Husserl holds the view that givenness through adumbrations (i.e. perspectival givenness) is an essential characteristic of the givenness of spatiotemporal things. He goes so far to say that we are dealing with an essential law. In this article I try to make sense of this claim. I am also dealing with a thought experiment that is designed to show that the givenness through adumbrations is just a consequence of our physiological make-up, a view that Husserl explicitly rejects. Amongst other things, (...) I defend Husserl by introducing the crucial distinction between first-person-imagination and third-person-imagination. (shrink)

Although artificial intelligence has been given an unprecedented amount of attention in both the public and academic domains in the last few years, its convergence with other transformative technologies like cloud computing, robotics, and augmented/virtual reality is predicted to exacerbate its impacts on society. The adoption and integration of these technologies within industry and manufacturing spaces is a fundamental part of what is called Industry 4.0, or the Fourth Industrial Revolution. The impacts of this paradigm shift on the human operators (...) who continue to work alongside and symbiotically with these technologies in the industry bring with it novel ethical issues. Therefore, how to design these technologies for human values becomes the critical area of intervention. This paper takes up the case study of robotic AI-based assistance systems to explore the potential value implications that emerge due to current design practices and use. The design methodology known as Value Sensitive Design (VSD) is proposed as a sufficient starting point for designing these technologies for human values to address these issues. (shrink)

The bi-polar confrontation between the Soviet Union and the USA involved many leading game theorists from both sides of the Iron Curtain: Oskar Morgenstern, John von Neumann, Michael Intriligator, John Nash, Thomas Schelling and Steven Brams from the United States and Nikolay Vorob’ev, Leon A. Petrosyan, Elena B. Yanovskaya and Olga N. Bondareva from the Soviet Union. The formalization of game theory took place prior to the Cold War but the geopolitical confrontation hastened and shaped its evolution. In our article (...) we outline four similarities and differences between Western GT and Soviet GT: 1) the Iron Curtain resulted in a lagged evolution of GT in the Soviet Union; 2) Soviet GT focused more on operations research and issues of centralized planning; 3) the contemporary Western view on Soviet GT was biased and Soviet contributions, including works on dynamic stability, non-emptiness of the core and many refinements, suggest that Soviet GT was able to catch up to the Western level relatively fast; 4) international conferences, including Vilnius, 1971, fostered interaction between Soviet game theorists and their Western colleagues. In general, we consider the Cold War to be a positive environment for GT in the West and in the Soviet Union. (shrink)

This chapter presents a task-based lesson sequence based on Judith Butler's Gender Trouble. Gender Trouble is a great piece of philosophical literature. However, as philosophical literature is a genre rarely found in EFL teaching, this chapter first demonstrates in detail the merits of this genre for the teaching ofEnglish for Academic Purposes. After a brief analysis of the source text, which deconstructs the entire sex-gender link and presents both sex and gender as free-floating, this chapter presents task-based methodology and how (...) it is utilized in a lesson aimed at building gender awareness and acceptance. In the target task students are asked to take the role of an ethics teacher at an Irish high school, in which the discussion arose whether the school should introduce unisex toilets and changing rooms in order to not discriminate against transsexual students. Tue study of Butler's philosophy will provide students with both the knowledge and language to accomplish this task. Open follow-up discussions often lead to powerful ethical insights in the context of gender, homo- and transsexuality. (shrink)

Within the framework of Positive Psychology and Needing Theories, this article reviews cultural practices or perceptions regarding what happiness is and how it can be achieved. Mainly research on Subjective Well-Being (SWB) has identified many cultural differences in the pursuit of happiness, often described as East-West splits along categories such as highly expressed affect vs. quiet affect, self-assertion vs. conformity to social norms, independence vs. interdependence and the like. However, it is the overall goal of this article to show that (...) whatever the normative content of a culture’s or subculture’s view of happiness may be, it involves the same basic psychological needs beyond how people may choose to report or express resulting emotions. In particular, the theory of happiness proposed by the Hellenistic philosopher Epicurus provides broader, more inclusive categories and concepts which can be used to explain and possibly harmonize assumptions from particular traditions. (shrink)

By understanding the sense in which Sextus thinks reason is deceptive we may clarify his attitude towards ordinary life. The deception, like that of the Siren's song, is practical rather than epistemic. It is not a matter of leading us to assent to false or unjustified conclusions but is rather a distraction from, or even corruption of, ordinary life.

