Las sociedades democráticas contemporáneas se caracterizan por dos fenómenos empíricos ineludibles: 1) La existencia de profundos, persistentes e inerradicables desacuerdos políticos al interior de cada sociedad democrática; 2) la necesidad de adoptar cursos de acción política comunes a todos los ciudadanos (Waldron, 2005: 18). La concepción democrática agregacionista, receptada por la mayoría de las constituciones políticas, ha mostrado ciertas deficiencias para atender a esta realidad. En respuesta, han surgido dos concepciones democráticas rivales, a saber: a) agonal-pluralista; y b) deliberativa-republicana. Este (...) artículo tendrá por objetivos: 1) reconstruir los presupuestos conceptuales y normativos de estas dos concepciones; 2) contrastarlas; y 3) esbozar argumentos en defensa de una concepción democrática deliberativa-republicana. Para ello, la metodología a emplear será la de la filosofía política analítica, a saber: a) la reconstrucción racional de conceptos; y b) el equilibrio reflexivo. El presente trabajo pretende contribuir al debate actual acerca de cuál es la mejor concepción normativa de democracia a adoptar en las condiciones normativas no ideales contemporáneas. (shrink)

El presente trabajo consta de tres partes esenciales que tienen como objetivo identificar y describir una parrhesia auténtica en Jesús, a la luz de los cursos dictados por Michel Foucault en el Collège de France. La primera y segunda parte se centran una caracterización,contrastación e indagación de las nociones elementales que constituyen los discursos de verdad en el ministerio de Jesús. En la tercera y última parte presento un acercamiento de Jesús con Diógenes y Sócrates,y cómo ciertos elementos de la (...) presencia de la parrhesia cínica presentes en Jesús posibilitan la idea de Jesús como un "héroe filosófico". (shrink)

The empirical study of belief is emerging at a rapid clip, uniting work from all corners of cognitive science. Reliance on belief in understanding and predicting behavior is widespread. Examples can be found, inter alia, in the placebo, attribution theory, theory of mind, and comparative psychological literatures. Research on belief also provides evidence for robust generalizations, including about how we fix, store, and change our beliefs. Evidence supports the existence of a Spinozan system of belief fixation: one that is automatic (...) and independent of belief rejection. Independent research supports the existence of a system of fragmented belief storage: one that relies on large numbers of causally isolated, context-sensitive stores of belief in memory. Finally, empirical and observational data support at least two systems of belief change. One system adheres, mostly, to epistemological norms of updating; the other, the psychological immune system, functions to guard our most centrally held beliefs from potential inconsistency with newly formed beliefs. Refining our under- standing of these systems can shed light on pressing real-world issues, such as how fake news, propaganda, and brainwashing exploit our psychology of belief, and how best to construct our modern informational world. (shrink)

Most physics theories are deterministic, with the notable exception of quantum mechanics which, however, comes plagued by the so-called measurement problem. This state of affairs might well be due to the inability of standard mathematics to “speak” of indeterminism, its inability to present us a worldview in which new information is created as time passes. In such a case, scientific determinism would only be an illusion due to the timeless mathematical language scientists use. To investigate this possibility it is necessary (...) to develop an alternative mathematical language that is both powerful enough to allow scientists to compute predictions and compatible with indeterminism and the passage of time. We suggest that intuitionistic mathematics provides such a language and we illustrate it in simple terms. (shrink)

Dans ce livre, Malebranche expose sa philosophie à travers des entretiens avec un philosophe, un janséniste et un mandarin chinois. Il explore les différentes dimensions de la métaphysique, de la religion et de la mort et cherche à répondre aux questions fondamentales de l'existence. Tout étudiant en philosophie trouvera ce livre intéressant et instructif. 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 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. 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)

This paper offers a framework for consciousness of internal reality. Recent PET experiments are reviewed, showing partial overlap of cortical activation during self-produced actions and actions observed from other people. This overlap suggests that representations for actions may be shared by several individuals, a situation which creates a potential problem for correctly attributing an action to its agent. The neural conditions for correct agency judgments are thus assigned a key role in self/other distinction and self-consciousness. A series of behavioral experiments (...) that demonstrate, in normal subjects, the poor monitoring of action-related signals and the difficulty in recognizing self-produced actions are described. In patients presenting delusions, this difficulty dramatically increases and actions become systematically misattributed. These results point to schizophrenia and related disorders as a paradigmatic alteration of a ''Who?'' system for self-consciousness. (shrink)

