An English translation of Pierre Bayle's posthumous last book, Entretiens de Maxime et de Themiste (1707), in which Bayle defends his skeptical position on the problem of the evil. This book is often cited and attacked by G.W. Leibniz in his Theodicy (1710). Over one hundred pages of original philosophical and historical material introduce the translation, providing it with context and establishing the work's importance.

Pierre Bayle’ın Tarihsel ve Eleştirel Sözlük adlı eserindeki “Spinoza” maddesi, Spinoza felsefesinin temel meselelerine dair genel bir bakış sunar. Söz konusu maddenin burada çevirisi sunduğumuz “N Çıkması”nda ise Bayle, özellikle Spinoza’nın Ethica adlı eserine odaklanarak kip, değişiklik, töz ve Tanrı gibi Spinoza metafiziğinin temel kavramlarına yönelik eleştiriler getirir.

Pierre Bayle and the impossibility of a rational debate on evil I claim that Bayle engaged with theodicy in order to show how philosophy was misused in religious matters. For Bayle, the debate on evil does not oppose dichotomically reason and religion, it just requires that the participants deal with revealed truths using reason alone. In this regard, Bayle does not only criticize the Calvinist theologians of his time, but also the very source of Christian (...) theology, Augustine of Hippo. En ese artículo, sugerimos que el debate sobre la teodicea bayleana tiene por finalidad hacer patente el uso ilegítimo que se hace de la filosofía al aplicarla al debate religioso. La discusión sobre el mal no supone una disputa entre la razón en sentido absoluto y la religión, sino que compromete el uso de la razón en la revelación, de modo exclusivo Por esa razón, como veremos, el filósofo de Rotterdam no limita su crítica a la teología calvinista de su tiempo sino que la dirige al mismo corazón de la teología cristiana: la obra de Agustin de Hipona. (shrink)

Contrary to what many interpretations claim, according to Bayle faith does not completely eliminate reason. It intervenes to reveal factual truths that can only be known through revelation (for example, that God allowed Adam and Eve to sin). To these factual truths can be applied a rational principle (an axiomatic and evident one, according to Bayle, which he calls a "common notion"), namely, that "what God does is well done." God allowed sin, so we must think it was (...) justified, even if we don't understand why. This approach is what I call, cum grano salis, Pierre Bayle's theodicy. (shrink)

(Dall'introduzione del volume) Nel terzo capitolo Simone Ghelli si lancia nell’impresa di ipotizzare un percorso di lettura leviano di cui non è dato trovare riscontri filologici precisi, ma che è tuttavia percepibile “nell’aria” e nelle opere del torinese. Si tratta di una risonanza con il pensiero filosofico di Pierre Bayle e della sua riflessione sulla sofferenza nell’orizzonte speculativo di Levi, il quale tornò sovente a meditare sul problema del male e sulla spinosa questione dell’assenza di Dio e dell’impossibilità (...) di fornire una giustificazione della vita e del mondo. Ghelli arriva così a sostenere che «la posizione di Levi esprime una profonda consapevolezza filosofica, una concatenazione non casuale di concetti e argomenti riconducibile a una tradizione ben precisa: quella dell’ateismo moderno». (shrink)

Early in the history of liberalism, its most important proponents were concerned with freedom of religion. As polities and individuals now accept a dizzying array of religions, this has receded to the background for most theorists. It nonetheless remains a concern. Freedom of speech is a similar concern and very much in the foreground for theorists looking at the current state of academia. In this essay, I argue that inappropriate limits to freedom of religion and inappropriate limits to freedom of (...) speech—especially in the form of de-platforming on college campuses—both have, as one of their effects, what I call harms of silence. This means we ought not have those limits, so should seek to change them where they exist. (shrink)

For most interpreters of the philosopher from Rotterdam, his doctrine of tolerance is solely a consequence of his religious and moral doctrines. In this article, I intend to show that his doctrine rest on the political doctrine of indivisible sovereignty and on the strictest separation between political obedience and religious membership. Baylean tolerance is a political doctrine that allows the articulation between freedom of conscience (individual), minority confessions (private associations), and public religion (acknowledged as official).