The exacerbating energy crises that are wreaking havoc around the globe, as well as the apparent effects of climate change, have spurred, amongst other causes, the concerted orientation towards amelioration aims such as the United Nations Sustainable Development Goals (SDGs) and environmental, social, and corporate governance (ESG). Although often presented as not only the solution to these global problems (if adopted wholesale), they are increasingly being used as a vehicle to traffic the centralisation of power and exacerbate growing authoritarian trends. (...) This chapter aims to demonstrate how the narratives surrounding ESG package the problem into what might otherwise be the solution to global problems, missing the forest for the trees. (shrink)

This article presents a detailed methodological outline for teaching culture through project work. It is argued that because project work makes it possible to gain transferrable and applicable knowledge and insight, it is the ideal tool for teaching culture with the aim of achieving real intercultural communicative competence (ICC). Preceding the pedagogical presentation, the term culture is conceptualized as small-c culture/deep culture, that is, as the sociopsychological programming of a given community. This concept is developed with practical examples and conceptualizations (...) for pedagogical implementability. Finally, a project course with American undergraduate students conducted in Germany is briefly presented. This presentation includes project sheets, the methodological rationale of each project, and the observations the participants made during the course. These observations include many aspects of the way German and U.S. American deep culture differ and also shed light on the “truth” behind some German cultural clichés. (shrink)

Neuroeducation as an amalgamation of neuroscience, cognitive science and educational psychology has the explicit aim of improving classroom teaching and learning and has repeatedly stressed the role of the teacher in student motivation and learning. This article briefly reviews the nature of human learning from the perspective of neuroeducation and presents four factors of successful learning as a consequence of this line of research. These four factors relate to the credibility of the teacher, individual differences, the role of a positive (...) classroom climate and the activation of previous knowledge. (shrink)

In this paper I explore some ways in which Cicero does not merely report Chrysippus’ view of psychotherapy and mental health in the Tusculan Disputations, but rather adapts them to suit his own Academic and practical purposes. In particular, I argue Cicero is unwilling to wholeheartedly endorse three key Stoic principles: (1) the uniformly rational nature of the mind, (2) the exclusive goodness of virtue, and (3) the possibility of attaining Stoic wisdom. As a result, he allows for greater ethical (...) significance to the removal of psychological disturbances and to the admittedly vulnerable tranquility and constancy achievable by those who fall short of Stoic wisdom. (shrink)

I examine the legitimacy of immigration controls in the context of Canada and this country’s restrictive immigration policies. Despite the fundamental, philosophical arguments against immigration restrictions, the necessity of immigration controls is rarely questioned in Canadian politics. In this paper I suggest that there is an incredible cynicism of Canadian immigration policies with respect to this country’s own political principles. The idea of international migration controls is neither sustainable from a larger liberal- theory perspective nor a political-economy viewpoint. I suggest (...) that geographers should imagine alternatives to the current systems of immigration control and the regulation of the international movement of people. (shrink)

This chapter explores two questions in detail: How should we determine the threshold for costs that individuals are asked to bear through insurance premiums or care-related out-of-pocket costs, including user fees and copayments? and What is an adequate relationship between costs and benefits? This chapter argues that preventing impoverishment is a morally more urgent priority than protecting households against income fluctuations, and that many health insurance plans may not adequately protect individuals from health care costs that threaten to drop their (...) financial status below a decent minimum. A design that places greater emphasis on preventing impoverishment and finances the achievement of that goal by reducing unnecessary subsidies to better-off households would better accord with a sufficientarian approach to health care. -/- . (shrink)

David Furley's work on the cosmologies of classical antiquity is structured around what he calls "two pictures of the world." The first picture, defended by both Plato and Aristotle, portrays the universe, or all that there is (to pan), as identical with our particular ordered world-system. Thus, the adherents of this view claim that the universe is finite and unique. The second system, defended by Leucippus and Democritus, portrays an infinite universe within which our particular kosmos is only one of (...) countless kosmoi. Aristotle's argument in De caelo I.9 that the world is necessarily unique is an important contribution to this debate. This argument holds interest because it shows Aristotle wrestling with an apparent inconsistency in his own philosophy, as deeply-held convictions within his cosmology collide with an equally deeply-held conviction within his metaphysics. The following three principles, each of which Aristotle appears committed to, are inconsistent: -/- The cosmic uniqueness principle. The world is necessarily unique. The cosmic form principle. The world is an ordered, structured unity. As such, the world has a form. The possibility of multiple instantiation principle. For all F, if F is a form, it is possible that there exist multiple Fs. In De caelo I.9, Aristotle argues that we can establish the uniqueness of the universe, reject the multiple instantiation principle, yet still retain the distinction between 'this world' and 'world in general,' if the following is true (as it is): the world takes up all the matter that exists. Aristotle illustrates this argument with one of the stranger analogies in his corpus: imagine an aquiline nose that takes up all the flesh in the universe. If this were so, then there could not exist any other aquiline objects whatsoever. (For this reason, we dub the De caelo I.9 argument the 'Cosmic Nose argument.') This paper is an interpretation of how this argument is supposed to proceed and an assessment of its success. The first section states the problem Aristotle is confronted with, sorts through Aristotle's various statements of the Cosmic Nose argument, which exhibit some sloppiness, and reconstructs charitably a single argument. We also spend some time examining the significance of Aristotle's example of a gigantic aquiline nose. We argue that, even charitably reconstructed, the argument appears to commit a serious modal fallacy. The remainder of the paper explores whether this modal fallacy can be overcome. We conclude that, although not a cogent argument for the uniqueness of the world (as this would require a significant revision of our current astronomy), the Cosmic Nose argument does succeed on its own terms. However, it should not be regarded as a free-standing argument for the uniqueness of the world. Instead, it depends crucially on the earlier argument in De caelo I.8 for the universe's uniqueness; De caelo I.9 should be viewed as an attempt to extend the conclusion of De caelo I.8 and to show how this conclusion can be made consistent with Aristotle's metaphysical principles about the nature of form. (shrink)

