Geometry defines entities that can be physically realized in space, and our knowledge of abstract geometry may therefore stem from our representations of the physical world. Here, we focus on Euclidean geometry, the geometry historically regarded as “natural”. We examine whether humans possess representations describing visual forms in the same way as Euclidean geometry – i.e., in terms of their shape and size. One hundred and twelve participants from the U.S. (age 3–34 years), and 25 participants from the Amazon (age (...) 5–67 years) were asked to locate geometric deviants in panels of 6 forms of variable orientation. Participants of all ages and from both cultures detected deviant forms defined in terms of shape or size, while only U.S. adults drew distinctions between mirror images (i.e. forms differing in “sense”). Moreover, irrelevant variations of sense did not disrupt the detection of a shape or size deviant, while irrelevant variations of shape or size did. At all ages and in both cultures, participants thus retained the same properties as Euclidean geometry in their analysis of visual forms, even in the absence of formal instruction in geometry. These findings show that representations of planar visual forms provide core intuitions on which humans’ knowledge in Euclidean geometry could possibly be grounded. (shrink)

Humans possess two nonverbal systems capable of representing numbers, both limited in their representational power: the first one represents numbers in an approximate fashion, and the second one conveys information about small numbers only. Conception of exact large numbers has therefore been thought to arise from the manipulation of exact numerical symbols. Here, we focus on two fundamental properties of the exact numbers as prerequisites to the concept of EXACT NUMBERS : the fact that all numbers can be generated by (...) a successor function and the fact that equality between numbers can be defined in an exact fashion. We discuss some recent findings assessing how speakers of Munduruc (an Amazonian language), and young Western children (3-4 years old) understand these fundamental properties of numbers. (shrink)

Geometry, etymologically the “science of measuring the Earth”, is a mathematical formalization of space. Just as formal concepts of number may be rooted in an evolutionary ancient system for perceiving numerical quantity, the fathers of geometry may have been inspired by their perception of space. Is the spatial content of formal Euclidean geometry universally present in the way humans perceive space, or is Euclidean geometry a mental construction, specific to those who have received appropriate instruction? The spatial content of the (...) formal theories of geometry may depart from spatial perception for two reasons: first, because in geometry, only some of the features of spatial figures are theoretically relevant; and second, because some geometric concepts go beyond any possible perceptual experience. Focusing in turn on these two aspects of geometry, we will present several lines of research on US adults and children from the age of three years, and participants from an Amazonian culture, the Mundurucu. Almost all the aspects of geometry tested proved to be shared between these two cultures. Nevertheless, some aspects involve a process of mental construction where explicit instruction seem to play a role in the US, but that can still take place in the absence of instruction in geometry. (shrink)

The purpose of this article is to present several immediate consequences of the introduction of a new constant called Lambda in order to represent the object ``nothing" or ``void" into a standard set theory. The use of Lambda will appear natural thanks to its role of condition of possibility of sets. On a conceptual level, the use of Lambda leads to a legitimation of the empty set and to a redefinition of the notion of set. It lets also clearly appear (...) the distinction between the empty set, the nothing and the ur-elements. On a technical level, we introduce the notion of pre-element and we suggest a formal definition of the nothing distinct of that of the null-class. Among other results, we get a relative resolution of the anomaly of the intersection of a family free of sets and the possibility of building the empty set from ``nothing". The theory is presented with equi-consistency results . On both conceptual and technical levels, the introduction of Lambda leads to a resolution of the Russell's puzzle of the null-class. (shrink)

Des branches entières des mathématiques sont fondées sur des liens posés entre les nombres et l’espace : mesure de longueurs, définition de repères et de coordonnées, projection des nombres complexes sur le plan… Si les nombres complexes, comme l’utilisation de repères, sont apparus relativement récemment (vers le XVIIe siècle), la mesure des longueurs est en revanche un procédé très ancien, qui remonte au moins au 3e ou 4e millénaire av. J-C. Loin d’être fortuits, ces liens entre les nombres et l’espace (...) reflèteraient une intuition fondamentale, universelle, façonnée au cours des millénaires par la sélection naturelle, et qui aurait servi de guide et d’inspiration aux mathématiciens au fil des siècles. (shrink)

Does geometry constitues a core set of intuitions present in all humans, regarless of their language or schooling ? We used two non verbal tests to probe the conceptual primitives of geometry in the Munduruku, an isolated Amazonian indigene group. Our results provide evidence for geometrical intuitions in the absence of schooling, experience with graphic symbols or maps, or a rich language of geometrical terms.

