Bernardi Perini, G. Aceto italico e poesia luciliana: Hor. Sat. I 7.--Bernardinello, S. Bessarione riassume la Fisica di Aristotele.--Bottecchia, M. E. I Mechanicha di Aristotele nel Parisinus graecus 2507.--Bottin, L. La tradizione araba della Retorica di Aristotele e il problema dell'exemplar decurtatum.--Chiereghin, F. Analogie di struttura tra la metodologia della storiografia filosofica di Platone e di Kant.--Ciani, M. G. Poesia come enigma.--Degani, E. Hippon. fr. 40 Med.--Donaldi, F. Note preparatorie all'edizione dell'Encomio di Elena gorgiano nella traduzione latina inedita di Pietro (...) Bembo.--Fumarola, V. Euripide e la tetralogia della femminilità.--Gentilini, A. Una consolatoria inedita del Bessarione.--Ghinatti, F. I culti greci di Paestum.--Longo, O. Note all'Elena e alle Nuvole.--Lunelli, A. Solis rota.--Meschini, A. Su alcuni luoghi del Reso.--Mignucci, M. In margine al concetto aristotelico di esistenza.--Mioni, E. L'Antologia greca da Massimo Planude a Marco Musuro.--Pianezzola, E. Haurio=ferio, perfodio. Un calco omerico mediato dagli scolii.--Pontani, F. M. La distruzione di Melos di Ghiannis Ritsos.--Rinaldi Mioni, G. Aspetto verbale nel greco classico e strutturalismo.--Riondato, E. Problematicità semantica ed etica nell'Etica a Nicomaco.--Serra, G. Alcune osservazioni sulle traduzioni dall'arabo in ebraico e in latino del De generatione et corruptione di Aristotele e dello pseudo-aristotelico Liber de causis.--Traina, A. Convexo nutantem pondere mundum (Verg. Ecl. 4,50).--Valentini, R. La reintroduzione dell'onciale e la datazione dei manoscritti greci in minuscola. (shrink)

This paper aims to offer a critique of a rigidly moralistic temperament in public discourse from the perspective of political realism. It unpacks three types of moralism in public discourse, and for each, it explains why it is normatively problematic from a realist perspective: ‘Moralist Causalism’ is the belief that moral preaching is an apt way to affect the world for the better; ‘Moralist Manicheism’ is a dichotomous division of the world between good and evil; ‘Moralist Absolutism’ is the conviction (...) that only morality matters when we answer the question, ‘What should we do?’. The paper then turns these negative criticisms into a positive recipe for how to look realistically at what is valuable in the world. First, there are not only multiple values in the world but also different sources of values (epistemic, instrumental, aesthetic…) which may conflict with one another. We call this requirement ‘Meta-Normative Pluralism’. Second, politics is pivotal because it is the sphere where the clashes among all other spheres of value are authoritatively resolved—a role which moralists usurp for morality. (shrink)

Why do we remember the past and not the future? What does it mean for time to "flow"? Do we exist in time or does time exist in us? In lyric, accessible prose, Carlo Rovelli invites us to consider questions about the nature of time that continue to puzzle physicists and philosophers alike. For most readers this is unfamiliar terrain. We all experience time, but the more scientists learn about it, the more mysterious it remains. We think of it (...) as uniform and universal, moving steadily from past to future, measured by clocks. Rovelli tears down these assumptions one by one, revealing a strange universe where at the most fundamental level time disappears. He explains how the theory of quantum gravity attempts to understand and give meaning to the resulting extreme landscape of this timeless world. Weaving together ideas from philosophy, science and literature, he suggests that our perception of the flow of time depends on our perspective, better understood starting from the structure of our brain and emotions than from the physical universe. (shrink)

The Heythrop Journal, Volume 63, Issue 5, Page 869-885, September 2022.