This paper focuses on the English philosopher Mary Astell’s marginalia in Lady Mary Wortley Montagu’s personal copy of the 1704 edition of Pierre Bayle’s Pensées diverses sur le comète (first published in 1682). I argue that Astell’s annotations provide good reasons for thinking that Bayle is biased toward atheism in this work. Recent scholars maintain that Bayle can be interpreted as an Academic Sceptic: as someone who honestly and impartially follows a dialectical method of argument in (...) order to obtain the goal of intellectual integrity. In her commentary, however, Astell suggests that: (i) if Bayle were honest and impartial in his inquiries, then he would not have pretended to attack popular superstition, only to undermine generally-held religious beliefs; and (ii) if Bayle valued intellectual integrity, then his argument for a society of virtuous atheists would not have relied upon a deceptive equivocation in terms. I conclude that the rediscovery of this marginalia is valuable for enhancing our appreciation of Astell as an astute reader of one of her most enigmatic contemporaries. (shrink)

Durante siglos, se consideró un deber del buen cristiano obligar, a todos los hombres a entrar en el seno de la Iglesia, puesto que de ello dependía su salvación eterna. Esta doctrina presupone que existe una nítida diferencia entre verdad religiosa y error. Para Bayle, sin embargo, la creencia religiosa solo puede aspirar a convertirse en una verdad putativa, sustentada en la convicción subjetiva del fiel, concepción que le permite desdibujar el propio concepto de herejía y criticar las persecuciones (...) religiosas de su tiempo. (shrink)

Pierre Bayle shows that, in order to avoid devastating objections, materialism should postulate that the property of thinking does not emerge from certain material combinations but is present in matter from the start and everywhere—a hypothesis recently revived and labelled “panpsychism”. There are reasons for entertaining the idea that Bayle actually considers this enhanced materialism to be tenable, as it might use the same line of defence that Bayle outlined for Stratonism. However, this would lead to (...) a view similar to Locke’s superaddition theory, and I contend that such cannot be Bayle’s position because he embraces the Cartesian principle that each substance has only one principal attribute. This makes untenable, in his eyes, any system that conjoins thought with matter in the same simple substance. By contrast, this makes clear which kinds of metaphysics and epistemology panpsychists need to adopt to defend their view. (shrink)

will give an overview of the fascinating communication between G. W. Leibniz and Pierre Bayle on pre-established harmony and sudden change in the soul which started from Bayle’s footnote H to the article “Rorarius” in his Dictionnaire historique et critique (1697) and ended in 1706 with Bayle’s death. I will compare the views presented in the communication to Leibniz’s reflections on the soul in his partly concurrent Nouveaux essais sur l’entendement humain (1704) and argue that many (...) topics in the communication with Bayle are discussed with more details in Nouveaux essais. I also argue that the communication helped Leibniz to respond to Locke’s views concerning uneasiness in An Essay Concerning Human Understanding, II, xxi. Bayle himself, however, was not able to completely understand Leibniz’s views on spontaneity as he was unaware of the contents of the Nouveaux essais, especially the systematic role of petites perceptions in Leibniz’s philosophy of mind. I will also reflect on whether the controversy could have ended in agreement if it would have continued longer. (shrink)

El análisis de los conceptos de espacio y tiempo es generalmente considerado uno de los aspectos menos satisfactorios de la obra de Hume. Kemp Smith ha demostrado que en esta sección del Tratado Hume estaba respondiendo a los argumentos que Pierre Bayle había utilizado para probar que el razonamiento humano siempre termina refutándose a sí mismo. En este ensayo expongo las falacias en los argumentos de Bayle, las cuales están basadas en una comprensión inadecuada del concepto de (...) extensión. Hume no logró detectar dichas falacias y repitió los mismos errores de Bayle, lo cual explica la absurda doctrina del espacio que defiende en el Tratado. (shrink)

A survey of Bayle's skeptical arguments regarding Descartes' criterion of truth, which Bayle refers to as "evidence." Bayle's arguments for degrees of evidence, as well as for the necessity and sufficiency of possessing a high degree of evidence in order to form virtuous beliefs, are surveyed as well.

I examine Bayle's infamous statement that Christian mysteries are not only "above" human reason, but are "against" it. I put it back in the context of 16th-17th century Reformed thought. I then discuss the relation between reason and faith according to Bayle.

