The early twentieth century was a lively time for the foundations of mathematics. This ensuing debates were, in large part, a reaction to the settheoretic and nonconstructive methods that had begun making their way into mathematical practice around the turn of the twentieth century. The controversy was exacerbated by the discovery that overly na¨ıve formulations of the fundamental principles governing the use of sets could result in contradictions. Many of the leading mathematicians of the day, including Hilbert, Henri (...) class='Hi'>Poincar´e, ´. (shrink)

The fundamental problem on which Ilya Prigogine and the Brussels- Austin Group have focused can be stated briefly as follows. Our observations indicate that there is an arrow of time in our experience of the world (e.g., decay of unstable radioactive atoms like Uranium, or the mixing of cream in coffee). Most of the fundamental equations of physics are time reversible, however, presenting an apparent conflict between our theoretical descriptions and experimental observations. Many have thought that the observed arrow of (...) time was either an artifact of our observations or due to very special initial conditions. An alternative approach, followed by the Brussels-Austin Group, is to consider the observed direction of time to be a basic physical phenomenon due to the dynamics of physical systems. This essay focuses mainly on recent developments in the Brussels-Austin Group after the mid 1980s. The fundamental concerns are the same as in their earlier approaches (subdynamics, similarity transformations), but the contemporary approach utilizes rigged Hilbert space (whereas the older approaches used Hilbert space). While the emphasis on nonequilibrium statistical mechanics remains the same, their more recent approach addresses the physical features of large Poincar´. (shrink)

Un problème fondamental dans la réflexion sur les fondements des mathématiques consiste à déterminer ce qu’est un axiome. Cette question est spécialement importante en vue de l’étude de nouveaux axiomes pour la théorie des ensembles (tels que les axiomes de grands cardinaux) dont la légitimité est fortement controversée ; cet article s’insère dans le débat. En analysant les écrits de Poincaré et de Hilbert, nous observons que, malgré les différences profondes dans la pensée de ces deux logiciens, ils parvinrent (...) à la même conception des axiomes de la géométrie qui ne seraient que des définitions déguisées. Nous généralisons cette conception des axiomes comme définitions de concepts à n’importe quel système axiomatique (en particulier aux axiomes de la théorie des ensembles). (shrink)

Around the turn of the century, Poincare and Hilbert each published an account of geometry that took the discipline to be an implicit definition of its concepts. The terms ‘point’, ‘line’, and ‘plane’ can be applied to any system of objects that satisfies the axioms. Each mathematician found spirited opposition from a different logicist—Russell against Poincare' and Frege against Hilbert— who maintained the dying view that geometry essentially concerns space or spatial intuition. The debates illustrate the emerging idea (...) of mathematics as the science of structure. The article closes with some remarks on structuralist and nonstructuralist themes in Frege's own development of arithmetic. (shrink)

This paper discusses Husserl’s views on physical theories in the first volume of his Logical Investigations, and compares them with those of his contemporaries Pierre Duhem and Henri Poincaré. Poincaré’s views serve as a bridge to a discussion of Husserl’s almost unknown views on physical geometry from about 1890 on, which in comparison even with Poincaré’s—not to say Frege’s—or almost any other philosopher of his time, represented a rupture with the philosophical tradition and were much more in tune with the (...) physical geometry underlying the Einstein-Hilbert general theory of relativity developed more than two decades later. (shrink)

In the early years of this century, Poincaré and Russell engaged in a debate concerning the nature of mathematical reasoning. Siding with Kant, Poincaré argued that mathematical reasoning is characteristically non-logical in character. Russell urged the contrary view, maintaining that (i) the plausibility originally enjoyed by Kant's view was due primarily to the underdeveloped state of logic in his (i.e., Kant's) time, and that (ii) with the aid of recent developments in logic, it is possible to demonstrate its falsity. (...) This refutation of Kant's views consists in showing that every known theorem of mathematics can be proven by purely logical means from a basic set of axioms. In our view, Russell's alleged refutation of Poincaré's Kantian viewpoint is mistaken. Poincaré's aim (as Kant's before him) was not to deny the possibility of finding a logical ‘proof’ for each theorem. Rather, it was to point out that such purely logical derivations fail to preserve certain of the important and distinctive features of mathematical proof. Against such a view, programs such as Russell's, whose main aim was to demonstrate the existence of a logical counterpart for each mathematical proof, can have but little force. For what is at issue is not whether each mathematical theorem can be fitted with a logical ‘proof’, but rather whether the latter has the epistemic features that a genuine mathematical proof has. (shrink)