This volume examines the limitations of mathematical logic and proposes a new approach to logic intended to overcome them. To this end, the book compares mathematical logic with earlier views of logic, both in the ancient and in the modern age, including those of Plato, Aristotle, Bacon, Descartes, Leibniz, and Kant. From the comparison it is apparent that a basic limitation of mathematical logic is that it narrows down the scope of logic confining it to the study of deduction, without (...) providing tools for discovering anything new. As a result, mathematical logic has had little impact on scientific practice. Therefore, this volume proposes a view of logic according to which logic is intended, first of all, to provide rules of discovery, that is, non-deductive rules for finding hypotheses to solve problems. This is essential if logic is to play any relevant role in mathematics, science and even philosophy. To comply with this view of logic, this volume formulates several rules of discovery, such as induction, analogy, generalization, specialization, metaphor, metonymy, definition, and diagrams. A logic based on such rules is basically a logic of discovery, and involves a new view of the relation of logic to evolution, language, reason, method and knowledge, particularly mathematical knowledge. It also involves a new view of the relation of philosophy to knowledge. This book puts forward such new views, trying to open again many doors that the founding fathers of mathematical logic had closed historically. (shrink)

One of the world's most renowned theoretical physicists, Carlo Rovelli has entranced millions of readers with his singular perspective on the cosmos. In Helgoland, Rovelli examines the enduring enigma of quantum theory. The quantum world Rovelli describes is as beautiful as it is unnerving. Helgoland is a treeless island in the North Sea where the 21-year-old Werner Heisenberg first developed quantum theory, setting off a century of scientific revolution. Full of alarming ideas (ghost waves, distant objects that seem to (...) be magically connected, cats that appear both dead and alive), quantum physics has led to countless discoveries and technological advancements. Today our understanding of the world is based on this theory, yet it is still profoundly mysterious. As scientists and philosophers continue to fiercly debate the theory's meaning, Rovelli argues that its most unsettling contradictions can be explained by seeing the world as fundamentally made of relationships, not substances. We and everything around us exist only in our interactions with one another. This bold idea suggests new directions for understanding the structure of reality and even the nature of consciousness. Rovelli makes learning about quantum mechanics an almost psychedelic experience. Shifting our perspective once again, he takes us on a riveting journey through the universe so we can better understand our place in it. (shrink)

Summary Acoustic depth is an elusive indicator that touches the world of emergencies, or perceptual focus, in a peculiar way. The realm in which these forms of recognition operate indeed links media theory to perception theory and aesthetic reflection. Expressions such as acoustic scene, sound depth or sharpness, or acoustic image when discussing the receptive forms of various microphone models, are just a few cases where imaginative synthesis translates the sense of phenomena arising from the resistance of sensory properties to (...) the structures of linguistic formalization. The language of media is full of these references, which seem to refer to a common sense that emerges in the differentiation of perceptual channels, but is rarely made explicit in a clear manner. To understand acoustic depht’s nature, we can use the concept of emergence: every time we hear a sound, that acoustic process is always surrounded by a myriad of small sounds that interact with it. The notion of emergence can be applied to anything present in the surrounding environment. It can be applied to any configuration that breaks the homogeneity of a perceptual field. So, we can analyze the complexity of this synthetic formation by tracing it back to increasingly simpler synthetic planes. When talking about composition, synthesis, and association, it has already the results of compositional operations and which provided the ultimate or primary material – either term suffices, depending on the direction we choose to take. These are essential factors in spatial orientation processes, but they are structurally opaque: we’ll work on three examples taken from classical music, ethnomusicology, and hearing aids. (shrink)

Sigieri di Brabante, maestro di filosofia presso la facoltà delle arti dell'università di Parigi, fu uno dei principali esponenti di quell'"aristotelismo radicale" che costituì uno dei principali obiettivi delle condanne del vescovo Étienne Tempier del 1270 e del 1277. Il De aeternitate mundi è la testimonianza di un corso tenuto da Sigieri nel 1272 sul problema se la specie umana sia stata creata nel tempo. Vengono qui esaminate sia in generale le tesi di Sigieri riguardo ai diversi argomenti affrontati, sia (...) nello specifico il problema della causazione per intermediari. Quest'ultimo tema rimanda non solo alle altre opere in cui Sigieri ha affrontato tali problematiche, ma anche ad una tradizione che trae le sue origini nella filosofia greca classica e si sviluppa nel medioevo latino e arabo. Segue la traduzione del testo di Sigieri, condotta sull'edizione critica curata da Bernardo Carlos Bazán. (shrink)

La presente investigación busca generar un diálogo entre la filosofía de las ciencias de Susan Haack y la teoría queer de Judith Butler. Para ello, recorreremos primero los hitos más importantes del feminismo y, en un segundo momento, veremos cómo estos desembocaron en la teoría queer. Luego, tomaremos como hilo conductor el problema del cuerpo y de la evidencia objetiva para analizar, en un tercer momento, la postura butleriana y, en un cuarto momento, la haackiana. Como sección conclusiva, pondremos ambas (...) posturas en diálogo considerando sus planteamientos en un caso concreto: la intersexualidad. (shrink)