The debates on the scientificity of social sciences in general, and sociology in particular, are recurring. From the original methodenstreitat the end the 19th Century to the contemporary controversy on the legitimacy of “regional epistemologies”, a same set of interrogations reappears. Are social sciences really scientific? And if so, are they sciences like other sciences? How should we conceive “research programs” Lakatos (1978) or “research traditions” for Laudan (1977) able to produce advancement of knowledge in the field of social and (...) human phenomena? Is the progress of knowledge in social sciences similar to the one generally observed in natural sciences? Is it possible to evaluate the relative merits of each one of these research programs? -/- These debates are important vectors of social and intellectual polarization. The historical divide between the positivist and the hermeneutics poles precedes the structure of the contemporary debate around the epistemic space of social sciences, It is not only a question of renewing the opposition between a monist view of sciences (e.g. McIntyre, 1996) and a dualistic one (e.g. Geertz, 1973) or even a trialist view of sciences (e.g. Lepenies, 1985). It is also a question of asserting dichotomies transformed into framework (including when it is a question of exceeding them): nature-culture, nomothetic-idiographic, models-narrative, structure-history, cause-reason, explanation-comprehension. -/- In this short introduction, we provide, in section 2, a first overview of this epistemological debate in social science. Section 3 proposes a different standpoint on the same questions, by introducing both ontological and methodological aspects in this basic epistemological debate. Namely, following (Hollis, 1994) oppositions of the explanation - understanding, causes - meaning, etc., types discussed in the firsts ection are comparatively examined together with oppositions of the structure - action, holism - individualism types. This allows us to discus show multi-agent design, by integrating various dimensions and standpoints in the same framework (Phan, Amblard, 2007, Chapters 1, 5, 14) can help us to shift these boundaries, and to bypass these oppositions. As model building and ontology design are at the core of this process (Phan, Amblard, 2007, Chapter 12), Section4 discusses various issues of the art of modelling, starting both from economists’ and sociologists’ current standpoints. (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)

This article-testimony can be seen as an example of a maybe new discipline that could be called "scientific metaphysics" made of thoughts experiments, definitions, some proofs, some explanations, some conjectures. Of course, to be called science, the discipline needs some possibility of "verification" too. We will see if it can be considered. -/- We start from a thought experiment: -/- Can the universe defined as U_Def be aware conscious of itself as whole? -/- This question is a variant of the (...) more familiar: -/- Can the universe be aware conscious? -/- We can distinguish two main approaches in human history in the attempts at answering this second question: 1) the approach by the bottom with a weak version of consciousness: it includes "panpsychic" like theories. 2) the approach by the head with a strong version of consciousness: it includes "holistic" theories. Spinoza's "Pantheism", for example, can be considered as one of them, even if some interpretations of Spinoza's metaphysics are not satisfied with the equation "god = universe". -/- The purpose developed in this article belongs to the second kind of approach. After a definition of the universe \emph{U}$_{\textit{Def}} $ in 7 points and the introduction of 3 premisses, one of them being devoted to our definition of "strong consciousness", we suggest an answer to the initial question and we draw the most important among numerous consequences: - semantical jump by META-abstraction and introduction of the holistic semantics; - extension of the natural language to a supra-natural language; - highlighting of a higher-order solipsism; - etc. -/- We devote some attention to the notion of "model" in its logical and philosophical acceptation and we introduce the notion of evolutional self-modelization. (shrink)

This article consists in two parts that are complementary and autonomous at the same time. -/- In the first one, we develop some surprising consequences of the introduction of a new constant called Lambda in order to represent the object ``nothing" or ``void" into a standard set theory. On a conceptual level, it allows to see sets in a new light and to give a legitimacy to the empty set. On a technical level, it leads to a relative resolution of (...) the anomaly of the intersection of a family free of sets. -/- In the second part, we show the interest of introducing an operator of potentiality into a standard set theory. Among other results, this operator allows to prove the existence of a hierarchy of empty sets and to propose a solution to the puzzle of "ubiquity" of the empty set. -/- Both theories are presented with equi-consistency results (model and interpretation). -/- Here is a declaration of intent : in each case, the starting point is a conceptual questionning; the technical tools come in a second time\\[0.4cm] \textbf{Keywords:} nothing, void, empty set, null-class, zero-order logic with quantifiers, potential, effective, empty set, ubiquity, hierarchy, equality, equality by the bottom, identity, identification. (shrink)