SummaryThe germs of future development, contained in Aristotle's logical works, are indicated, and their influence on the later evolution of logic is explained.The history of symbolic logic since Boole's Mathematical analysis and De Morgan's Formal logic, both of which were published in 1847, is divided into four approximately subsequent phases, viz.:1. algebra of logic; this phase is characterized by Boole's work;2. logical foundation of mathematics; this phase is characterized by Frege's, Peano's and Russell's work, by the discovery of the antonomies (...) of logic and set theory, by the Couturat‐Poincaré debate and by the rise of Brouwer's intuitionism;3. intuitive metamathematics, concentrating in Hilbert's attempts towards a consistency proof for classical analysis; the discovery of Gödel's theorem necessitated a change of policy;4. axiomatic methodology, deriving from Hilbert's metamathematics and culminating so far in Tarski's semantics. — E. W. B. (shrink)

The ArgumentL. E. J. Brouwer and David Hubert, two titans of twentieth-century mathematics, clashed dramatically in the 1920s. Though they were both Kantian constructivists, their notoriousGrundlagenstreitcentered on sharp differences about the foundations of mathematics: Brouwer was prepared to revise the content and methods of mathematics (his “Intuitionism” did just that radically), while Hilbert's Program was designed to preserve and constructively secure all of classical mathematics.Hilbert's interests and polemics at the time led to at least three misconstruals of intuitionism, (...) misconstruals which last to our own time: Current literature often portrays popular views of intuitionism as the product of Brouwer's idiosyncratic subjectivism; modern logicians view intuitionism as simply applying a non-standard formal logic to mathematics; and contemporary philosophers see that logic as based upon a pure assertabilist theory of meaning. These pictures stem from the way Hilbert structured the controversy.Even though Brouwer's own work and behavior occasionally reinforce these pictures, they are nevertheless inaccurate accounts of his approach to mathematics. However, the framework provided by the Brouwer-Hilbert debate itself does not supply an adequate correction of these inaccuracies. For, even if we eliminate these mistakes within that framework, Brouwer's position would still appear fragmented and internally inconsistent. I propose a Kantian framework — not from Kant's philosophy of mathematics but from his general metaphysics — which does show the coherence and consistency of Brouwer's views. I also suggest that expanding the context of the controversy in this way will illuminate Hilbert's views as well and will even shed light upon Kant's philosophy. (shrink)

The primary concern of this thesis is to investigate the explicit philosophy of mathematics in the work of Henri Poincare. In particular, I argue that there is a well-founded doctrine which grounds both Poincare's negative thesis, which is based on constructivist sentiments, and his positive thesis, via which he retains a classical conception of the mathematical continuum. The doctrine which does so is one which is founded on the Kantian theory of synthetic a priori intuition. I begin, therefore, by outlining (...) Kant's theory of the synthetic a priori, especially as it applies to mathematics. Then, in the main body of the thesis, I explain how the various central aspects of Poincare's philosophy of mathematics - e.g. his theory of induction; his theory of the continuum; his views on impredicativiti his theory of meaning - must, in general, be seen as an adaptation of Kant's position. My conclusion is that not only is there a well-founded philosophical core to Poincare's philosophy, but also that such a core provides a viable alternative in contemporary debates in the philosophy of mathematics. That is, Poincare's theory, which is secured by his doctrine of a priori intuitions, and which describes a position in between the two extremes of an "anti-realist" strict constructivism and a "realist" axiomatic set theory, may indeed be true. (shrink)

Epistemological issues associated with Cantorian set theory were at the center of the foundational debates from 1900 onward. Hermann Weyl, as a central actor, saw this as a smoldering crisis that burst into flames after World War I. The historian Herbert Mehrtens argued that this “foundations crisis” was part of a larger conflict that pitted moderns, led by David Hilbert, against various counter-moderns, who opposed the promotion of set theory and trends toward abstract theories. Among counter-moderns, L.E.J. Brouwer went (...) a step further by proposing new foundational principles based on his philosophy of intuitionism. Meanwhile, Felix Hausdorff emerged as a leading proponent of the new modern style. In this essay, I offer a reassessment of the foundations crisis that stresses the marginal importance of the various intellectual issues involved. Instead, I offer an interpretation that focuses on tensions within the German mathematical community that led to a dramatic power struggle for control of the journal Mathematische Annalen. (shrink)

A central theme in the foundational debates in the early Twentieth century in response to the paradoxes was to invoke the notion of the indefinite extensibility of certain concepts e,g. definability (the Richard paradox) and class (the Zermelo-Russell contradiction). Dummett has recently revived the notion, as the real lesson of the paradoxes and the source of Frege's error in basic law five of the Grundgesetze. The paper traces the historical and conceptual evolution of the concept and critices Dummett's argument that (...) the proper lesson of the paradoxes is that set theory is a theory of indefinitely extensible domains. (shrink)