I first explain the scholastic (Scotist) thesis on the independence of essences Bayle alludes to in the passage of the Continuation des Pensée Diverses where he presents the Stratonicians' and the Chinese philosophers' retorsion. Then, I show that this retorsion applies to the argument of the existence of God based on "aseity", but not to the occasionalist argument based on the "quod nescis" principle. I conclude that materialism (the "Stratonician hypothesis") cannot be, for Bayle, a satisfying system.

In this paper I uncover the identities of the interlocutors of Pierre Bayle's Entretiens de Maxime et de Themiste, and I show the significance of these identities for a proper understanding of the Entretiens and of Bayle's thought more generally. Maxime and Themiste represent the philosophers of late antiquity, Maximus of Tyre and Themistius. Bayle brought these philosophers into dialogue in order to suggest that the problem of evil, though insoluble by means of speculative reason, could (...) be dissolved and thus avoided through mutual toleration. I conclude by comparing Bayle's "theodicy of toleration" with Kant's notion of authentic theodicy. (shrink)

For the philosopher of Rotterdam, religious coercion has two essential sources of illegitimacy: the linking of religious and ecclesiastical belief and the use of politics for religious purposes. Bayle responds to it, with his doctrine of freedom of conscience, on one hand and by means of the essential distinction between voluntary religious affiliation and political obligation, on the other hand. From my perspective, his doctrine of tolerance does not involve an atheist state, nor does it mean the rejection of (...) the presence of religion in the public space or its displacement to the intimate sphere of the conscience. This paper proposes a reading of Baylean tolerance as a political doctrine that allows the articulation between freedom of conscience, minority confessions, and official religion. Thus, the Baylean theoretical model could be considered a proposal to provide a normative form to the practice of toleration present in the seventeenth -century Netherlands. (shrink)

Pierre Bayle is perhaps most well-known for arguing in his Dictionary (1697) that the problem of evil cannot be solved by reason alone. This skepticism about theodicy is usually credited to a religious crisis suffered by Bayle in 1685 following the unjust imprisonment and death of his brother, the death of his father, and the revocation of the Edict of Nantes. But in this paper I argue that Bayle was skeptical about theodicy a decade earlier than (...) these events, from at least the time of his Sedan philosophy course (1675–77). I then argue that both the Various Thoughts on the Comet (1683) and Philosophical Commentary on Luke 4:23 (1686–88), which are usually read as treatments of superstition and toleration respectively, are works that also closely engage the problem of evil and demonstratethe skepticism of Bayle toward theodicy. (shrink)

In her Remarks Upon Some Writers (1743), Catharine Trotter Cockburn takes a seemingly radical stance by asserting that it is possible for atheists to be virtuous. In this paper, I examine whether or not Cockburn’s views concerning atheism commit her to a naturalistic ethics and a so-called radical enlightenment position on the independence of morality and religion. First, I examine her response to William Warburton’s critique of Pierre Bayle’s arguments concerning the possibility of a society of virtuous atheists. (...) I argue that this response shows Cockburn vacillating between a moral naturalism, on the one hand, and a theistic morality, on the other. Second, I draw on Cockburn’s letters to her niece Ann Arbuthnot, and her opinions concerning mystical ideas about “the will of God” in north-east Scotland in the mid-eighteenth century. I maintain that these letters give us a fuller appreciation of Cockburn’s naturalistic position. My conclusion is that Cockburn’s ideas concerning atheism prompt us to consider the close interplay between secular and religious principles in so-called radical ideas of the period. (shrink)

It is usually assumed that political modernity and the reformation go hand in hand. Authors such as Hegel, Tocqueville, Jellinek or Martha Nussbaum find in the protestant reformation the origin of ideas such as political freedom or freedom of conscience. In this paper, I will try to analyze the relationship between these two concepts in two fundamental characters in the Calvinist tradition. John Calvin, its founding father, on the one hand, and, on the other, Pierre Bayle, the Rotterdam (...) philosopher who pushed Calvinism to its most heterodox forms in the XVII century. I will show how they both understand the interpretation of the Bible and the political arrangements that they defended for their close context. (shrink)