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)

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)

All humans share a universal, evolutionarily ancient approximate number system (ANS) that estimates and combines the numbers of objects in sets with ratio-limited precision. Interindividual variability in the acuity of the ANS correlates with mathematical achievement, but the causes of this correlation have never been established. We acquired psychophysical measures of ANS acuity in child and adult members of an indigene group in the Amazon, the Mundurucú, who have a very restricted numerical lexicon and highly variable access to mathematics education. (...) By comparing Mundurucú subjects with and without access to schooling, we found that education significantly enhances the acuity with which sets of concrete objects are estimated. These results indicate that culture and education have an important effect on basic number perception. We hypothesize that symbolic and nonsymbolic numerical thinking mutually enhance one another over the course of mathematics instruction. (shrink)

Do laypeople think that moral responsibility is compatible with determinism? Recently, philosophers and psychologists trying to answer this question have found contradictory results: while some experiments reveal people to have compatibilist intuitions, others suggest that people could in fact be incompatibilist. To account for this contradictory answers, Nichols and Knobe (2007) have advanced a ‘performance error model’ according to which people are genuine incompatibilist that are sometimes biased to give compatibilist answers by emotional reactions. To test for this hypothesis, we (...) investigated intuitions about determinism and moral responsibility in patients suffering from behavioural frontotemporal dementia. Patients suffering from bvFTD have impoverished emotional reaction. Thus, the ‘performance error model’ should predict that bvFTD patients will give less compatibilist answers. However, we found that bvFTD patients give answers quite similar to subjects in control group and were mostly compatibilist. Thus, we conclude that the ‘performance error model’ should be abandoned in favour of other available model that best fit our data. (shrink)

In this article, I criticize Véronique Zanetti on the topic of moral compromise. As I understand Zanetti, a compromise could only be called a “moral compromise” if (i) it does not originate under coercive conditions, (ii) it involves conflict whose subject matter is moral, and (iii) “the parties support the solution found for what they take to be moral reasons rather than strategic interests.” I offer three criticisms of Zanetti. First, Zanetti ignores how some parties may not have reason (...) to seek social peace at all. Zanetti’s claim that there is consensus on the aim of social peace can involve idealising away from disagreement in a manner that Zanetti accuses Rawls of. Second, even if there is consensus on the aim of seeking social peace, this leaves open the possibility of disagreement about which society different people should belong to. This idealises away from real world conflict concerning borders. Indeed, Zanetti does not mention that her ‘central example’ of moral disagreement, the German Abortion compromise, was enacted in the wake of German reunification. Third, there are at least two things that can be called the ‘German Abortion compromise.’ The compromise that Zanetti speaks of was imposed by the German Federal Constitutional Court. The court declared unconstitutional a law passed in 1992 that had been negotiated in parliament. Zanetti does not dwell on this lack of democratic credentials. Even the substance of the court-imposed solution is itself a dubious example of a moral compromise between parties based on what is acceptable to their reason. -/- (penultimate version - If you would like the .pdf of the final version for personal scholarly use, please contact me through the email address on my profile or my CV.). (shrink)

A response to a declaration in 'Le Monde', 'Luttons efficacement contre les théories du complot' by Gérald Bronner, Véronique Campion-Vincent, Sylvain Delouvée, Sebastian Dieguez, Karen Douglas, Nicolas Gauvrit, Anthony Lantian, and Pascal Wagner-Egger, published on June the 6th, 2016.

This volume aims to develop a philosophical diagnostic of the present, focussing on contemporary technoscience. psychoanalysis submits contemporary technoscientific discourse to a symptomatic reading, analysing it with evenly-poised attention and from an oblique perspective. Psychoanalysis is not primarily interested in protons, genes or galaxies, but rather in the ways in which they are disclosed and discussed, focussing on the symptomatic terms, the metaphors and paradoxes at work in technoscientific discourse. This monograph presents a psychoanalytical assessment of technoscience. The first four (...) chapters provide a short introduction into the psychoanalysis of technoscience, its basic concepts and methods, as developed Sigmund Freud, Carl Gustav Jung, Gaston Bachelard and Jacques Lacan. In subsequent chapters, this approach is fleshed out with the help of case histories (palaeoanthropology, classical conditioning and virology). Psychoanalysis reveals that, rather than by disinterested curiosity, technoscience is driven by desire, resistance and the will to control. Moreover, the focus is on primal scenes, such as Dubois’ quixotic quest for the missing link and Pavlov’s discovery of the conditioned reflex. In addition, psychoanalysis opts for triangulation: understanding technoscientific research by comparing it to “different scenes”: to genres of the imagination, notably novels, so that, in this volume, the discovery of a Homo erectus skull by Dubois is compared to missing link novels by Jules Verne and Jack London (dating from the same period), Pavlov’s discovery of the conditioned reflex is compared with B.F. Skinner’s novel Walden Two and virology as a research field is considered through the lens of viral fiction. (shrink)