An isomorphism is built between the separable complex Hilbert space (quantum mechanics) and Minkowski space (special relativity) by meditation of quantum information (i.e. qubit by qubit). That isomorphism can be interpreted physically as the invariance between a reference frame within a system and its unambiguous counterpart out of the system. The same idea can be applied to Poincaré’s conjecture (proved by G. Perelman) hinting another way for proving it, more concise and meaningful physically. Mathematically, the isomorphism means the invariance (...) to choice, the axiom of choice, well-ordering, and well-ordering “theorem” (or “principle”) and can be defined generally as “information invariance”. (shrink)

A homeomorphism is built between the separable complex Hilbert space (quantum mechanics) and Minkowski space (special relativity) by meditation of quantum information (i.e. qubit by qubit). That homeomorphism can be interpreted physically as the invariance to a reference frame within a system and its unambiguous counterpart out of the system. The same idea can be applied to Poincaré’s conjecture (proved by G. Perelman) hinting at another way for proving it, more concise and meaningful physically. Furthermore, the conjecture can be (...) generalized and interpreted in relation to the pseudo-Riemannian space of general relativity therefore allowing for both mathematical and philosophical interpretations of the force of gravitation due to the mismatch of choice and ordering and resulting into the “curving of information” (e.g. entanglement). Mathematically, that homeomorphism means the invariance to choice, the axiom of choice, well-ordering, and well-ordering “theorem” (or “principle”) and can be defined generally as “information invariance”. Philosophically, the same homeomorphism implies transcendentalism once the philosophical category of the totality is defined formally. The fundamental concepts of “choice”, “ordering” and “information” unify physics, mathematics, and philosophy and should be related to their shared foundations. (shrink)

Philosophers have long debated ‘substrate’ and ‘bundle’ theories as to how properties hold together in objects ― but have neglected to consider that every chemical entity is defined by closure of relationships among components ― here designated ‘Closure Louis de Broglie.’ That type of closure underlies the coherence of spectroscopic and chemical properties of chemical substances, and is importantly implicated in the stability and definition of entities of many other types, including those usually involved in philosophic discourse ― such as (...) roses, statues, and tennis balls. Characteristics of composites are often presumed to ‘supervene on’ properties of components. This assumption does not apply when cooperative interactions among components are significant. Once correlations dominate, then adequate descriptions must involve different entities and relationships than those that are involved in ‘fundamental-level’ description of similar but uncorrelated systems. That is to say, descriptions must involve different semantics than would be appropriate if cooperative interactions were insignificant. This is termed ‘Closure Henri Poincaré. Networks of chemical reactions that have certain types of closure of processes display properties that make other more-complex coherences possible. This is termed ‘Closure Jacques Cauvin.’ Each of these three modes of closure provides a sufficient basis for warranted recognition of causal interaction, thus each of them has epistemological significance. Other modes of epistemologically-important closure probably exist. It is important to recognize that causal efficacy generally depends on closure of relationships of constituents. (shrink)

Édouard Le Roy as early as 1901 observed the existence of an intellectual movement seeking to break from traditional positivism and set for himself the task of drawing up the program of this new positivism. Noting that this program precedes the Vienna Circle, I endeavor to determine its nature and to evaluate its impact on logical positivism. Viewed in this light, the discussions between Le Roy, Poincaré and Duhem appear more prolonged and substantial than is usually thought. What we have (...) here is perhaps not a homogeneous doctrine but a vigorous intellectual movement, from which logical positivists were able to borrow specific theses in their attempts to mitigate Mach's strict positivism; more important still, they had before them an example of neopositivism. History is not the only concern: among the issues debated, one encounters the claim that facts are theory-laden. This claim still stirs controversy today. An inquiry into the origins of the claim is one way of clarifying the arguments involved. (shrink)

Constantin Caratheodory offered the first systematic and contradiction free formulation of thermodynamics on the basis of his mathematical work on Pfaff forms. Moreover, his work on measure theory provided the basis for later improved formulations of thermodynamics and physics of continua where extensive variables are measures and intensive variables are densities. Caratheodory was the first to see that measure theory and not topology is the natural tool to understand the difficulties (ergodicity, approach to equilibrium, irreversibility) in the Foundations of Statistical (...) Physics. He gave a measure-theoretic proof of Poincaré's recurrence theorem in 1919. This work paved the way for Birkhoff to identify later ergodicity as metric transitivity and for Koopman and von Neumann to introduce spectral analysis of dynamical systems in Hilbert spaces. Mixing provided an explanation of the approach to equilibrium but not of irreversibility. The recent extension of spectral theory of dynamical systems to locally convex spaces, achieved by the Brussels–Austin groups, gives new nontrivial time asymmetric spectral decompositions for unstable and/or non-integrable systems. In this way irreversibility is resolved in a natural way. (shrink)