An explorative contribution to the ongoing discussion of thought experiments. While endorsing the majority view that skepticism about thought experiments is not well justified, in what follows we attempt to show that there is a kind of “bodiliness” missing from current accounts of thought experiments. That is, we suggest a phenomenological addition to the literature. First, we contextualize our claim that the importance of the body in thought experiments has been widely underestimated. Then we discuss David Gooding's work, which contains (...) the only explicit recognition of the importance of the body to understanding thought experiments. Finally, we introduce a phenomenological perspective of the body, which will give us the opportunity to sketch the power and promise of a phenomenological approach to thought experiments. (shrink)

The usage of Quantum Similarity through the equation Z = {∀Θ∈Z→∃s ∈ S ʌ ∃t ∈ T: Θ= (s,t)}., represents a way to analyze the way communication works in our DNA. Being able to create the object set reference for z being (s,t) in our DNA strands, we are able to set logical tags and representations of our DNA in a completely computational form. This will allow us to have a better understanding of the sequences that happen in our DNA. (...) With this approach, we can also utilize mathematical formulas such as the Euler–Mascheroni constant, regressional analysis, and computational proofs to answer important questions on Quantum biology, Quantum similarity, and Theoretical Physics. (shrink)

This chapter looks at Euler’s relation to Newton, and at his role in the rise of ‘Newtonian’ mechanics. It aims to give a sense of Newton’s complicated legacy for Enlightenment science, and to raise awareness that some key ‘Newtonian’ results really come from Euler.

From the exponential function of Euler’s equation to the geometry of a fundamental form, a calculation of the fine-structure constant and its relationship to the proton-electron mass ratio is given. Equations are found for the fundamental constants of the four forces of nature: electromagnetism, the weak force, the strong force and the force of gravitation. Symmetry principles are then associated with traditional physical measures.

Logic diagrams have been increasingly studied and applied for a few decades, not only in logic, but also in many other fields of science. The history of logic diagrams is an important subject, as many current systems and applications of logic diagrams are based on historical predecessors. While traditional histories of logic diagrams cite pioneers such as Leibniz, Euler, Venn, and Peirce, it is not widely known that Kant and the early Kantians in Germany and England played a crucial (...) role in popularising Euler(-type) diagrams. In this paper, the role of the Kantians in the late eighteenth and early nineteenth centuries will be analysed in more detail. It shows that diagrams (or intuition in general) were a highly contentious topic that depend on the philosophical attitude and went beyond logic to touch on issues of physics, metaphysics, linguistics and, above all, mathematics. (shrink)

Logicians commonly speak in a relatively undifferentiated way about pre-euler diagrams. The thesis of this paper, however, is that there were three periods in the early modern era in which euler-type diagrams (line diagrams as well as circle diagrams) were expansively used. Expansive periods are characterized by continuity, and regressive periods by discontinuity: While on the one hand an ongoing awareness of the use of euler-type diagrams occurred within an expansive period, after a subsequent phase of regression (...) the entire knowledge about the systematic application and the history of euler-type diagrams was lost. I will argue that the first expansive period lasted from Vives (1531) to Alsted (1614). The second period began around 1660 with Weigel and ended in 1712 with lange. The third period of expansion started around 1760 with the works of Ploucquet, euler and lambert. Finally, it is shown that euler-type diagrams became popular in the debate about intuition which took place in the 1790s between leibnizians and Kantians. The article is thus limited to the historical periodization between 1530 and 1800. (shrink)