It is usual to identify initial conditions of classical dynamical systems with mathematical real numbers. However, almost all real numbers contain an infinite amount of information. I argue that a finite volume of space can’t contain more than a finite amount of information, hence that the mathematical real numbers are not physically relevant. Moreover, a better terminology for the so-called real numbers is “random numbers”, as their series of bits are truly random. I propose an alternative classical mechanics, which is (...) empirically equivalent to classical mechanics, but uses only finite-information numbers. This alternative classical mechanics is non-deterministic, despite the use of deterministic equations, in a way similar to quantum theory. Interestingly, both alternative classical mechanics and quantum theories can be supplemented by additional variables in such a way that the supplemented theory is deterministic. Most physicists straightforwardly supplement classical theory with real numbers to which they attribute physical existence, while most physicists reject Bohmian mechanics as supplemented quantum theory, arguing that Bohmian positions have no physical reality. (shrink)

Do scientific theories limit human knowledge? In other words, are there physical variables hidden by essence forever? We argue for negative answers and illustrate our point on chaotic classical dynamical systems. We emphasize parallels with quantum theory and conclude that the common real numbers are, de facto, the hidden variables of classical physics. Consequently, real numbers should not be considered as ``physically real" and classical mechanics, like quantum physics, is indeterministic.

It is usual to identify initial conditions of classical dynamical systems with mathematical real numbers. However, almost all real numbers contain an infinite amount of information. I argue that a finite volume of space can’t contain more than a finite amount of information, hence that the mathematical real numbers are not physically relevant. Moreover, a better terminology for the so-called real numbers is “random numbers”, as their series of bits are truly random. I propose an alternative classical mechanics, which is (...) empirically equivalent to classical mechanics, but uses only finite-information numbers. This alternative classical mechanics is non-deterministic, despite the use of deterministic equations, in a way similar to quantum theory. Interestingly, both alternative classical mechanics and quantum theories can be supplemented by additional variables in such a way that the supplemented theory is deterministic. Most physicists straightforwardly supplement classical theory with real numbers to which they attribute physical existence, while most physicists reject Bohmian mechanics as supplemented quantum theory, arguing that Bohmian positions have no physical reality. (shrink)

Copyright ©2005–2010 All rights reserved. Jonathan Bennett [Brackets] enclose editorial explanations. Small ·dots· enclose material that has been added, but can be read as though it were part of the original text. Occasional •bullets, and also indenting of passages that are not quotations, are meant as aids to grasping the structure of a sentence or a thought. Every four-point ellipsis . . . . indicates the omission of a brief passage that seems to present more difficulty than it is worth. (...) Larger omissions are reported, between brackets, in normal-sized type. The numbering of the segments of each dialogue is Malebranche’s. (shrink)

Henrich and Boyd (2002) were the first to propose a formal model of the role of attraction in cultural evolution. They came to the surprising conclusion that, when both attraction and selection are at work, final outcomes are determined by selection alone. This result is based on a deterministic view of cultural attraction, different from the probabilistic view introduced in Sperber (1996). We defend this probabilistic view, show how to model it, and argue that, when both attraction and selection are (...) at work, both affect final outcomes. (shrink)

The claim that the observation of a violation of a Bell inequality leads to an alleged alternative between nonlocality and non-realism is annoying because of the vagueness of the second term.

How might a human communication system be bootstrapped in the absence of conventional language? We argue that motivated signs play an important role (i.e., signs that are linked to meaning by structural resemblance or by natural association). An experimental study is then reported in which participants try to communicate a range of pre-specified items to a partner using repeated non-linguistic vocalization, repeated gesture, or repeated non-linguistic vocalization plus gesture (but without using their existing language system). Gesture proved more effective (measured (...) by communication success) and more efficient (measured by the time taken to communicate) than non-linguistic vocalization across a range of item categories (emotion, object, and action). Combining gesture and vocalization did not improve performance beyond gesture alone. We experimentally demonstrate that gesture is a more effective means of bootstrapping a human communication system. We argue that gesture outperforms non-linguistic vocalization because it lends itself more naturally to the production of motivated signs. (shrink)