Response to the paper “The Biomedical Ethics Ontology Proposal: Excellent Aims, Questionable Methods" by James DuBois, published in the Journal of Empirical Research on Human Research Ethics.

In this eleventh book of scilogs – called in-turns and out-turns –, one may find new and old questions and solutions, referring mostly to topics on Neutrosophy, but also Multispace, with miscellaneous addition of topics on Physics, Mathematics, or Sociology – email messages to research colleagues, or replies, notes about authors, articles, or books, spontaneous ideas, and so on. -/- Exchanging ideas with Prem Kumar Singh, Feng Liu, Nicolae Bălașa, Jimmy Quellet, Minodora Rușchița, Frank Gelli, A. R. Vătuiu, Victor Christianto, (...) Vladimir I. Rogozhin, Robert Neil Boyd, Akira Kanda, Stefan Spaarmann, Oliver Consa, Yabin Shao, Junle Zhuo, Nivetha Martin, Said Broumi, Jean Dezert, Erick González, Tomasz Witczak, B. De Baets, I. Couso, D. Dubois, L. Good, Mihaela Colhon, Atiqe Ur Rahman, Muhammad Saeed, Muhammad Ihsan, Edeline Nancy, Shawkat Alkhazaleh, Shazia Rana, Vasantha Kandasamy, Santanu Acharjee, Mohamed Al-Shmrani, Parimala Manie, Mehmet Unver, Murat Olgun, Adel Aleidhri, Akira Kanda, Ilanthenral Kandasamy, Mircea Zărnescu, R. Tayebi Khorami, Arsham Borumand Saeid, Maisam Jdid, M. Abobala, Riad Hamido, Rafael Rojas, Esmaeil Zarei, Faisal Khan, Rouzbeh Abbassi, Adel Al-Odhari, Henry Garrett, Ackbar Rezaei, Saeid Jafari, Karthika Muthusamy, Harish Garg, Huda E. Khalid, Gonca D. Güngör, Muslim A. Noah Zainal, Fakhry Asad Agusfrianto, Madeleine Al-Tahan, Mariam Hariri, Yudi Mahatma, Masoud Ghods, Marco Brigliadori, Luis Enrique Aponte Pérez, Amr Mohammed, M. Aslam (in order of reference in the book). (shrink)

In this ninth book of scilogs collected from my nest of ideas, one may find new and old questions and solutions, – in email messages to research colleagues, or replies, and personal notes, some handwritten on the planes to, and from international conferences, about topics on Neutrosophy and its applications, such as: Neutrosophic Bipolar Set, Linguistic Neutrosophic Set, Neutrosophic Resonance Frequency, n-ary HyperAlgebra, n-ary NeutroHyperAlgebra, n-ary AntiHyperAlgebra, Plithogenic Crisp Graph, Plithogenic Fuzzy Graph, Plithogenic Intuitionistic Fuzzy Graph, Plithogenic Neutrosophic Graph, Plithogenic (...) Real Number Graph, Plithogenic Complex Number Graph, Plithogenic Neutrosophic Number Graph, and many more. -/- Exchanging ideas with: Tareq Al-Shami, Riad Khidr Al-hamido, Mohammad Akram, B. De Baets, Robert Neil Boyd, Said Broumi, Terman Frometa-Castillo, Yilmaz Ceven, D. Dubois, Harish Garg, L. Godo, Erik Gonzalez, Yanhui Guo, Mohammad Hamidi, E. Hüllermeier, W. B. Vasantha Kandasamy, Mary Jansi, Nivetha Martin, Mani Parimala, Akbar Rezaei, Bouzina Salah, Christy Vincent, Jun Ye.‬‬‬. (shrink)