I maintain that among the main views concerning the central questions of epistemology (in particular, the question of justified belief) are evidentialism, (Pyrrhonian) scepticism and fideism. In this paper, I first present the arguments in favour of a form of evidentialism, according to which no false belief can be epistemically justified on the basis of evidence. Second, I consider the historical emergence of evidentialism during the period of the early Enlightenment. In particular, I explore the disagreement between Pierre (...) class='Hi'>Bayle and Jean-Pierre de Crousaz, which demonstrates the emergence of the modern opposition between evidentialism and fideism. (shrink)

The aim of this paper is to present the copy principle from execution of the principle of separability for the purpose of elucidating the discussions conducted by Hume in understanding the composition of space and its implications for the sciences that operate with spatial constructions. The particular epistemic gain here is to do this within a model of empiricism. Given that there are several irregularities in the manner of analyzing a complex and extracting simple elements from it, as will be (...) demonstrated here, we seek to show that separating a complex considering its simple qualities and decomposing a complex to determine its simple quantities is completely different. Thus, we seek to show how Hume needed to recreate his own cognitive model, strongly based on noting our perceptions, to be able to use it to conceive the composition of space and the operations of geometry that must make reference to it. (shrink)

A relação entre os modos e a substância na filosofia de Espinosa é tida tradicionalmente como de inerência, de maneira semelhante, grosso modo, à relação entre os acidentes e as substâncias na filosofia aristotélica. Essa concepção de inerência foi contestada por Edwin Curley a partir de 1969. Esta monografia, no primeiro capítulo, procura defender que a relação entre os modos e a substância em Espinosa é de inerência, contra Curley, explicando em que consiste essa relação e diferenciando-a da concepção aristotélica (...) de inerência. No segundo capítulo, são apresentadas e respondidas objeções elaboradas por Pierre Bayle ainda no século XVIII contra a concepção de inerência dos modos na substância em Espinosa e que serviram como apoio para os ataques de Curley. (shrink)

This article aims to deepen the question of atheism within Primo Levi’s work from a philosophical point of view. Taking into account the current debate on the «sacred» in Levi’s moral reflection, instead I propose an opposite perspective, according to which atheism stands for both the conditio sine qua non and the landing place of his ethics. At first, I aim to reconstruct the way in which Levi articulates the disassociation between God and Evil, underling how, according to Levi, the (...) concept of Providence is not only illogical, but particularly immoral. Such a perspective evokes a certain affinity with the atheistic tradition which opposed to Christian theodicy over modern philosophy. The conclusion is devoted to an in-depth analysis of the meaning of «Luck» as the only plausible ethical reason for survival. (shrink)

Résumé Charles Wolfe vient de publier Lire le matérialisme (ENS Éditions, 2020), où il esquisse une histoire des différentes formes de matérialisme, y compris le matérialisme vitaliste et les versions du XXe et du XXIe siècle. Pierre-François Moreau, auteur de la préface de l’ouvrage, entame ici une discussion sur les problèmes et les ressources d’une telle histoire.

Is calculation possible without language? Or is the human ability for arithmetic dependent on the language faculty? To clarify the relation between language and arithmetic, we studied numerical cognition in speakers of Mundurukú, an Amazonian language with a very small lexicon of number words. Although the Mundurukú lack words for numbers beyond 5, they are able to compare and add large approximate numbers that are far beyond their naming range. However, they fail in exact arithmetic with numbers larger than 4 (...) or 5. Our results imply a distinction between a nonverbal system of number approximation and a language-based counting system for exact number and arithmetic. (shrink)

Ce texte présente une partie de la pensée trouvée au sein de l’oeuvre de jeunesse du philosophe japonais Ōmori Shōzō qui appartient à l’école de Tokyo. L’objet de l’analyse proposée est celui de la logique. Le défi est de décrire que la nécessité des énoncés logiques exacts repose sur l’expérience. Ainsi cet examen découvre et expose le logicisme hyper empirique auquel Ōmori nous invite. Nous parlerons du sens possible de la logique « non scientifique » pour insister ensuite sur le (...) sens scientifique de cette dernière. Finalement, nous discuterons de la provenance de la nécessité que comportent en elles les phrases logiques. Nous présenterons ainsi deux origines distinctes de la nécessité. (shrink)

