-vous nous en indiquer les raisons ?ALAIN DUBUC. — Je ne crois pas que le souverainisme soit un mouvement..

Living out of silence, out of a fully functioning, lovingly attentive mind, and not just out of thought, out of a partially functioning mind, is requisite for depth or profundity in living or relating. A fully attentive, truly silent or meditative mind sees that there is real dualism of time and the timeless and that time and the timeless each has its own unique value. The timeless, or real silence, that which alone can make for depth in one's living and (...) relating, can be there only when, in one's awareness, time and all that is related to time, have come to an end. An examination of a wide variety of statements made by writers, both past and present, shows that these understandings are seldom there in contemporary writings, just as they were not there in writings that have come down to us from the past. 'Living beyond the One and the Many' invites readers to consider the possibility that what is presented in it can bring deep meaning to one's way of living in the world"--Publisher's description, back cover. (shrink)

Bolzano fut le premier philosophe à établir une distinction explicite entre les procédés déductifs qui nous permettent de parvenir à la certitude d’une vérité et ceux qui fournissent son fondement objectif. La conception que Bolzano se fait du rapport entre ce que nous appelons ici, d’une part, « conséquence subjective », à savoir la relation de raison à conséquence épistémique et, d’autre part, la « conséquence objective », c’est-à-dire la fondation , suggère toutefois que Bolzano défendait une conception « explicativiste (...) » de la preuve : les preuves par excellence sont celles qui reflètent l’ordre de la fondation objective. Dans cet article nous faisons état des problèmes liés à une telle conception et argumentons en faveur d’une démarcation plus stricte entre la préoccupation ontologique et la préoccupation épistémologique dans l’élaboration d’une théorie de la preuve.Bolzano was the first to establish an explicit distinction between the deductive methods that allow us to recognise the certainty of a given truth and those that provide its objective ground. His conception of the relation between what we, in this paper, call “subjective consequence”, i.e. the relation from epistemic reason to consequence and “objective consequence”, i.e. grounding however suggests that Bolzano advocated an “explicativist” conception of proof : proofs par excellence are those that reflect the objective order of grounding. In this paper, we expose the problems involved by such a conception and argue in favour of a more rigorous demarcation between the ontological and the epistemological concern in the elaboration of a theory of proof. (shrink)

Beth has tried to vindicate the kantian doctrine of mathematical intuition in the frame of contemporary logic. The paper proposes a critical evaluation of this attempt. The theory of mathematical intuition that is exposed in the Critic of Pure Reason is twofold: on one hand, the intuition of the "first principles", as it is analyzed in the Aesthetics, on the other hand, the intuition which is involved in the proofs, as it is analyzed in the Methodology. Contrasting with most defenders (...) of Kant, who try to show that the first kind of intuition remains, in some way, compatible with the non-euclidean geometries, Beth wants to defend the second kind of intuition, by suggesting that it is nothing else than the "instanciation" method, well-known in the predicate calculus. I show that this strategy of defending Kant is unsuccessful. (shrink)

W ciągu 30 lat dokonała się głęboka przemiana w relacji między Internetem a aktywnością naukową. Nastąpiło przesunięcie funkcji Internetu, który przestał być jedynie instrumentem współpracy akademickiej, a stał się również narzędziem używanym przez media społecznościowe, zezwalające na maksymalną dyfuzję irracjonalizmu i starego faktualizmu. Aby zrozumieć tę przemianę, należy ponownie zbadać mechanizmy zbieżności opinii. Wynika ona z istnienia wspólnego świata, który ukazuje nam te same fakty i determinuje nieustanną rewizję przekonań każdej osoby. W tym procesie asymptotycznej zbieżności opinii nie wymaga się (...) żadnej komunikacji między jednostkami. Oczywiście, jeśli fakty znane przez jednych są komunikowane innym, konwergencja znacznie przyspiesza, i to tak bardzo, że wiedzę musimy ująć jako rezultat zbiorowej aktywności, w której wymiana informacji jest jednym z jej istotnych źródeł. Z jednej strony takie poznawcze współdziałanie wydaje się naturalne i łatwe do implementacji. Biorąc pod uwagę właściwości informacji, które przechowujemy, nawet jeśli je udostępniamy, to dzielenie się informacją przestaje być przedmiotem zwykłych trudności związanych ze współpracą. Z drugiej strony takie współdziałanie jest produktywne z samej natury: współpraca między kimś, kto zna φ, i kimś, kto wie, że φ implikuje ψ u obydwu jako mających wiedzę ψ, której żaden z nich nie posiadał przed wymianą informacji. Wczesny Internet pozwolił na ekstremalną intensywność tej informacyjnej współpracy. Obecnie mamy do czynienia z odmienną sytuacją. Poszczególne wyznaczniki rosnącej porowatości między naukowcami a opinią publiczną wzmocniły rolę wymiany. Nie jest to już wymiana informacji, lecz wymiana opinii. Stronniczość tkwiąca w naturze ludzkiej, a szczególnie potwierdzenie tej stronniczości, prowadzi do odwrócenia relacji między faktami a opiniami. Szukamy faktów potwierdzających podzielane przez nas opinie, wątpiąc w te, które ich nie określają, i tworzymy fakty do potwierdzenia tego, o czym jesteśmy przekonani. Dlatego przechodzimy od współdziałania do przynależności, dzieląc Internet na homogeniczne grupy wyznawców. (shrink)