Facts happen at every interaction, but they are not absolute: they are relative to the systems involved in the interaction. Stable facts are those whose relativity can effectively be ignored. In this work, we describe how stable facts emerge in a world of relative facts and discuss their respective roles in connecting quantum theory and the world. The distinction between relative and stable facts resolves the difficulties pointed out by the no-go theorem of Frauchiger and Renner, and is consistent with (...) the experimental violation of the Local Friendliness inequalities of Bong et al.. Basing the ontology of the theory on relative facts clarifies the role of decoherence in bringing about the classical world and solves the apparent incompatibility between the ‘linear evolution’ and ‘projection’ postulates. (shrink)

Many moral philosophers have criticized intensive animal farming because it can be harmful to the environment, it causes pain and misery to a large number of animals, and furthermore eating meat and animal-based products can be unhealthful. The issue of industrially farmed animals has become one of the most pressing ethical questions of our time. On the one hand, utilitarians have argued that we should become vegetarians or vegans because the practices of raising animals for food are immoral since they (...) minimize the overall happiness. Deontologists, on the other hand, have argued that the practices of raising animals for food are immoral because animals have certain rights and we have duties toward them. Some virtue ethicists remain unconvinced of deontic and consequentialist arguments against the exploitation of animals and suggest that a virtue-based approach is better equipped to show what is immoral about raising and using animals for food, and what is virtuous about ethical veganism. (shrink)

In this paper we argue that Sen's defence of liberal democracy suffers from a moralistic and pro-liberal bias that renders it unable to take pluralism as seriously as it professes to do. That is because Sen’s commitment to respecting pluralism is not matched by his account of how to individuate the sorts of preferences that ought to be included in democratic deliberation. Our argument generalises as a critique of the two most common responses to the fact of pluralism in contemporary (...) (i.e. post-Rawls) liberalism: a broadly procedural understanding of autonomy and the idea of deliberative democracy. That is to say, the difficulties with pluralism we identify can be traced back to the particular version of Kantian deontology prevalent in contemporary liberalism, and to the equally prevalent aspiration to ground political legitimacy in a moralised consensus. (shrink)

Quantum mechanics is not about 'quantum states': it is about values of physical variables. I give a short fresh presentation and update on the *relational* perspective on the theory, and a comment on its philosophical implications.

We discuss the principles for a primitive, object-linguistic notion of consequence proposed by ) that yield a version of Curry’s paradox. We propose and study several strategies to weaken these principles and overcome paradox: all these strategies are based on the intuition that the object-linguistic consequence predicate internalizes whichever meta-linguistic notion of consequence we accept in the first place. To these solutions will correspond different conceptions of consequence. In one possible reading of these principles, they give rise to a notion (...) of logical consequence: we study the corresponding theory of validity by showing that it is conservative over a wide range of base theories: this result is achieved via a well-behaved form of local reduction. The theory of logical consequence is based on a restriction of the introduction rule for the consequence predicate. To unrestrictedly maintain this principle, we develop a conception of object-linguistic consequence, which we call grounded consequence, that displays a restriction of the structural rule of reflexivity. This construction is obtained by generalizing Saul Kripke’s inductive theory of truth. Grounded validity will be shown to satisfy several desirable principles for a naïve, self-applicable notion of consequence. (shrink)

Contrary to claims about the irrelevance of philosophy for science, I argue that philosophy has had, and still has, far more influence on physics than is commonly assumed. I maintain that the current anti-philosophical ideology has had damaging effects on the fertility of science. I also suggest that recent important empirical results, such as the detection of the Higgs particle and gravitational waves, and the failure to detect supersymmetry where many expected to find it, question the validity of certain philosophical (...) assumptions common among theoretical physicists, inviting us to engage in a clearer philosophical reflection on scientific method. (shrink)

In his 1956 book ‘The Direction of Time’, Hans Reichenbach offered a comprehensive analysis of the physical ground of the direction of time, the notion of physical cause, and the relation between the two. I review its conclusions and argue that at the light of recent advances in physics Reichenbach analysis provides the best account for the physical underpinning of these notions. I integrate results in cosmology, and on the physical underpinning of records and agency into Reichenbach’s account, and discuss (...) which questions it leaves open. (shrink)