We aim to do two things in this article. On the positive end, our goal is to explain how some seemingly incompatible aspects of belief live together, by presenting distinct mechanistic explanations of each of them: in particular we want to show how belief can be discerning, credulous, rational, and irrational. After clarifying our positive view, we take aim at some competitor views in the second half of the paper, particularly offering critiques of epistemic vigilance and social marketplace accounts of (...) belief. We conclude by inviting proponents to provide an architecture for belief that can be tested against existing models. (shrink)

This study investigates the social–psychological mechanisms leading individuals in organizations to engage in environmental citizenship behaviors, which entail keeping abreast of, and participating in, the environmental affairs of a company. Informed by the corporate greening and organizational behavior literature, we suggested that an employee’s level of involvement in the management of a company’s environmental impact was the overt manifestation of his or her discretionary sense of commitment to environmental concerns in the work context, and that such commitment developed through the (...) interplay of individual, organizational, and supervisory factors. Our general findings support the idea that when environmental protection is valued and encouraged by the company and line managers, organization members are more likely to experience a volitional sense of attachment and responsibility to corporate environmental goals and values, which is enacted through citizenship behaviors. We also expected that individual ecological beliefs would strengthen the environmental commitment of employees via identification with, and adherence to, the socially responsible cause embodied by the organization and its managerial staff. But it did not. On the contrary, the data indicated that corporate environmental policy is more likely to influence an employee’s level of environmental commitment when he or she holds weak versus strong personal ecological beliefs. Theoretical and managerial implications of our findings are discussed. (shrink)

This paper compares two explanations of the process by which human communication systems evolve: iterated learning and social collaboration. It then reports an experiment testing the social collaboration account. Participants engaged in a graphical communication task either as a member of a community, where they interacted with seven different partners drawn from the same pool, or as a member of an isolated pair, where they interacted with the same partner across the same number of games. Participants’ horizontal, pair‐wise interactions led (...) “bottom up” to the creation of an effective and efficient shared sign system in the community condition. Furthermore, the community‐evolved sign systems were as effective and efficient as the local sign systems developed by isolated pairs. Finally, and as predicted by a social collaboration account, and not by an iterated learning account, interaction was critical to the creation of shared sign systems, with different isolated pairs establishing different local sign systems and different communities establishing different global sign systems. (shrink)

This monograph proposes a new way of implementing interaction in logic. It also provides an elementary introduction to Constructive Type Theory. The authors equally emphasize basic ideas and finer technical details. In addition, many worked out exercises and examples will help readers to better understand the concepts under discussion. One of the chief ideas animating this study is that the dialogical understanding of definitional equality and its execution provide both a simple and a direct way of implementing the CTT approach (...) within a game-theoretical conception of meaning. In addition, the importance of the play level over the strategy level is stressed, binding together the matter of execution with that of equality and the finitary perspective on games constituting meaning. According to this perspective the emergence of concepts are not only games of giving and asking for reasons, they are also games that include moves establishing how it is that the reasons brought forward accomplish their explicative task. Thus, immanent reasoning games are dialogical games of Why and How. (shrink)

Discussions on indeterminism in physics focus on the possibility of an open future, i.e. the possibility of having potential alternative future events, the realisation of one of which is not fully determined by the present state of affairs. Yet, can indeterminism affect also the past, making it open as well? We show that by upholding principles of finiteness of information one can entail such a possibility. We provide a toy model that shows how the past could be fundamentally indeterminate, while (...) also explaining the intuitive (and observed) asymmetry between the past—which can be remembered, at least partially—and the future—which is impossible to fully predict. (shrink)

We present a new proof of soundness/completeness of tableaux with respect to dialogical games in Classical First-Order Logic. As far as we know it is the first thorough result for dialogical games where finiteness of plays is guaranteed by means of what we call repetition ranks.