Résumé. En trente ans, le rapport d’Internet à l’entreprise scientifique a changé. Nous sommes passés d’un instrument de collaboration scientifique à un dispositif de réseaux sociaux qui assure la plus large diffusion à l’irrationalisme et à l’alt-factualisme. Pour comprendre ce changement, il convient de réexaminer les mécanismes de la convergence des opinions. La première source de cette convergence est l’existence d’un monde commun, qui nous expose aux mêmes faits et qui détermine par révision successive des croyances de chacun, sans que (...) la moindre communication soit requise, une convergence asymptotique des opinions, et ce quelles que soient les croyances de départ. Naturellement, si les faits connus par les uns sont communiqués aux autres, cette convergence s’accélère considérablement, si bien que nous devons considérer la connaissance comme le résultat d’une activité collective, et l’échange d’informations comme l’une de ses sources nécessaires. D’une part, cette coopération épistémique est naturelle et facilement implémentable : en vertu des propriétés caractéristiques de l’information, qui est un bien que nous conservons lorsque nous le donnons, le partage informationnel est exempt des difficultés qui affectent généralement la coopération. D’autre part, cette coopération est intrinsèquement productive : la collaboration entre celui qui sait que φ et celui qui sait que φ implique ψ met chacun des deux agents en possession de la connaissance de ψ, qui n’était pourtant détenue par personne avant l’échange. L’internet des débuts donne à cette coopération informationnelle une ampleur inégalée. La situation actuelle est différente. Un certain nombre de facteurs, dont la porosité croissante entre les scientifiques et le large public, ont mis au premier plan l’échange, non des informations factuelles, mais celui des opinions. Les biais notoires de la psychologie humaine, au premier rang desquels le biais de confirmation, tendent à inverser le rapport entre les faits et les opinions. On cherche les faits confirmant les opinions entretenues, on met en doute les faits récalcitrants et l’on crée des faits corroborants. En bref, on passe d’une problématique de la coopération à une logique de l’affiliation, segmentant l’internet en groupes doxastiques homogènes. (shrink)

RésuméSelon K. Gödel, les restrictions méthodologiques des constructivistes sont aberrantes, et le point de vue réaliste est beaucoup plus fécond: il est hi‐même parvenu à ses résultats logiques fondarnentaux en donnant une place à la notion de vérite, qui n'est pas de type combinatoire. Le premier théorème d'incomplétude est hi‐même un argument décisif en faveur du réalisme, si l'on accepte le principe d'«accessibilité» en vertu duquel nous pouvons décider de toutes les propriétés de nos constructions intellectuelles. Par ailleurs, il existe (...) un large spectre d'arguments permettant de statuer sur un énoncé indécidable dans un système formel. La thèse mécaniste, selon laquelle l'intelligence humaine peut être pensée sans distorsion significative sur le modèle d'une machine de Turing, est donc inacceptable.SummaryAccording to K. Gödel, the methodological restrictions of the constructivists are aberrant, and the realist point of view is much more fruitful. He reached these fundamental logical results himself by making place for a non‐cornbinatorial notion of truth. The first incompletness theorem is itself a decisive argument in favor of realism, provided that the principle of «accessibility» is accepted, by virtue of which we are capable of determining all the properties of our intellectual constructions. Moreover, there are numerous arguments that permit the evaluation of an undecidable statement in a formal system. The mechanistic thesis, according to which the functioning of the human mind, without significant distorsion, can be compared to a Turing machine, is now unacceptable.ZusammenfassungNach Gödel sind die methodologischen Einschränkungen der Konstruktivisten irrig, und er hält den realistischen Standpuukt für viel fruchtbarer. Er selbst erreichte seine grundlegenden logischen Ergebnisse dadurch, dass er Platz machte für einen nichtkombinatorischen Begriff der Wahrheit. Das erste Unvollständigkeitstheorem ist selbst ein entscheidendes Argument zugunsten des Realismus, sofern das «Zugänglichkeitsprinzip» akzeptiert wird, wonach wir fähig sind, alle Eigenschaften unserer intellektuellen Konstruktionen zu bestinmen. Zudem gibt es zahlreiche Argumente, die die Beurteilung einer unentscheidbaren Aussage in einem formalen System erlauben. Die mechanistische These, nach welcher das Funktionieren des menschlichen Geistes ohne wesentliche Verzerrung mit einer Turingmaschine verglichen werden kann, ist heute nicht mehr annehmbar. (shrink)