A quantum theory of the photon is developed in a natural manner. Newton-Wigner and Wightman demonstrated that the photon could not be strictly localized according to natural criteria. These investigations involved the identification of an elementary system with a uirrep of the Poincare group. We identify a particle with the localized measurement of the states satisfying the uirrep. In the case of zero mass and unit spin, the photon is identified with those components of the state that can be localized. (...) A c-number four-vector potential and Lorentz condition are derived from the relativistic wave equation. The Wightman localization is demonstrated for the three independent space components of the vector potential, and the photon is identified with these components. A position operator and probability density follow immediately from the localization. A consequence of the subjective definition of a photon is that the transformations of the vector potential are unitary, and hence the unitary scalar product can be obtained for the four-vector potential. A Hilbert space is defined for the three space components of the vector potential. A position operator and probability density are derived from the scalar product, which compare directly with those obtained from the localization and the non-relativistic theory. As the longitudinal and scalar polarizations do not contribute to the measured transition probability, they are considered virtual. Lastly, a conserved four-vector current is derived from the scalar product. The possibility of observing a strict localization of the photon in the laboratory is suggested. (shrink)

A tese é de que a concepção de Duhem da ciência antecipa, entre outros elementos, o modelo de escolha de teorias científicas associado com as concepções de Popper, Lakatos e Kuhn. No contexto do seu debate com Poincaré, Duhem propõe um modelo metodológico de escolha racional de teorias formado, também, de componentes extralógicos. O modelo substitui a metodologia bipartida, teoria e natureza, por uma tripartida, confrontação entre duas teorias e natureza. Tal metodologia verifica-se adequada para descrever o processo de (...) escolha de teoria formado das etapas da refutação e rejeição. Ambas as propostas revelam seu enfoque histórico-crítico cuja tese é a interdependência entre história e teoria da ciência. A interdependência configura-se num laboratório para a elaboração, a avaliação e teste das propostas metafísicas e metodológicas para a construção de uma teoria da ciência. (shrink)

This paper presents a systematic study of the prehistory of the traditional subsystems of second-order arithmetic that feature prominently in the reverse mathematics program of Friedman and Simpson. We look in particular at: (i) the long arc from Poincar\'e to Feferman as concerns arithmetic definability and provability, (ii) the interplay between finitism and the formalization of analysis in the lecture notes and publications of Hilbert and Bernays, (iii) the uncertainty as to the constructive status of principles equivalent to Weak (...) K\"onig's Lemma, and (iv) the large-scale intellectual backdrop to arithmetical transfinite recursion in descriptive set theory and its effectivization by Borel, Lusin, Addison, and others. (shrink)

MethodologyA new hypothesis on the basic features characterizing the Foundations of Mathematics is suggested.Application of the methodBy means of it, the several proposals, launched around the year 1900, for discovering the FoM are characterized. It is well known that the historical evolution of these proposals was marked by some notorious failures and conflicts. Particular attention is given to Cantor's programme and its improvements. Its merits and insufficiencies are characterized in the light of the new conception of the FoM. After the (...) failures of Frege's and Cantor's programmes owing to the discoveries of an antinomy and internal contradictions, respectively, the two remaining, more radical programmes, i.e. Hilbert's and Brouwer's, generated a great debate; the explanation given here is their mutual incommensurability, defined by means of the differences in their foundational features.ResultsThe ignorance of this phenomenon explains the inconclusiveness of a century-long debate between the advocates of these two proposals. Which however have been so greatly improved as to closely approach or even recognize some basic features of the FoM.Discussion on the resultsYet, no proposal has recognized the alternative basic feature to Hilbert's main one, the deductive organization of a theory, although already half a century before the births of all the programmes this alternative was substantially instantiated by Lobachevsky's theory on parallel lines. Some conclusive considerations of a historical and philosophical nature are offered. In particular, the conclusive birth of a pluralism in the FoM is stressed. (shrink)

La logique de l'infini (Texte de juillet 1909)--La morale et la science.--L'évolution des lois.--Les rapports de la matière et de l'éther.--La logique de l'infini; (Texte du 3 mai 1912)--L'espace et le temps.--L'hypothèse des quanta.--L'union pour l'éducation morale.--Pourquoi l'espace a trois dimensions.--Appendice: Les fondements de la géométrie. Cornot et les principes du calcul infinitésimal. Le libre examen en matière scientifique. Le démon d'Arrhénius.