Arnold Sommerfeld introduced the fine-structure constant that determines the strength of the electromagnetic interaction. Following Sommerfeld, Wolfgang Pauli left several clues to calculating the fine-structure constant with his research on Johannes Kepler's view of nature and Pythagorean geometry. The Laplace limit of Kepler's equation in classical mechanics, the Bohr-Sommerfeld model of the hydrogen atom and Julian Schwinger's research enable a calculation of the electron magnetic moment anomaly. Considerations of fundamental lengths such as the charge radius of the proton and mass (...) ratios suggest some further foundational interpretations of quantum electrodynamics. (shrink)

The thesis of Delius's book is that statements of self-awareness such as "I am aware that I see a cat" possess what he calls 'Cartesian characteristics' of indubitability or absolute self-evidence. He argues that this is the case in virtue of the fact that such statements are not about anything independent of themselves. The book is described as a 'semantical inquiry', but it is not by any means a contribution to the philosophy of language of the predictable sort. Statements of (...) self-awareness express what Delius calls 'egological experiences', and the subject of the book is most accurately described as consisting in the relations between egological statements and egological experiences, in a sense made clear in the course of the book. (shrink)

En las siguientes notas, se pretende realizar una pequeña digresión, relativa a los tópicos mencionados en el título de la misma; puesto que tales no fueron abordados en el pasado Homenaje realizado por el Instituto de Física, de la U de A. Consideramos más que perogrullo tratar de justificar la importancia y vigencia en el desarrollo de las Matemáticas y Física a lo largo del Siglo XVIII como en la actualidad de tales temas; por ende presentamos una breve descripción de (...) los métodos y problemas atacados por Euler y sus contemporáneos empleando dicha Heurística. De antemano señalamos que éstas, constituyen un intento vehementemente pauperrimo, para honrar lamemoria de quien es considerado el Shakespeare de lasMatemáticas:Universal, rico en detalles e inagotable. (shrink)

Euler’s interpretation of Newton’s gravity (NG) as Archimedes’ thrust in a fluid ether is presented in some detail. Then a semi-heuristic mechanism for gravity, close to Euler’s, is recalled and compared with the latter. None of these two ‘‘gravitational ethers’’ can obey classical mechanics. This is logical since the ether defines the very reference frame, in which mechanics is defined. This concept is used to build a scalar theory of gravity: NG corresponds to an incompressible ether, a compressible (...) ether leads to gravitational waves. In the Lorentz–Poincaré version, special relativity is compatible with the ether, but, with the heterogeneous ether of gravity, it applies only locally. A correspondence between metrical effects of uniform motion and gravitation is assumed, yet in two possible versions (one is new). Dynamics is based on a (non-trivial) extension of Newton’s second law. The observational status for the theory with the older version of the correspondence is summarized. (shrink)

This book is written for those who wish to learn some basic principles of formal logic but more importantly learn some easy methods to unpick arguments and assess their value for truth and validity. -/- The first section explains the ideas behind traditional logic which was formed well over two thousand years ago by the ancient Greeks. Terms such as ‘categorical syllogism’, ‘premise’, ‘deduction’ and ‘validity’ may appear at first sight to be inscrutable but will easily be understood with examples (...) bringing the subjects to life. Traditionally, Venn diagrams have been employed to test arguments. These are very useful but their application is limited and they are not open to quantification. The mid-section of this book introduces a methodology that makes the analysis of arguments accessible with the use of a new form of diagram, modified from those of the mathematician Leonhard Euler. These new diagrammatic methods will be employed to demonstrate an addition to the basic form of syllogism. This includes a refined definition of the terms ‘most’ and ‘some’ within propositions. This may seem a little obscure at the moment but one will readily apprehend these new methods and principles of a more modern logic. (shrink)

The work is an attempt to transfer a structure from Euclidean plane (pure geometrical) under the physical observation limit (resolving power) to a physical space (observable space). The transformation from the mathematical space to physical space passes through the observation condition. The mathematical modelling is adopted. The project is based on two stapes: (1) Looking for a simple mathematical model satisfies the definition of Euclidian plane; (2)That model is examined against three observation resolution conditions (resolved, unresolved and partially resolved). The (...) simplest mechanical model satisfies the definition of Euclidian plane is a planetary gear. The interesting examination of the mechanical model is that is under partial resolution. That examination shows analogous equation for Euler’s formula. The derived complex formula contains the resolved (observable) quantities of the mechanical system and satisfies the linear wave equation. The interpretation of this complex formula is: it is a function related to the position vector of a point in the small wheel of the partially resolved planetary gear system. The function is in terms of the observable quantities only. The work shows the possibility of transformation from real to complex space. The work is purely classical but the result of the partial resolution shows a function similar to the Quantum mechanics wave function. (shrink)