This volume contains new and original papers on Martin Heidegger's complex relation to Friedrich Nietzsche's philosophy. The authors not only critically discuss the many aspects of Heidegger's reading of Nietzsche, they also interpret Heidegger's thought from a Nietzschean perspective. Here is presented for the first time an overview of not only Heidegger's and Nietzsche's philosophy but also an overview of what is alive - and dead - in their thinking. Many authors through a reading of Heidegger and Nietzsche deal with (...) current issues such as technology, ecology, and politics. This volume is of interest for everyone interested in Heidegger's and Nietzsche's thought. Contributors include: Babette Babich, Charles Bambach, Robert Bernasconi, Virgilio Cesarone, Stuart Elden, Michael Eldred, Markus Enders, Charles Feitosa, Véronique Fóti, Luanne T. Frank, Jeffery Kinlaw, Theodore Kisiel, William D. Melaney, Eric Sean Nelson, Abraham Olivier, Friederike Rese, Karlheinz Ruhstorfer, Harald Seubert, Robert Sinnerbrink, Robert Switzer, Jorge Uscatescu Barrón, Nancy A. Weston, Dale Wilkerson, Angel Xolocotzi, Jens Zimmermann. (shrink)

A reply to Gérald Bronner, Véronique Campion-Vincent, Sylvain Delouvée, Sebastian Dieguez, Nicolas Gauvrit, Anthony Lantian, and Pascal Wagner-Egger's piece, '“They” Respond: Comments on Basham et al.’s “Social Science’s Conspiracy-Theory Panic: Now They Want to Cure Everyone”.

In this article I present the phenomenological tradition as a new grounding for human rights as universal rights. The hypothesis defended is to conciliate Husserl’s phenomenological method and Reinach’s a priori law in order to offer a new grounding to human rights. In order to combine Husserl and Reinach’s ideas, I propose to expand the comprehension of a priori. It would be present as eidos of each object and I name it as material a priori; it also be present in (...) the eidetic relations and I name it as formal a priori. Yet the object would have an essence, a necessary content, a material a priori, and necessary states of affairs, necessary relations and connections, a formal a priori. Reinach, in The A priori Foundations of the Civil Law, describes eidetic relations, such as, the relation between promise, claim and obligation. I propose three eidetic universalities to ground law, these are what I will call human rights. I also face a few difficulties presented by DuBois and De Vecchi derived from the amoral approach of a priori laws. Then, I highlight the difference between this proposition and Albert’s. Finally, I defend the proposition that a priori laws are beyond natural and positive laws. (shrink)

Coleman Hughes argues for a "colorblind" approach to morality and policy: we should try to treat people without regard to race. I argue that colorblindness is less feasible, and less desirable, than it sounds. Hughes conceives of race as being skin-deep, not the sort of thing one should care about. But in American politics, "races" are often really ethnic groups, defined by a shared culture and history -- two things that we might reasonably care about. A colorblind ethos asks ethnic (...) minorities not to be partial towards their group and to instead join in the "melting pot." Understandably, not everyone will want to do this, and the result is both a moral and practical challenge for colorblind politics. (Currently rewriting this to submit to the Journal of American Affairs; comments welcome.). (shrink)

My project is to explain why the question ‘How does it feel to be a white problem?’ cannot be answered in the fluttering grammar of white talk. The whiteness of white talk lies not only in its having emerged from white mouths, but also in its evasiveness—in its attempt to suppress fear and anxiety, and its consequential [if unintended] reinscription and legitimation of racist oppression. I White talk is designed, indeed scripted, for the purposes of evading, rejecting, and remaining ignorant (...) about the injustices that flow from whiteness and its attendant privileges. I want to suggest a new point of entry—a way to flip the script, so to speak. -/- I begin with some observations about the basic advantages and disadvantages of using white talk as a route into the white problem. My account develops an expanded version of Alice MacIntyre’s definition of white talk that is attentive to the racialized bodily scripts that accompany white talk. I argue that white talk persists because it has an enduring and powerful moral, ontological, and epistemic pay off for white folks. I explore each payoff with an eye towards clarifying how white talk functions to maintain the illusion that we are invulnerable beings. Next, I pause to reply to the popular objection that this particular critique of white talk silences white people in conversations on race. If we cannot address the question ‘how does it feel to be a white problem’ in the fluttering grammar of white talk, then how shall we begin? In closing, I suggest that we might reduce fluttering by replacing white talk with a discourse of vulnerability, where vulnerability is defined not as weakness, but as a condition for potential. I offer some brief guidelines for how we might start this conversation. (shrink)