O presente artigo se propõe a analisar a relação entre o Supremo Tribunal Federal e os media, e como as notícias jurídicas do Plenário da mais importante Corte do país são transmitidas pela TV Justiça, pelos canais comerciais, e pelos novos media. Ademais, busca-se explorar a influência dos novos media na democratização da informação referente ao Judiciário. Em termos metodológicos, será utilizada abordagem hipotética dedutiva, com base em pesquisa bibliográfica e documental. Não obstante, este trabalho pretende demostrar como os canais (...) comerciais se incumbem de espetacularizar as imagens do Plenário do STF, com intuitos mercadológicos e de lucro. (shrink)

The target article is an attempt to make some progress on the problem of color realism. Are objects colored? And what is the nature of the color properties? We defend the view that physical objects (for instance, tomatoes, radishes, and rubies) are colored, and that colors are physical properties, specifically types of reflectance. This is probably a minority opinion, at least among color scientists. Textbooks frequently claim that physical objects are not colored, and that the colors are "subjective" or "in (...) the mind." The article has two other purposes: first, to introduce an interdisciplinary audience to some distinctively philosophical tools that are useful in tackling the problem of color realism and, second, to clarify the various positions and central arguments in the debate. (shrink)

We consider the question of the manner of the internalization of the geometry and topology of physical space in the mind, both the mechanism of internalization and precisely what structures are internalized. Though we will not argue for the point here, we agree with the long tradition which holds that an understanding of this issue is crucial for addressing many metaphysical and epistemological questions concerning space.

Perception and thought are often, although not exclusively, concerned with information about the world. In the case of perceiving though, unlike thinking, it is widely believed that there is an additional element involved, a subjective feeling or, as it is often put, something that it is like to be perceiving. Qualia are these characteristic feelings that accompany perceiving. One motivation for the idea that we experience qualia is that there is a clear difference between seeing a red tomato and thinking (...) that a tomato is red and that the difference has to do with some extra element present in the case of seeing that is absent in the case of thinking. Philosophical attempts to understand qualia and their place in the world have played a central role in recent debates about the nature of mind and its place in the world. Before getting to those debates, we will take a more detailed look at the distinction between the content of perceptual experiences,what they tell us about the world, and their qualitative or phenomenal character, what it is like to experience them. (shrink)

Our reply is in three parts. The first part concerns some foundational issues in the debate about color realism. The second part addresses the many objections to the version of physicalism about color ("productance physicalism") defended in the target article. The third part discusses the leading alternative approaches and theories endorsed by the commentators.

Neste artigo pretende-se discutir a dimensão política presente na origem da teoria do reconhecimento de Axel Honneth, partindo da constatação de que durante a reelaboração de sua tese de habilitação, publicada em 1992 com o título de Luta por reconhecimento, o autor se posiciona pela primeira vez diante do debate entre liberais e comunitaristas e elabora seu conceito formal de eticidade como uma resposta às limitações de cada uma dessas correntes da teoria política contemporânea.

There is an influential, ongoing debate between traditionalists and experimentalists about how to carry out conceptual analysis by means of the method of possible cases. The debate concerns whose intuitions are evidentially relevant to philosophical theories, and which methods are most appropriate for collecting such evidence. The aim of this paper is not to take sides in this debate, but to question the monopoly that the method of possible cases has in contemporary discussions of philosophical methodology. Since (...) early analytic philosophy is replete with methods of conceptual analysis that make no essential use of intuitions, these discussions are inevitably myopic. In particular, it will be argued that Frege’s logical analysis of arithmetic, Hilbert’s axiomatic analysis of geometry, and Poincaré’s transcendental analysis of physics are non-psychologistic methods that yield profound philosophical conclusions. None of these methods are carried out from the philosopher’s armchair or the scientist’s laboratory; instead they properly belong to mathematics and physics. Thus, by ignoring these methods, both traditionalists and experimentalists have neglected the significant role that the exact sciences can play in conceptual analysis. (shrink)