The present dissertation presents an examination of the Carrollian logic through the reconstruction of its syllogistic theory. Lewis Carroll was one of the main responsible for the dissemination of logic during the nineteenth century, but most of his logical writings remained unknown until a posthumous publication of 1977. The reconstruction of the Carrollian syllogistic theory was based on the comparison of the two books on author's logic, "The Game of Logic" and "Symbolic Logic". The analysis of the Carrollian syllogistics starts (...) from a study of the historical context of development of the logic and the developments of syllogistics previous to the contribution of the author. Situated in the historical period of algebraical logic, Carrollian syllogistics is characterized as a conservative extension of the Aristotelian syllogistics, the main innovation is the use of negative terms and the introduction of a diagrammatic method suitable for the representation of negative terms. The diagrammatic method of the Carrollian syllogistics presents advances in relation to the methods of Euler and Venn. The use of negative terms also requires a redefinition of the notion of syllogism, simplifying and expanding the amount of arguments amenable to logical treatment. Carroll does not use four, but only three categorical propositions in his syllogistic, with interpretation of existential presuppositions congruent with a syntactic-existential reading. Carrollian syllogistics uses some techniques found in the work of algebraists of logic and also made the same confusions between notions of "class" and "member" that were common in the period. Convinced of the social utility of logic and dedicated to popularize it, Carroll priorized a creation of new didactics for the teaching of logic in his works, where he can include his diagrammatic method of solving syllogisms. Carroll made only scant considerations of his conception of logic. Based on the small considerations found throughout the study and on the constant claim of the social utility of logic, it is suggested that Carroll is close to the so-called pragmatic position, which considers a logic as an instrument of regulation of discourse. (shrink)

We examine the influence of word choices on mathematical practice, i.e. in developing definitions, theorems, and proofs. As a case study, we consider Euclid’s and Euler’s word choices in their influential developments of geometry and, in particular, their use of the term ‘polyhedron’. Then, jumping to the twentieth century, we look at word choices surrounding the use of the term ‘polyhedron’ in the work of Coxeter and of Grünbaum. We also consider a recent and explicit conflict of approach between (...) Grünbaum and Shephard on the one hand and that of Hilton and Pedersen on the other, elucidating that the conflict was engendered by disagreement over the proper conceptualization, and so also the appropriate word choices, in the study of polyhedra. (shrink)

This essay explores Kant’s concept of absolute space in the Metaphysical Foundations from the perspective of the development of the relationist interpretation of bodily interactions in the center-of-mass reference frame, a strategy that Huygens had originally pioneered and which Mach also endorsed. In contrast to the interpretations of Kant that stress a non-relationist, Newton-inspired orientation in his critical period work, it will be argued that the content and function of Kant’s utilization of this reference frame strategy places him much closer (...) to Huygens’ relationism than the absolute notions of space and motion favored by Newton and Euler. (shrink)

VAN PRAAG (Paul), Introduction : le Père Henri Bosmans, histo­rien des mathématiques (pp. 7-16). SAUVAGE (Pierre), Notice biographique du Père Henri Bosmans (pp. 17-25). HERMANS (Michel), Henri Bosmans : sa formation et ses réseaux de rela­tions (pp. 27-72). DELANGHE (Richard), Quelques aspects de la vie et de l’œuvre de Paul Mansion (1844-1919) (pp. 73-82). BRIGAGLIA (Aldo), Saccheri vu par Corrado Segre en Italie et par Mansion et Bosmans en Belgique / traduit de l’italien par Bruna GAINO et Patricia RADELET-DE GRAVE (...) (pp. 83-104). MAWHIN (Jean), La tentative belge d’édition des œuvres complètes d’Euler vue par Henri Bos­mans (pp. 105-133). GOLVERS (Noël), Henri Bosmans, s.j., et la mission jésuite en Chine / traduit du néerlandais par Anne-Sophie MEURICE (pp. 135-152). ROMANO (Antonella), Henri Bosmans, jésuite et historien des mathéma­tiques dans la Belgique du premier XXe siècle (pp. 153-168). SAUVAGE (Pierre), Le Père Henri Bosmans et l’historiographie au tournant du XXe siècle (pp. 169-187). RADELET-DE GRAVE (Patricia), Le fonds Henri Bos­mans / avec un ajout de Michel HERMANS (pp. 189-215). MANSION (Paul), Correspondance de Paul Mansion adres­sée à Henri Bosmans / introduction, trans­cription et annotation par Michel HERMANS (pp. 217-251). HEEFFER (Albrecht) – HERMANS (Michel) – STOFFEL (Jean-François), Bibliographie d’Henri Bosmans (pp. 253-298). (shrink)