This article argues that political realists have at least two strategies to provide distinctively political normative judgements that have nothing to do with morality. The first ground is instrumental normativity, which states that if we believe that something is a necessary means to a goal we have, we have a reason to do it. In politics, certain means are required by any ends we may intend to pursue. The second ground is epistemic normativity, stating that if something is true, this (...) gives us a reason to believe it. In politics, there are certain empirical regularities that ought to be acknowledged for what they are. Both sources are flawed. Instrumental normativity only requires coherence between attitudes and beliefs, and one can hang on to false beliefs to preserve attitudes incompatible with reality. I may desire to eschew power relations, and accordingly I may imagine politics to be like a camping trip. Epistemic normativity, on the other hand, operates critically, striking down existing normative claims. It shows us that politics is nothing like a camping trip, but it doesn’t tell us what we should do about it. We conclude by showing that if the two are taken together, they remedy each other’s flaws. (shrink)

Is reality three-dimensional and becoming real (Presentism), or is reality four-dimensional and becoming illusory (Eternalism)? Both options raise difficulties. I argue that we do not need to be trapped by this dilemma. There is a third possibility: reality has a more complex temporal structure than either of these two naive options. Fundamental becoming is real, but local and unoriented. A notion of present is well defined, but only locally and in the context of approximations.

This paper explores the scope and limits of rational consensus through mutual respect, with the primary focus on the best known formal model of consensus: the Lehrer–Wagner model. We consider various arguments against the rationality of the Lehrer–Wagner model as a model of consensus about factual matters. We conclude that models such as this face problems in achieving rational consensus on disagreements about unknown factual matters, but that they hold considerable promise as models of how to rationally resolve non-factual disagreements.

The project of growing meat artificially represents for some the next best thing to humanity. If successful, it could be the solution to several problems, such as feed- ing a growing global population while reducing the environmental impact of raising animals for food and, of course, reducing the amount and degree of animal cruelty and suffering that is involved in animal farming. In this paper, I argue that the issue of the morality of such a project has been framed only (...) in terms of the best conse- quences for the environment, animals, and humans, or in terms of deontic princi- ples. I argue that to appreciate how deep and difficult this issue is, it is necessary to consider it in terms of a virtue-oriented approach. Such an approach will reveal aspects that are not apparent, not contemplated by typical approaches, but are essen- tial to our understanding of the morality of lab-grown meat. As I argue, evaluating the issue from a virtue-oriented perspective suggests that the project of in vitro meat should not be supported because it stems from unvirtuous motivations. (shrink)

In what follows I consider the apparent contrast between two kinds of theories of context: a theory of objective context - exemplified in the works of Kaplan and Lewis - and a theory of subjective context -exemplified in the works of McCarthy and Giunchiglia. I consider then some difficulties for the objective theory. I don't give any formalization; instead I give some theoretical points about the problem. A possible result could be the abandon of the double indexing for a development (...) a multi-context theory (I give an example of a case). However other results could be possible and a challenge is posed to solve problems using the best results from each tradition of research. (shrink)

Substructural logics and their application to logical and semantic paradoxes have been extensively studied. In the paper, we study theories of naïve consequence and truth based on a non-reflexive logic. We start by investigating the semantics and the proof-theory of a system based on schematic rules for object-linguistic consequence. We then develop a fully compositional theory of truth and consequence in our non-reflexive framework.

We study the relationships between two clusters of axiomatizations of Kripke’s fixed-point models for languages containing a self-applicable truth predicate. The first cluster is represented by what we will call ‘\-like’ theories, originating in recent work by Halbach and Horsten, whose axioms and rules are all valid in fixed-point models; the second by ‘\-like’ theories first introduced by Solomon Feferman, that lose this property but reflect the classicality of the metatheory in which Kripke’s construction is carried out. We show that (...) to any natural system in one cluster—corresponding to natural variations on induction schemata—there is a corresponding system in the other proving the same sentences true, addressing a problem left open by Halbach and Horsten and accomplishing a suitably modified version of the project sketched by Reinhardt aiming at an instrumental reading of classical theories of self-applicable truth. (shrink)

At least since Kuhn’s Structure, philosophers have studied the influence of social factors in science’s pursuit of truth and knowledge. More recently, formal models and computer simulations have allowed philosophers of science and social epistemologists to dig deeper into the detailed dynamics of scientific research and experimentation, and to develop very seemingly realistic models of the social organization of science. These models purport to be predictive of the optimal allocations of factors, such as diversity of methods used in science, size (...) of groups, and communication channels among researchers. In this paper we argue that the current research faces an empirical challenge. The challenge is to connect simulation models with data. We present possible scenarios about how the challenge may unfold. (shrink)