Philosophy of science emerged as a distinctive part of philosophy in the twentieth century. It set its own agenda, the systematic study of the metaphysical and epistemological foundations of science, and acquired its own professional structure, departments and journals. Its defining moment was the meeting (and the clash) of two courses of events: the breakdown of the Kantian philosophical tradition and the crisis in the sciences and mathematics in the beginning of the century. The emergence of the new Frege-Russell logic, (...) the arithmetisation of geometry and the collapse of classical mechanics called into question the neat Kantian scheme of synthetic a priori principles. But the thought that some a priori (framework) principles should be in place in order for science to be possible had still had a strong grip on the thinkers of the European continent. A heated intellectual debate started concerning the status of these a priori principles. The view that dominated the scene after the dust had settled was that the required framework principles were conventions. The seed of this thought was found in Poincaré’s writings, but in the hands of the Logical Positivists, it was fertilised with Frege’s conception of analyticity and Hilbert’s conception of implicit definitions. The consolidation of modern physics lent credence to the view that a priori principles can be revised; hence, a new conception of relativised a priori emerged. The linguistic turn in philosophy re-oriented the subject-matter of philosophical thinking about science to the language of science. Formal-logical methods and conceptual analysis were taken to be the privileged philosophical tools. Not only, it was thought, do they clarify and perhaps solve (or dissolve) traditional philosophical problems; they also make philosophy rigorous and set it apart from empirical science. In the 1930s, philosophy of science became the logic of science; it became synonymous to anti-psychologism, anti-historicism and anti-naturalism.. (shrink)

C. Lloyd Morgan is mostly known for Morgan’s canon, still a popular and frequently quoted principle in comparative psychology and ethology. There has been a fair amount of debate on the canon’s interpretation, function, and value regarding the research on animal minds, usually referring to it as an isolated principle. In this paper we rather shed light on Morgan’s overall scientific program and his vision for comparative psychology. We argue that within his program Morgan identified crucial conceptual, ontological, and (...) methodical issues, that are still fundamental to the current research on animal minds. This also highlights a new aspect of his role as one of the “founding fathers” of modern comparative psychology. In order to understand Morgan’s program, we briefly outline the historical context in which he began his work on a science of comparative psychology. We will then emphasize to what extent his taxonomy of psychological capacities, the development of his metaphysics for a comparative psychology, and his newly introduced interdisciplinary procedures justify Morgan’s distinctive approach to still rather sensitive issues. In doing so, we aim to provide a more comprehensive picture of Morgan’s methodological signature and we contend that a proper understanding of his canon can only be gained by taking it as part of this program. We finally understand his most renown considerations as part of his struggle to ascertain the limits and possibilities of the discipline he contributed to set up, and thus emphasize the need to keep the discussion going, notably on the accessibility of other minds than one’s own and on the limits of one’s research perspectives. (shrink)

Towards the middle of the 18th century, Pierre-Louis Moreau de Maupertuis proposed the “principle of least action” as a fundamental law of physics and as a proof of the existence of God. Samuel König and other contemporary authors criticized Maupertuis’ work. There ensued a fierce discussion concerning this subject, in which Leonhard Euler, the king Frédéric II of Prussia and Voltaire took part. This paper discusses that debate, emphasizing its extrascientific features and analyzing the interests that motivated the actions (...) of the people involved in that episode. RESUMO: Em meados do século XVIII, Pierre-Louis Moreau de Maupertuis propôs o “princípio de ação mínima”, que seria uma lei fundamental da física, além de constituir uma prova da existência de Deus. O trabalho de Maupertuis foi criticado por Samuel König e outros autores da época. Ocorreu uma violenta discussão a respeito desse assunto, da qual participaram Leonhard Euler, o rei Frédéric II da Prússia e Voltaire. Este artigo estuda o debate ocorrido, enfatizando especialmente os aspectos extracientíficos e analisando os interesses que motivaram as ações das pessoas envolvidas nesse episódio. (shrink)

The Dangerous Book for Boys Abstract: Seventeenth and eighteenth century discussions of the senses are often thought to contain a profound truth: some perceptible properties are secondary qualities, dispositions to produce certain sorts of experiences in perceivers. In particular, colors are secondary qualities: for example, an object is green iff it is disposed to look green to standard perceivers in standard conditions. After rebutting Boghossian and Velleman’s argument that a certain kind of secondary quality theory is viciously circular, we discuss (...) three main lines of argument for the secondary quality theory. The first is inspired by an intuitively compelling picture of perception articulated by Reid; the second is that the secondary quality theory is a conceptual truth; the third line of argument is presented in Johnston’s influential paper ‘How to speak of the colors’. We conclude that all these arguments fail, and that the secondary quality theory is unmotivated. Keywords: color, secondary quality, disposition, vision, perception.. (shrink)