In this paper we argue that there were several currents, ideas and problems in 19th-century logic that motivated John Venn to develop his famous logic diagrams. To this end, we first examine the problem of uncertainty or over-specification in syllogistic that became obvious in Euler diagrams. In the 19th century, numerous logicians tried to solve this problem. The most famous was the attempt to introduce dashed circles into Euler diagrams. The solution that John Venn developed for this problem, (...) however, came from a completely different area of logic: instead of orienting to syllogistic like Euler diagrams, Venn applied Boolean algebra to improve visual reasoning. Venn’s contribution to solving the problem of elimination also played an important role. The result of this development is still known today as the ‘Venn Diagram’. (shrink)

In this paper, we analyze and discuss Schopenhauer’s n-term diagrams for eristic dialectics from a graph-theoretical perspective. Unlike logic, eristic dialectics does not examine the validity of an isolated argument, but the progression and persuasiveness of an argument in the context of a dialogue or even controversy. To represent these dialogue situations, Schopenhauer created large maps with concepts and Euler-type diagrams, which from today’s perspective are a specific form of graphs. We first present the original method with Euler-type (...) diagrams, then give the most important graph-theoretical definitions, then discuss Schopenhauer’s diagrams graph-theoretically and finally give an example of how the graphs or diagrams can be used to analyze dialogues. (shrink)

In a recent paper in Astrophysics and Space Science Vol. 364 no. 11 (2019), S. Ershkov & D. Leschenko presented a new solving procedure for Euler-Poisson equations for solving momentum equations of the CR3BP near libration points for uniformly rotating planets having inclined orbits in the solar system with respect to the orbit of the Earth. The system of equations of the CR3BP has been explored with regard to the existence of an analytic way of presentation of the approximated (...) solution in the vicinity of libration points. A new and elegant ansatz has been suggested in their publication whereby, in solving, the momentum equation is reduced to a system two coupled Riccati ODEs. In this paper, we presented a numerical solution of such coupled Riccati ODEs using Mathematica software package. (shrink)

A gas in a box is perhaps the most important model system studied in thermodynamics and statistical mechanics. Usually, studies focus on the gas, whereas the box merely serves as an idealized confinement. The present article focuses on the box as the central object and develops a thermodynamic theory by treating the geometric degrees of freedom of the box as the degrees of freedom of a thermodynamic system. Applying standard mathematical methods to the thermody- namics of an empty box allows (...) equations with the same structure as those of cosmology and classical and quantum mechanics to be derived. The simple model system of an empty box is shown to have interesting connections to classical mechanics, special relativity, and quantum field theory. (shrink)

A work on the philosophy of mathematics (2017) -/- ‘Number’, such a simple idea, and yet it fascinated and absorbed the greatest proportion of human geniuses over centuries, not to mention the likes of Pythagoras, Euclid, Newton, Leibniz, Descartes and countless maths giants like Euler, Gauss and Hilbert, etc.. Einstein thought of pure maths as the poetry of logical ideas, the exactitude of which, although independent of experience, strangely seems to benefit the study of the objects of reality. And, (...) interestingly as well as surprisingly we are nowhere near any clear understandings of numbers despite discoveries of many productive usages of numbers. This is - rightly or wrongly - a humble attempt to approach the subject from an angle hitherto unthought-of. (shrink)

The discussions which follow rest on a distinction, first expounded by Husserl, between formal logic and formal ontology. The former concerns itself with (formal) meaning-structures; the latter with formal structures amongst objects and their parts. The paper attempts to show how, when formal ontological considerations are brought into play, contemporary extensionalist theories of part and whole, and above all the mereology of Leniewski, can be generalised to embrace not only relations between concrete objects and object-pieces, but also relations between what (...) we shall call dependent parts or moments. A two-dimensional formal language is canvassed for the resultant ontological theory, a language which owes more to the tradition of Euler, Boole and Venn than to the quantifier-centred languages which have predominated amongst analytic philosophers since the time of Frege and Russell. Analytic philosophical arguments against moments, and against the entire project of a formal ontology, are considered and rejected. The paper concludes with a brief account of some applications of the theory presented. (shrink)