We propose a modular ontology of the dynamic features of reality. This amounts, on the one hand, to a purely spatial ontology supporting snapshot views of the world at successive instants of time and, on the other hand, to a purely spatiotemporal ontology of change and process. We argue that dynamic spatial ontology must combine these two distinct types of inventory of the entities and relationships in reality, and we provide characterizations of spatiotemporal reasoning in the light of the interconnections (...) between them. (shrink)

The mapping of numbers onto space is fundamental to measurement and to mathematics. Is this mapping a cultural invention or a universal intuition shared by all humans regardless of culture and education? We probed number-space mappings in the Mundurucu, an Amazonian indigene group with a reduced numerical lexicon and little or no formal education. At all ages, the Mundurucu mapped symbolic and nonsymbolic numbers onto a logarithmic scale, whereas Western adults used linear mapping with small or symbolic numbers and logarithmic (...) mapping when numbers were presented nonsymbolically under conditions that discouraged counting. This indicates that the mapping of numbers onto space is a universal intuition and that this initial intuition of number is logarithmic. The concept of a linear number line appears to be a cultural invention that fails to develop in the absence of formal education. (shrink)

Organismal death is foundational to the evolution of life, and many biological concepts such as natural selection and life history strategy are so fashioned only because individuals are mortal. Organisms, irrespective of their organization, are composed of basic functional units—cells—and it is our understanding of cell death that lies at the heart of most general explanatory frameworks for organismal mortality. Cell death can be exogenous, arising from transmissible diseases, predation, or other misfortunes, but there are also endogenous forms of death (...) that are sometimes the result of adaptive evolution. These endogenous forms of death—often labeled programmed cell death, PCD—originated in the earliest cells and are maintained across the tree of life. Here, we consider two problematic issues related to PCD (and cell mortality generally). First, we trace the original discoveries of cell death from the nineteenth century and place current conceptions of PCD in their historical context. Revisions of our understanding of PCD demand a reassessment of its origin. Our second aim is thus to structure the proposed origin explanations of PCD into coherent arguments. In our analysis we argue for the evolutionary concept of PCD and the viral defense-immunity hypothesis for the origin of PCD. We suggest that this framework offers a plausible account of PCD early in the history of life, and also provides an epistemic basis for the future development of a general evolutionary account of mortality. (shrink)

French text publication of the manuscript of the English article en-titled "Physics, History of" and published by Duhem in Volume 12 of the 1911 "Catholic Encyclopedia".

Why would a philosopher choose to convey his ideas in the form of Manga? This discussion between Masahiro Morioka, author of Manga Introduction to Philosophy, and the translator of its French edition, Pierre Bonneels, shows how philosopher and artist Morioka became acquainted, through images, with fundamental abstract notions. After a short historical analysis of the aesthetic advantages of Manga, consideration is given to this unique way of provoking thought. On this basis, theoretical aspects of “time” and the “I” proposed (...) by Ōmori Shōzō are compared with Morioka’s Manga presentation. Although the questions raised are universal, the authors note that the use of Japanese metaphors enables these two thinkers to draw on a concrete understanding of notions like temporality and identity. (shrink)

The aim of this paper is to assess the relevance of somatic evolution by natural selection to our understanding of cancer development. I do so in two steps. In the first part of the paper, I ask to what extent cancer cells meet the formal requirements for evolution by natural selection, relying on Godfrey-Smith’s (2009) framework of Darwinian populations. I argue that although they meet the minimal requirements for natural selection, cancer cells are not paradigmatic Darwinian populations. In the second (...) part of the paper, I examine the most important examples of adaptation in cancer cells. I argue that they are not significant accumulations of evolutionary changes, and that as a consequence natural selection plays a lesser role in their explanation. Their explanation, I argue, is best sought in the previously existing wiring of the healthy cells. (shrink)

Recent empirical and conceptual research has shown that moral considerations have an influence on the way we use the adverb 'intentionally'. Here we propose our own account of these phenomena, according to which they arise from the fact that the adverb 'intentionally' has three different meanings that are differently selected by contextual factors, including normative expectations. We argue that our hypotheses can account for most available data and present some new results that support this. We end by discussing the implications (...) of our account for folk psychology. (shrink)