O objetivo de meu texto consiste em reconstruir um aspecto da recepção da compreensão de Duns Scotus sobre a noção de ente em dois autores pertencentes à geração que imediatamente o sucedeu: no franciscano Guilherme de Alnwick e em seu confrade Francisco de Meyronnes. O problema que surge nessa primeira recepção de Scotus pode ser assim resumido: uma vez que tenhamos aceitado que a noção de ente é simultaneamente unívoca, primeira, a mais geral e a mais simples das noções, como (...) podemos evitar a ameaça de se ter de conceder que a ciência de tal noção – que a metafísica, noutras palavras – não seja capaz de se distinguir claramente de uma investigação que não lida necessariamente com realidades extramentais? Ou, pondo a questão em outros termos: não nos vemos depois de Scotus condenados a ter de escolher entre uma noção de ente como uma noção real ou como uma noção perfeitamente geral? Veremos que, tratando da mesma questão, Alnwick e Meyronnes seguem diferentes caminhos, cada um deles com seus custos e méritos. The aim of my text is to reconstruct the reception of Duns Scotus's comprehension of the notion of being between two authors belonging to the generation which immediately follows his: the Franciscan William of Alnwick and his confrere Francis of Meyronnes. The issue that arises in this early reception of Scotus's can be summarized as follows: once we have accepted that the notion of being is simultaneously univocal, primary, the most general and the simplest possible notion, how can we avoid the threat of having to concede that the science of such a notion – that metaphysics, in other words – is not capable of distinguishing itself clearly from an investigation that does not necessarily have to do with extramental realities? Or, rephrasing the question: after Scotus, are we not condemned to having to choose between the notion of being as a real notion or the notion of being as a perfectly general notion? We shall see that, addressing the same issue, Alnwick and Meyrones follow different paths, each one with its own costs and its own merits. (shrink)

The Dangerous Book for Boys Abstract: Seventeenth and eighteenth century discussions of the senses are often thought to contain a profound truth: some perceptible properties are secondary qualities, dispositions to produce certain sorts of experiences in perceivers. In particular, colors are secondary qualities: for example, an object is green iff it is disposed to look green to standard perceivers in standard conditions. After rebutting Boghossian and Velleman’s argument that a certain kind of secondary quality theory is viciously circular, we discuss (...) three main lines of argument for the secondary quality theory. The first is inspired by an intuitively compelling picture of perception articulated by Reid; the second is that the secondary quality theory is a conceptual truth; the third line of argument is presented in Johnston’s influential paper ‘How to speak of the colors’. We conclude that all these arguments fail, and that the secondary quality theory is unmotivated. Keywords: color, secondary quality, disposition, vision, perception.. (shrink)

Em 2024, comemoram-se os 180 anos da redação dos Manuscritos econômico-filosóficos de 1844 de Marx. Diferentemente da escola althusseriana, a hipótese do presente artigo é que os Manuscritos - mesmo com seus limites – apresentam vetores que elucidam certos traços filosóficos do pensamento de Marx. Com este intuito, foram destacados três aspectos do texto: a tomada de posição materialista por parte de Marx (que envolve uma crítica de fundo ao pensamento religioso); no âmbito desta posição, a emergência de uma subjetividade (...) propriamente humana (que supera progressivamente sua determinação natural). E o debate com a filosofia de Hegel, debate necessário tendo em vista o surgimento de uma bibliografia contemporânea que parece não ter compreendido adequadamente a distância entre os dois pensadores. O artigo se encerra localizando em O capital algumas marcas (por certo complexificadas) da investigação realizada nos Manuscritos de 1844. (shrink)