Intellectual history still quite commonly distinguishes between the episode we know as the Scientific Revolution, and its successor era, the Enlightenment, in terms of the calculatory and quantifying zeal of the former—the age of mechanics—and the rather scientifically lackadaisical mood of the latter, more concerned with freedom, public space and aesthetics. It is possible to challenge this distinction in a variety of ways, but the approach I examine here, in which the focus on an emerging scientific field or cluster of (...) disciplines—the ‘life sciences’, particularly natural history, medicine, and physiology —is, not Romantically anti-scientific, but resolutely anti-mathematical. Diderot bluntly states, in his Thoughts on the interpretation of nature, that “We are on the verge of a great revolution in the sciences. Given the taste people seem to have for morals, belles-lettres, the history of nature and experimental physics, I dare say that before a hundred years, there will not be more than three great geometricians remaining in Europe. The science will stop short where the Bernoullis, the Eulers, the Maupertuis, the Clairauts, the Fontaines and the D’Alemberts will have left it.... We will not go beyond.” Similarly, Buffon in the first discourse of his Histoire naturelle speaks of the “over-reliance on mathematical sciences,” given that mathematical truths are merely “definitional” and “demonstrative,” and thereby “abstract, intellectual and arbitrary.” Earlier in the Thoughts, Diderot judges “the thing of the mathematician” to have “as little existence in nature as that of the gambler.” Significantly, this attitude—taken by great scientists who also translated Newton or wrote careful papers on probability theory, as well as by others such as Mandeville—participates in the effort to conceptualize what we might call a new ontology for the emerging life sciences, very different from both the ‘iatromechanism’ and the ‘animism’ of earlier generations, which either failed to account for specifically living, goal-directed features of organisms, or accounted for them in supernaturalistic terms by appealing to an ‘anima’ as explanatory principle. Anti-mathematicism here is then a key component of a naturalistic, open-ended project to give a successful reductionist model of explanation in ‘natural history’, a model which is no more vitalist than it is materialist—but which is fairly far removed from early modern mechanism. (shrink)

Schemes of diagrammatic representation have been so familiarly introduced into logical treatises during the last century or so, that many readers, even of those who have made no professional study of logic, may be supposed to be acquainted with the general nature and object of such devices. Of these schemes one only, viz. that commonly called "Eulerian circles," has met with any general acceptance. A variety of others indeed have been proposed by ingenious and celebrated logicians, several of which would (...) claim notice in a historical treatment of the subject; but they mostly do not seem to me to differ in any essential respect from that of Euler. They rest upon the same leading principle, and are subject all alike to the same restrictions and defects. We must therefore cast about for some new scheme of diagrammatic representation which shall be competent to indicate imperfect knowledge on our part; for this will at once enable us to appeal to it step by step in the process of working out our conclusions. I have never seen any hint at such a scheme, though the want seems so evident that one would suppose that something of the kind must have been proposed before. (shrink)

The perpetual secretary of the Berlin Academy Johann Heinrich Samuel Formey is best known as a populariser of Christian Wolff’s doctrines. As of Formey’s activity in the Berlin Academy, scholars have mostly emphasized his role in the controversy over monads with Leonhard Euler, while overlooking other interesting contributions Formey presented in the “speculative philosophy” class of the Academy. In this paper, I analyse two articles Formey published in 1747 on the Mémoires de l’Académie de Berlin, namely the Preuves de (...) l’existence de Dieu, ramenées aux notions communes and the Examen de la preuve qu’on tire des fins de la nature, pour établir l’existence de Dieu. In these texts, Formey presents some of Wolff’s methodological and metaphysical ideas, in an implicit dialogue with other members of the Academy – in particular, with the president Pierre-Louis Moreau de Maupertuis – who were also interested in metaphysics and the philosophical method. Formey reworks the Wolffian arguments as to make them more accessible, in order to promote an open confrontation over core philosophical questions. Far from adopting a controversial tone, Formey’s attitude is rather conciliatory: any disagreement, as he thinks, can be easily settled once the true method for philosophizing is made available to everybody. (shrink)

Kant's obscure essay entitled An Attempt to Introduce the Concept of Negative Quantities into Philosophy has received virtually no attention in the Kant literature. The essay has been in English translation for over twenty years, though not widely available. In his original 1983 translation, Gordon Treash argues that the Negative Quantities essay should be understood as part of an ongoing response to the philosophy of Christian Wolff. Like Hoffmann and Crusius before him, the Kant of 1763 is at odds with (...) the Leibnizian-Wolffian tradition of deductive metaphysics. He joins his predecessors in rejecting the assumption that the law of contradiction alone can provide proof of the principle of sufficient reason: -/- In his rejection of the possibility of deducing all philosophic truth from the law of contradiction, however, and in the clear recognition that this impossibility has immediate consequences for defense of the law of sufficient reason, Kant's work most definitely and positively constitutes a line of succession from Hoffmann and Crusius (Treash, 1983, p. 25). -/- The recognition that Kant's Negative Quantities essay is part of a response to the tradition of deductive metaphysics is, without a doubt, an important contribution to the Kant literature. However, there is still more to be said about this neglected essay. The full significance of the paper becomes known through its ties to a second, empiricist line of succession. Clues to this second line of succession can be found in Kant's prefatory remarks concerning Euler's 1748 Reflections on Space and Time and Crusius' 1749 Guidance in the Orderly and Careful Consideration of Natural Events. As I will show, these prefatory remarks suggest a reading of Kant's Negative Quantities paper that reaches beyond German deductive metaphysics to engage a debate regarding the application of mathematics in philosophy initiated by George Berkeley. (shrink)