The aim of this master’s thesis is to analyse and highlight the interaction between science, politics and law. More precisely, our research question concerns the use of scientific arguments in social spheres (notably in politics and law) instead of legal or political arguments. In fact, we want to raise the way in which certain actors invoke scientific arguments to impose "objective" elements of fact in debate and, in this way, refrain from politically and "subjectively" discussing these same elements (or, at (...) least, their social consequences). This Master’s thesis will adopt an interdisciplinary theoretical framework (chapter 1) mobilising philosophy of science, philosophy of law, sociology of law, legal technique and analytical theories. Then, we will apply it to a case study: the European regulation of genetically modified organisms (GMOs) after the European Court of Justice (CJEU) ruling of 25 July 2015 (chapter 2). The first chapter will provide theoretical elements to rethink the interaction between science, politics and law. The first section will propose a 'state of the art’ of the philosophical literature on the relationship between science (as a regime of truth) and politics. This master’s thesis will assess a truth under construction rather than a transcendental truth. Section 2 anticipates authoritarian claims based on science by considering the relationship science can have with power (Foucault). A solid review of philosophical, sociological and legal literature highlights the risks of giving decision-making power to an all-powerful science. Notably, the use of science to justify discriminatory policies is emphasised as these policies could not be challenged because, at the time, it was considered an objective scientific truth. Finally, section 3 offers a critique of the narratives of neutral and objective science, through the approach of science in action. This sociological approach presented all the doubts and subjectivity of science in action. The second chapter will propose a case study to illustrate the theoretical framework. We have chosen GMOs because they constitute a hybrid 'event', marked by scientific controversies, and with major socio-economic implications. The legal framework of GMOs in the European Union will be presented in the first section. In addition, the legal status of new breeding techniques (NBTs) will be examined. The second section will analyse the ruling of the European Court of Justice which made NBTs subject to GMO regulation. Finally, the third section will propose a reflection on the philosophy of law on the modes of existence of scientific, legal and political disciplines. (shrink)

I propose a systematic survey of the various attitudes proponents of enaction (or enactivism) entertained or are entertaining towards representationalism and towards the use of the concept “mental representation” in cognitive science. For the sake of clarity, a set of distinctions between different varieties of representationalism and anti-representationalism are presented. I also recapitulate and discuss some anti-representationalist trends and strategies one can find the enactive literature, before focusing on some possible limitations of eliminativist versions of enactive anti-representationalism. These limitations are (...) here taken as opportunities for reflecting on the fate of enactivism in its relations with representationalism and anti-representationalism. (shrink)

Cross cultural studies have played a pivotal role in elucidating the extent to which behavioral and mental characteristics depend on specific environmental influences. Surprisingly, little field research has been carried out on a fundamentally important perceptual ability, namely the perception of biological motion. In this report, we present details of studies carried out with the help of volunteers from the Mundurucu indigene, a group of people native to Amazonian territories in Brazil. We employed standard biological motion perception tasks inspired by (...) over 30 years of laboratory research, in which observers attempt to decipher the walking direction of point-light (PL) humans and animals. Do our effortless skills at perceiving biological activity from PL animations, as revealed in laboratory settings, generalize to people who have never before seen representational depictions of human and animal activity? The results of our studies provide a clear answer to this important, previously unanswered question. Mundurucu observers readily perceived the coherent, global shape depicted in PL walkers, and experienced the classic inversion effects that are typically found when such stimuli are turned upside down. In addition, their performance was in accord with important recent findings in the literature, in the abundant ease with which they extracted direction information from local motion invariants alone. We conclude that the effortless, veridical perception of PL biological motion is a spontaneous and universal perceptual ability, occurring both inside and outside traditional laboratory environments. (shrink)

In this paper, we evaluate the project of resurgence of metaphysics based on the pecularity of the quantum domain, a project that is supported by some contemporary philosophers. Beyond the general arguments against scientific realism that are still applicable here, we show that this project is faced with the three following issues that, we believe, make it unrealizable: (a) the problem raised by the realistic interpretation of the wave function, as a description of a ‘concrete physical fact’ of the independent (...) reality; (b) the lack of any experimental counterpart of the (non-local) hidden variables quantum theories, and, in some cases, their incompatibility with the quantum predictions; and (c) the fact that the key-properties of quantum phenomena, like their non-locality, essentially depend on the observables that are used for their description and cannot then be assigned to any ‘independent’ reality. (shrink)