Biological diversity would apparently seem the most intuitive and easily studied of all the ecological concepts. However, in practice biodiversity has suffered from great number of definitions that vary with the specific needs of the different researchers, thus making it extremely confusing as an ecological concept. In this paper, I shortly review the concept of biodiversity showing that there exists a substantial ambiguity among ecologists as far as biodiversity conceptualization and evaluation is concerned. I conclude that, due to this major (...) disagreement on its very nature, biodiversity may be defined simply as a set of multivariate summary statistics for quantifying different characteristics of community structure. (shrink)

These are lectures prepared for a series of seminars I am invited to give at Princeton’s Philosophy Department in November 2024.

Marcus William Hunt argues that when co-parents disagree over whether to raise their child (or children) as a vegan, they should reach a compromise as a gift given by one parent to the other out of respect for his or her authority. Josh Millburn contends that Hunt’s proposal of parental compromise over veganism is unacceptable on the ground that it overlooks respect for animal rights, which bars compromising. However, he contemplates the possibility of parental compromise over ‘unusual eating,’ of animal-based (...) foods obtained without the violation of animal rights. I argue for zero parental compromise, rejecting a rights-oriented approach, and propose a policy that an ethical vegan parent and a non-vegan co-parent should follow to determine how to raise their children. (shrink)

The concept of evidence has gone unanalysed in much of the current debate between proponents and critics of evidence-based medicine. In this paper I will suggest that part of the controversy rests on an understanding of the word “evidence” that is too broad, and therefore contains the contradictions that allow both camps to defend their position and charge their adversaries. I will argue that reconciling the different meanings of the word ‘evidence’ in “evidence-based medicine” should help put EBM in its (...) rightful place. (shrink)

Ethical veganism is the view that raising animals for food is an immoral practice that must be stopped because of the harm it causes to the animals, the environment, and our health. Carlo Alvaro argues the only way to stop that harm is to acquire the virtues that enable us to act justly and benevolently toward animals.

Choice can be defined in thermodynamical terms, and shown to have a thermodynamic cost: choosing between a binary alternative at temperature T dissipates an energy $$E\ge kT\ln 2$$.

There are fields of research on NE which still need attention: the edition of the text the style and rhetorical and logical instruments employed by Aristotle in setting out his position. After indicating the situation of the research on the text of NE, I describe some rhetorical devices used by Aristotle in his work: the presence of a preamble, clues about how the argument will be developed, a tendency to introduce new arguments in an inconspicuous way and the articulation of (...) general definitions through more specific analyses. At a deeper level NE seems to be organised on the model of investigating definitions described in the second Book of the Postenor Analytics, and not according the so-called' dialectical method'. In conclusion I argue that NE is not an early or a confused work, as some scholars maintain, but rather a skilful construction, the fruit of a mature intelligence. (shrink)

The project of growing meat artificially represents for some the next best thing to humanity. If successful, it could be the solution to several problems, such as feeding a growing global population while reducing the environmental impact of raising animals for food and, of course, reducing the amount and degree of animal cruelty and suffering that is involved in animal farming. In this paper, I argue that the issue of the morality of such a project has been framed only in (...) terms of the best consequences for the environment, animals, and humans, or in terms of deontic principles. I argue that to appreciate how deep and difficult this issue is, it is necessary to consider it in terms of a virtue-oriented approach. Such an approach will reveal aspects that are not apparent, not contemplated by typical approaches, but are essential to our understanding of the morality of lab-grown meat. As I argue, evaluating the issue from a virtue-oriented perspective suggests that the project of in vitro meat should not be supported because it stems from unvirtuous motivations. (shrink)

The paper distinguishes between two kinds of mathematics, natural mathematics which is a result of biological evolution and artificial mathematics which is a result of cultural evolution. On this basis, it outlines an approach to the philosophy of mathematics which involves a new treatment of the method of mathematics, the notion of demonstration, the questions of discovery and justification, the nature of mathematical objects, the character of mathematical definition, the role of intuition, the role of diagrams in mathematics, and the (...) effectiveness of mathematics in natural science. (shrink)