Resumo: Este artigo busca colocar a filosofia de David Hume diante de algumas teorias contemporâneas a respeito do tema das razões para agir ou motivantes. Há certa dificuldade em se afirmar que Hume aborda as razões motivantes, um conceito contemporâneo voltado a explicar aquilo que efetivamente impele um agente e referente ao lugar do desejo e da crença. Há dois grupos, intitulados respectivamente como humeanos e não-humeanos, de modo que para o primeiro, supostamente mais alinhado a Hume, o desejo tem (...) lugar garantido e até certa primazia na motivação para o ato e a crença um papel limitado. Já para o segundo, o desejo não é sempre fundamental para motivar as ações e a crença pode tomar a dianteira nesse aspecto. Apesar do desafio de se colocar o próprio Hume junto a esses debatedores que orbitam sobre seu pensamento, é possível aproximar tais intelectuais no intuito de se investigar se Hume não teria uma perspectiva sobre as razões motivantes, quando ele reflete sobre a ação humana ao tratar das paixões, da crença e da razão. Esta investigação também contribui para se ampliar a compreensão a respeito das considerações de Hume sobre o uso do intelecto na esfera prática. Palavras-chave: Desejo; Crença; Razão; Ação; Motivação; Disposição Hume and the contemporary debate about motivating reasons Abstract: This paper aims to compare David Humes’s philosophy with some contemporary theories about reasons for action or motivating reasons. It is hard to claim that Hume uses the idea of motivating reasons, a concept about the explanation of what makes someone act and what is the function of desire and belief. There are nowadays two groups we highlight. First, Humeans are those who supposedly are closer to the own philosophy of Hume and think that desire has a primary place and belief a limited role when we think about motivating reasons. Second, the Non-Humeans think that desire is not necessary the basis of action, and belief is sufficient to convince the agent. Despite the issue of taking Hume’s thoughts close to those who developed their theories around the modern philosopher, it is possible to create a bridge among them to check if he does not have a perspective about motivating reasons when he investigates human actions focusing on the concepts of passion, belief, and reason. That paper can also contribute to showing what Hume thinks about using intellect in the practical dimension. Keywords: Desire; Belief; Reason; Action; Motivation; Disposition Hume et le débat contemporain sur les raisons motivantes Résumé: Dans cet article nous comparons la philosophie de David Humes avec certaines théories contemporaines sur les raisons d'agir ou les raisons motivantes. Il est difficile de prétendre si Hume utilise l'idée de raisons motivantes, un concept sur l'explication de ce qui fait agir quelqu'un et qui est la fonction du désir et de la croyance. Il y a aujourd'hui deux groupes que on met en évidence. Les huméens sont ceux qui sont censés être plus proches de la propre philosophie de Hume et pensent que le désir a une place primordiale et la croyance un rôle limité lorsque nous pensons aux raisons motivantes. Les non-humiens pensent que le désir n'est pas nécessairement la base de l'action et que la croyance suffit à convaincre l'agent. Malgré la question de rapprocher les pensées de Hume de ceux qui ont développé leurs théories autour du philosophe moderne, il est possible de créer un pont entre eux pour vérifier s'il n'a pas une perspective sur les raisons motivantes lorsqu'il enquête sur les actions humaines en se concentrant sur les concepts de la passion, la croyance et la raison. Cet article peut également contribuer à montrer ce que pense Hume de l'utilisation de l'intellect dans la dimension pratique. Mots-clés: Désire; Croyance; Raison; Action; Motivation; Disposition Data de registro: 08/08/2022 Data de aceite: 13/12/2022. (shrink)

The Dangerous Book for Boys Abstract: Seventeenth and eighteenth century discussions of the senses are often thought to contain a profound truth: some perceptible properties are secondary qualities, dispositions to produce certain sorts of experiences in perceivers. In particular, colors are secondary qualities: for example, an object is green iff it is disposed to look green to standard perceivers in standard conditions. After rebutting Boghossian and Velleman’s argument that a certain kind of secondary quality theory is viciously circular, we discuss (...) three main lines of argument for the secondary quality theory. The first is inspired by an intuitively compelling picture of perception articulated by Reid; the second is that the secondary quality theory is a conceptual truth; the third line of argument is presented in Johnston’s influential paper ‘How to speak of the colors’. We conclude that all these arguments fail, and that the secondary quality theory is unmotivated. Keywords: color, secondary quality, disposition, vision, perception.. (shrink)

Neste ensaio, pretendemos sugerir algumas vantagens da apresentação do ceticismo na forma de um argumento cético geral, discutir o princípio de fechamento utilizado neste argumento, mostrar que o confiablismo externalista é incapaz de explicar as implicações deste argumento geral e defender uma posição internalista cancelabilista como a mais adequadamente munida de ferramentas para avaliação dos desafios céticos.

From Brouwer To Hilbert: The Debate on the Foundations of Mathematics in the 1920s offers the first comprehensive introduction to the most exciting period in the foundation of mathematics in the twentieth century. The 1920s witnessed the seminal foundational work of Hilbert and Bernays in proof theory, Brouwer's refinement of intuitionistic mathematics, and Weyl's predicativist approach to the foundations of analysis. This impressive collection makes available the first English translations of twenty-five central articles by these important contributors (...) and many others. The articles have been translated for the first time from Dutch, French, and German, and the volume is divided into four sections devoted to (1) Brouwer, (2) Weyl, (3) Bernays and Hilbert, and (4) the emergence of intuitionistic logic. Each section opens with an introduction which provides the necessary historical and technical context for understanding the articles. Although most contemporary work in this field takes its start from the groundbreaking contributions of these major figures, a good, scholarly introduction to the area was not available until now. Unique and accessible, From Brouwer To Hilbert will serve as an ideal text for undergraduate and graduate courses in the philosophy of mathematics, and will also be an invaluable resource for philosophers, mathematicians, and interested non-specialists. (shrink)