How do humans manage to keep track of a gradually changing object or person as the same persisting individual despite the fact that the extraction of information about this individual must often rely on heterogeneous information sources and heterogeneous tracking methods? The article introduces the Empirical Tracking of Individuals theory to address this problem. This theory proposes an analysis of the concept of integrated tracking, which refers to the capacity to acquire, store, and update information about the identity and location (...) of individuals in our environment. It hypothesizes that certain functions of attention are a key to explaining how the cognitive flexibility of the human mind overcomes the heterogeneity of sources and methods in integrated tracking. At least two premises lend support to this hypothesis. First, heterogeneity of tracking sources is overcome by the combination of information from multiple perceptual modalities and a phenomenon of multisensory 'transparency'. Second, heterogeneity of tracking sources and methods may also be overcome by inferences that combine information across domains to acquire reasons to believe propositions about the target's location and identity. (shrink)

In this paper we claim that pragmatist philosophical practice is incompatible with scientistic philosophy. The kind of pragmatism used for making this case follows the spirit and method of philosophical pragmatists such as William James, John Dewey, Richard Rorty, and a related pragmatic tradition, Confucian Philosophy. Pragmatism starts from immediate experience, and refuses to cleave off the reality and salience of what is found in such experience in the process of thinking. Pragmatism also concerns itself with social problems, broadly conceived. (...) In contrast to this focus on immediate experience, the influence of science in much philosophizing involves a kind of scientism through which the relevance, value, and even reality of experience is brought into question. It also concerns itself with a narrowly defined set of so-called philosophical problems. In this regard, pragmatist philosophical practice is fundamentally opposed to scientistic philosophical practice. We will start by modelling the kind of philosophical practice that stems from pragmatism, and the role of immediate experience in it. Subsequently, we will introduce two modes of philosophizing that diminish if not negate the role of experience. One is bald naturalist philosophizing, and the other is a priori scientific philosophizing. In the last section, we will show how main commitments of both of these traditions are incompatible with a pragmatist philosophy that remains committed to the original impulse of pragmatism. (shrink)

[R]eflection is a system of thought no less closed than insanity, with this difference that it understands itself and the madman too, whereas the madman does not understand it.– Merleau-Ponty, Phen...

This paper explores the role of iconicity in spoken language and other human communication systems. First, we concentrate on graphical and gestural communication and show how semantically motivated iconic signs play an important role in creating such communication systems from scratch. We then consider how iconic signs tend to become simplified and symbolic as the communication system matures and argue that this process is driven by repeated interactive use of the signs. We then consider evidence for iconicity at the level (...) of the system in graphical communication and finally draw comparisons between iconicity in graphical and gestural communication systems and in spoken language. (shrink)

This paper explores the role of iconicity in spoken language and other human communication systems. First, we concentrate on graphical and gestural communication and show how semantically motivated iconic signs play an important role in creating such communication systems from scratch. We then consider how iconic signs tend to become simplified and symbolic as the communication system matures and argue that this process is driven by repeated interactive use of the signs. We then consider evidence for iconicity at the level (...) of the system in graphical communication and finally draw comparisons between iconicity in graphical and gestural communication systems and in spoken language. (shrink)

This book features 20 essays that explore how Latin medieval philosophers and theologians from Anselm to Buridan conceived of habitus, as well as detailed studies of the use of the concept by Augustine and of the reception of the medieval doctrines of habitus in Suàrez and Descartes. Habitus are defined as stable dispositions to act or think in a certain way. This definition was passed down to the medieval thinkers from Aristotle and, to a lesser extent, Augustine, and played a (...) key role in many of the philosophical and theological developments of the time. Written by leading experts in medieval and modern philosophy, the book offers a historical overview that examines the topic in light of recent advances in medieval cognitive psychology and medieval moral theory. Coverage includes such topics as the metaphysics of the soul, the definition of virtue and vice, and the epistemology of self-knowledge. The book also contains an introduction that is the first attempt at a comprehensive survey of the nature and function of habitus in medieval thought. The material will appeal to a wide audience of historians of philosophy and contemporary philosophers. It is relevant as much to the historian of ancient philosophy who wants to track the historical reception of Aristotelian ideas as it is to historians of modern philosophy who would like to study the progressive disappearance of the term “habitus” in the early modern period and the concepts that were substituted for it. In addition, the volume will also be of interest to contemporary philosophers open to historical perspectives in order to renew current trends in cognitive psychology, virtue epistemology, and virtue ethics. (shrink)

With his massive redeployment hypothesis (MRH), Anderson claims that novel cognitive functions are likely to rely on pre-existing circuits already possessing suitable resources. Here, we put forward recent findings from studies in numerical cognition in order to show that the role of sensorimotor experience in the ontogenetical development of a new function has been largely underestimated in Anderson's proposal.