Truth-theoretic deflationism holds that truth is simple, and yet that it can fulfil many useful logico-linguistic roles. Deflationism focuses on axioms for truth: there is no reduction of the notion of truth to more fundamental ones such as sets or higher-order quantifiers. In this paper I argue that the fundamental properties of reasonable, primitive truth predicates are at odds with the core tenets of classical truth-theoretic deflationism that I call fix, express, and quantify. Truth may be regarded as a broadly (...) logical, sui generis notion. However, this has little to do with the original aims of the deflationary theory of truth. (shrink)

This paper challenges the ‘Standard Account’ of the so-called endoxic method that Aristotle articulates in a well-known passage from book VII of the Nicomachean Ethics. That account is problematic because it misreads what Aristotle says and thereby attributes to him an unusually rigid and conservative method that he himself does not seem to employ. This paper carefully analyzes the semantics and syntax of the book VII passage in order to present a novel and improved understanding of the endoxic method. This (...) improved account helps adjudicate scholarly debates about the method’s purpose and scope. (shrink)

Following the invitation of the editors of Foundations of Physics, I give here a personal assessment of string theory, from the point of view of an outsider, and I compare it with the theory, methods, and expectations of my own field.

A solution to the issue of time in quantum gravity is proposed. The hypothesis that time is not defined at the fundamental level (at the Planck scale) is considered. A natural extension of canonical Heisenberg-picture quantum mechanics is defined. It is shown that this extension is well defined and can be used to describe the "non-Schrödinger regime," in which a fundamental time variable is not defined. This conclusion rests on a detailed analysis of which quantities are the physical observables of (...) the theory; a main technical result of the paper is the identification of a class of gauge-invariant observables that can describe the (observable) evolution in the absence of a fundamental definition of time. The choice of the scalar product and the interpretation of the wave function are carefully discussed. The physical interpretation of the extreme "no time" quantum gravitational physics is considered. (shrink)

The philosophy of mathematics of the last few decades is commonly distinguished into mainstream and maverick, to which a ‘third way’ has been recently added, the philosophy of mathematical practice. In this paper the limitations of these trends in the philosophy of mathematics are pointed out, and it is argued that they are due to the fact that all of them are based on a top-down approach, that is, an approach which explains the nature of mathematics in terms of some (...) general unproven assumption. As an alternative, a bottom-up approach is proposed, which explains the nature of mathematics in terms of the activity of real individuals and interactions between them. This involves distinguishing between mathematics as a discipline and the mathematics embodied in organisms as a result of biological evolution, which however, while being distinguished, are not opposed. Moreover, it requires a view of mathematical proof, mathematical definition and mathematical objects which is alternative to the top-down approach. (shrink)

Le terme archê dans l’ Éthique à Nicomaque III désigne le « principe » d’une chose au sens de ce qui a pouvoir sur elle, la cause motrice des actions. Ce pouvoir de domination est exprimé par l’expression eph’hêmin, et c’est Aristote qui l’introduit pour la première fois dans le débat sur la responsabilité morale. Les chapitres où il discute le concept d’ eph’hêmin sont clairement de nature dialectique, et son analyse se situe très probablement à l’intérieur d’un débat académique (...) sur ces thèmes, dont on trouve des traces dans les Lois. Les disciples de Platon pouvaient trouver des difficultés à comprendre les thèses de Platon sur le rapport entre action et caractère, et Aristote propose une solution originale, fondée sur sa théorie des quatre causes. Contre Platon, il refuse de rejeter la responsabilité des actions et du caractère mauvais sur la cité et les éducateurs, et place l’origine du caractère dans les actions et les choix de l’individu. Avec ce choix, Aristote élargit le problème de la responsabilité humaine de la question traditionnelle de savoir si les méchants sont responsables de leurs mauvaises actions au problème général de la responsabilité de toutes les actions, bonnes ou mauvaises. (shrink)

While Gödel's (first) incompleteness theorem has been used to refute the main contentions of Hilbert's program, it does not seem to have been generally used to stress that a basic ingredient of that program, the concept of formal system as a closed system - as well as the underlying view, embodied in the axiomatic method, that mathematical theories are deductions from first principles must be abandoned. Indeed the logical community has generally failed to learn Gödel's lesson that Hilbert's concept of (...) formal system as a closed system is inadequate and continues to use it as if there were no incompleteness theorem. In this paper I will stress the role of Gödel's incompleteness theorem in showing the inadequacy of such a concept of formal system and the need for a more articulated view of mathematical theories. More generally I will argue that Gödel's result entails that, as an alternative to mathematical logic, a new concept of logic is required: logic as the theory of communicating inference processes. (shrink)