Article Authors Metrics Comments Media Coverage Abstract Author Summary Introduction Results Discussion Supporting information Acknowledgments Author Contributions References Reader Comments (0) Media Coverage (0) Figures Abstract During language processing, humans form complex embedded representations from sequential inputs. Here, we ask whether a “geometrical language” with recursive embedding also underlies the human ability to encode sequences of spatial locations. We introduce a novel paradigm in which subjects are exposed to a sequence of spatial locations on an octagon, and are asked to (...) predict future locations. The sequences vary in complexity according to a well-defined language comprising elementary primitives and recursive rules. A detailed analysis of error patterns indicates that primitives of symmetry and rotation are spontaneously detected and used by adults, preschoolers, and adult members of an indigene group in the Amazon, the Munduruku, who have a restricted numerical and geometrical lexicon and limited access to schooling. Furthermore, subjects readily combine these geometrical primitives into hierarchically organized expressions. By evaluating a large set of such combinations, we obtained a first view of the language needed to account for the representation of visuospatial sequences in humans, and conclude that they encode visuospatial sequences by minimizing the complexity of the structured expressions that capture them. (shrink)

Kant argued that Euclidean geometry is synthesized on the basis of an a priori intuition of space. This proposal inspired much behavioral research probing whether spatial navigation in humans and animals conforms to the predictions of Euclidean geometry. However, Euclidean geometry also includes concepts that transcend the perceptible, such as objects that are infinitely small or infinitely large, or statements of necessity and impossibility. We tested the hypothesis that certain aspects of nonperceptible Euclidian geometry map onto intuitions of space that (...) are present in all humans, even in the absence of formal mathematical education. Our tests probed intuitions of points, lines, and surfaces in participants from an indigene group in the Amazon, the Mundurucu, as well as adults and age-matched children controls from the United States and France and younger US children without education in geometry. The responses of Mundurucu adults and children converged with that of mathematically educated adults and children and revealed an intuitive understanding of essential properties of Euclidean geometry. For instance, on a surface described to them as perfectly planar, the Mundurucu's estimations of the internal angles of triangles added up to ∼180 degrees, and when asked explicitly, they stated that there exists one single parallel line to any given line through a given point. These intuitions were also partially in place in the group of younger US participants. We conclude that, during childhood, humans develop geometrical intuitions that spontaneously accord with the principles of Euclidean geometry, even in the absence of training in mathematics. (shrink)

We describe an ontology of philosophy that is designed to aid navigation through philosophical literature, including literature in the form of encyclopedia articles and textbooks and in both printed and digital forms. The ontology is designed also to serve integration and structuring of data pertaining to the philosophical literature, and in the long term also to support reasoning about the provenance and contents of such literature, by providing a representation of the philosophical domain that is oriented around what philosophical literature (...) is about. (shrink)

Developing earlier studies of the system of numbers in Mundurucu, this paper argues that the Mundurucu numeral system is far more complex than usually assumed. The Mundurucu numeral system provides indirect but insightful arguments for a modular approach to numbers and numerals. It is argued that distinct components must be distinguished, such as a system of representation of numbers in the format of internal magnitudes, a system of representation for individuals and sets, and one-to-one correspondences between the numerosity expressed by (...) the number and its metrics. It is shown that while many-number systems involve a compositionality of units, sets and sets composed of units, few-number languages, such as Mundurucu, do not have access to sets composed of units in the usual way. The nonconfigurational character of the Mundurucu language, which is related to a property for which we coin the term 'low compositionality power', accounts for this and explains the curious fact that Mundurucus make use of marked one-to-one correspondence strategies in order to overcome the limitations of the core system at the perceptual/motor interface of the language faculty. We develop an analysis of a particular construction, parallel numbers, which has not been studied before, elucidating the whole system. This analysis, we argue, sheds new light on classical philosophical, psychological and linguistic debates about numbers and numerals and their relation to language, and more particularly, sheds light on few-number languages. (shrink)