It is commonly assumed that moral deliberation requires that the alternatives available in a choice situation are evaluatively comparable. This comparability assumption is threatened by claims of incomparability, which is often established by means of the small improvement argument (SIA). In this paper I argue that SIA does not establish incomparability in a stricter sense. The reason is that it fails to distinguish incomparability from a kind of evaluative indeterminacy which may arise due to the vagueness of the evaluative comparatives (...) ‘better than,’ ‘worse than,’ and ‘equally as good as.’. (shrink)

The following paper argues that issues in paradigmatic proposals for solving the new demarcation problem stem from absolutist assumptions about judgments of value legitimacy. Both the problem of uninformativeness (Larroulet Philippi 2020; Fernandez-Pinto 2014, 2015) and the problem of ambiguous judgments of cases (Hicks 2014; Intemann 2017) are explained by an absolutist pretension contained in one of the main aims of these proposals: providing criteria for differentiating legitimate from illegitimate uses of values, without qualification. After presenting the problems and showing (...) how they stem from that common source, we will sketch a way forward, inspired mainly by Joseph Rouse’s Beyond Epistemic Sovereignty (1996), advancing routes that can allow philosophers of science to evade these pitfalls and engage with scientific practice in a more salutary manner. (shrink)

En el presente trabajo se ofrece, hasta donde nos consta, la única traducción al español del capítulo “Sobre el ajedrez” de la obra enciclopédica _De naturis rerum_ escrita hacia el año 1190 por el filósofo inglés Alejandro Neckam (1157-1217). El capítulo mencionado, que sigue a otro sobre los jugadores de dados, es relevante no solamente para comprender la continuidad de una actitud anti-lúdica que hunde sus raíces en el pensamiento de los primeros cristianos sino para advertir la recepción del ajedrez (...) musulmán en la Inglaterra medieval cristiana tanto en sus representaciones simbólicas como en las reglas del juego. (shrink)

This longitudinal study investigated the capability of various positive psychological resources to directly or indirectly protect specific well-being outcomes and moderate the effects on well-being of health and economic threats in a lockdown situation during the 2020 health crisis in France. At the beginning of lockdown, participants completed self-assessment questionnaires to document their initial level of well-being and state of nine different well-established psychological resources, measured as traits: optimism, hope, self-efficacy, gratitude toward the world, self-transcendence, wisdom, gratitude of being, peaceful (...) disengagement, and acceptance. Three weeks later, a weekly follow-up was started to record changes in well-being and reported threats for a duration of 5 weeks. Results show that psychological resources efficiently protected well-being in a variety of ways: they buffered the adverse effects of reported threats to health and wealth, increased the well-being averages, and reduced the decline in well-being over time. More specifically, emotional well-being was positively predicted by hope, gratitude of being, and, to a lesser level, by acceptance; psychological well-being by self-efficacy, personal wisdom, and gratitude of being; social well-being only by gratitude toward the world; and inner well-being by optimism, gratitude of being, and acceptance. The study emphasizes the importance of cultivating psychological resources in ordinary times to protect individuals' well-being when difficult and extraordinary circumstances occur. It also offers clues to the kind of resources one may want to develop. (shrink)

In a 1993 paper, I argued that empirical treatments of the epistemologyused by scientists in experimental work are too abstract in practice tocounter relativist efforts to explain the outcome of scientificcontroversies by reference to sociological forces. This was because, atthe rarefied level at which the methodology of scientists is treated byphilosophers, multiple mutually inconsistent instantiations of theprinciples described by philosophers are employed by contestingscientists. These multiple construals change within a scientificcommunity over short time frames, and these different versions ofscientific methodology (...) can determine the outcome of a controversy. Iillustrated with a comparatively detailed analysis of the methodologyused by biologists debating the existence of an entity called thebacterial mesosome between the mid-1950s and the mid-1970s. This 1993piece has drawn several critiques in the philosophical literature. Inthis present piece I respond to these critiques and argue that they failto address the core argument of the original paper, and I reflectfurther on the methodologies of philosophers of science pursuingempirical or `naturalistic' epistemology. (shrink)

This article describes a new type of medical-legal partnership (MLP) that targets the health and justice concerns of people enmeshed in the U.S criminal justice system: a partnership between clinicians who care for people with criminal system involvement and public defenders. This partnership offers an opportunity to not only improve patient health outcomes but also to facilitate less punitive court dispositions, such as jointly advocating for community-based rehabilitation and treatment rather than incarceration.

Quantum physics, which offers an explanation of the world on the smallest scale, has fundamental implications that pose a serious challenge to ordinary logic. Particularly counterintuitive is the notion of entanglement, which has been explored for the past 30 years and posits an ubiquitous randomness capable of manifesting itself simultaneously in more than one place. This amazing 'non-locality' is more than just an abstract curiosity or paradox: it has entirely down-to-earth applications in cryptography, serving for example to protect financial information; (...) it also has enabled the demonstration of 'quantum teleportation', whose infinite possibilities even science-fiction writers can scarcely imagine. This delightful and concise exposition does not avoid the deep logical difficulties of quantum physics, but gives the reader the insights needed to appreciate them. From 'Bell's Theorem' to experiments in quantum entanglement, the reader will gain a solid understanding of one of the most fascinating areas of contemporary physics. (shrink)

We argue that two powerful error-theoretic concepts provide a general framework that satisfactorily accounts for key aspects of the explanation of physical patterns. This method gives an objective criterion to determine which mathematical models in a class of neighboring models are just as good as the exact one. The method also emphasizes that abstraction is essential for explanation and provides a precise conceptual framework that determines whether a given abstraction is explanatorily relevant and justified. Hence, it increases our epistemological understanding (...) of how one should go about reconstructing scientific practices by making clear that, at a fundamental level, a key aspect of mathematical modeling consists in exactly solving nearby problems. (shrink)

We designed a new protocol requiring French adult participants to group a large number of Munsell colour chips into three or four groups. On one, relativist, view, participants would be expected to rely on their colour lexicon in such a task. In this framework, the resulting groups should be more similar to French colour categories than to other languages categories. On another, universalist, view, participants would be expected to rely on universal features of perception. In this second framework, the resulting (...) groups should match colour categories of three and four basic terms languages. In this work, we first collected data to build an accurate map of French colour terms categories. We went on testing how native French speakers spontaneously sorted a set of randomly presented coloured chips and, in line with the relativist prediction, we found that the resulting colour groups were more similar to French colour categories than to three and four basic terms languages. However, the same results were obtained in a verbal interference condition, suggesting that participants rely on language specific and nevertheless perceptual, colour categories. Collectively, these results suggest that the universalist/relativist dichotomy is a too narrow one. (shrink)

Human cognition and behavior are dominated by symbol use. This paper examines the social learning strategies that give rise to symbolic communication. Experiment 1 contrasts an individual-level account, based on observational learning and cognitive bias, with an inter-individual account, based on social coordinative learning. Participants played a referential communication game in which they tried to communicate a range of recurring meanings to a partner by drawing, but without using their conventional language. Individual-level learning, via observation and cognitive bias, was sufficient (...) to produce signs that became increasingly effective, efficient, and shared over games. However, breaking a referential precedent eliminated these benefits. The most effective, most efficient, and most shared signs arose when participants could directly interact with their partner, indicating that social coordinative learning is important to the creation of shared symbols. Experiment 2 investigated the contribution of two distinct aspects of social interaction: behavior alignment and concurrent partner feedback. Each played a complementary role in the creation of shared symbols: Behavior alignment primarily drove communication effectiveness, and partner feedback primarily drove the efficiency of the evolved signs. In conclusion, inter-individual social coordinative learning is important to the evolution of effective, efficient, and shared symbols. (shrink)

An innovative literary analysis of Freud's "Wolf Man.".

ABSTRACT This paper examines consequences of the computer revolution in mathematics. By comparing its repercussions with those of conceptual developments that unfolded in the nineteenth century, I argue that the key epistemological lesson to draw from the two transformative periods is that effective and successful mathematical practices in science result from integrating the computational and conceptual styles of mathematics, and not that one of the two styles of mathematical reasoning is superior. Finally, I show that the methodology deployed by applied (...) mathematicians in modern scientific computing is a paradigmatic instance of this key lesson. (shrink)