Without doubt, the principle of least action is a fundamental principle in classical mechanics. Contemporary physicists, however, consider the PLA as a purely mathematical principle – even an axiom which they cannot completely justify. Such an account stands in sharp contrast with the historical meaning of the PLA. When the principle was introduced in the 1740s, by Pierre-Louis Moreau de Maupertuis, its meaning was much more versatile. For Maupertuis the principle of least action signified that nature is thrifty or economical (...) in all its actions, i.e., that nature avoids to do anything unnecessary. Maupertuis understood the principle in teleological terms and even considered the principle as an expression of God’s wisdom. It has been correctly pointed out by historians that Maupertuis in his later years moved towards a more speculative and metaphysical approach, whereas his contemporary Euler and later Lagrange, wanted to avoid such theological and metaphysical implications and frame the PLA in purely mathematical terms. Such readings, however, have had the unintended side-effect that they lose out of sight the question how the mathematical and metaphysical aspect of the principle of least action fit together within Maupertuis’ own work. Investigating if and how the mathematical and metaphysical aspects of the PLA are compatible within Maupertuis’ thought will be the main goal of this paper. (shrink)

One of the greatest philosophical controversies of the eighteenth century was the competition organized in 1746 by the Berlin Academy of Sciences. Although the specific object of the competition was the theory of monads, this particular question nevertheless referred to a deeper and more radical opposition between the two contending parties, Newtonians and Wolffians. In this contribution, we will first focus on the reasons for Newtonian opposition to Wolff’s philosophy. In this context, particular attention will be paid to the positions (...) of Euler and Maupertuis. We will then proceed to a comparison between the positions of Wolff and Maupertuis on the crucial question of the relationship between mathematical and philosophical method. Our analysis will attempt to show the existence, in Maupertuis’s thought, of an effort to apply the mathematical method to disciplines other than mathematics itself, which will allow us to determine his opposition to Wolffian philosophy. Finally, we will clarify the affinities and divergences between Wolff and Maupertuis, trying to show that the real reasons for their opposition should be sought in their respective epistemologies and metaphysics. (shrink)

It is customary to draw a circle to represent a collection of objects. This makes it easy to represent logical relations between classes thanks to topological relations between spaces. The aim of this paper is to discuss the process by which spaces represent visually classes.

Anne TIHON, Théorie et réalité : l’exemple de l’astronomie an­cienne (pp. 7-23) ; Isabelle DRAELANTS, Les encyclopédies com­me sommes des connaissances, d’Isidore de Séville au XIIIe siè­cle, avec les fondements antiques (pp. 25-50) ; Andrée COLINET, Alchimie antique et médiévale avant 1300 : mystères et réalités (pp. 51-70) ; Baudouin VAN DEN ABEELE, Quelques pas de grue à travers l’histoire naturelle médiévale : un regard diversifié sur le réel (pp. 71-98) ; Régine LEURQUIN, L’astrolabe plan (pp. 99- 117) ; Patricia (...) RADELET-DE GRAVE, Copernic, Stevin, Galilée et la réalité des orbites célestes (pp. 119-151) ; Brigitte VAN TIGGELEN, Étiqueter ou définir : le réalisme dans la nomen­cla­ture chimique aux XVIIe et XVIIIe siècles (pp. 153-183) ; Michel GHINS, L’existence de l’espace et du temps selon Leon­hard Euler (pp. 185-193) ; Chantal TILMANS-CABIAUX, Le rap­port de l’idée théorique à l’expérimentation chez Hahnemann : le système homéo­pathique naissant et le réalisme (pp. 195-214) ; Jean MAWHIN, La Terre tourne-t-elle ? À propos de la philosophie scientifique de Poincaré (pp. 215-252) ; Michel WILLEM, Paul Lévy et les fondements du calcul des probabilités (pp. 253-263). (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)

From the beginning of the 16th century to the end of the 18th century, there were not less than ten philosophers who focused extensively on Venn’s ostensible analytical diagrams, as noted by modern historians of logic (Venn, Gardner, Baron, Coumet et al.). But what was the reason for early modern philosophers to use logic or analytical diagrams? Among modern historians of logic one can find two theses which are closely connected to each other: M. Gardner states that since the Middle (...) Ages certain logic diagrams were used just in order to teach “dull-witted students”. Therefore, logic diagrams were just a means to an end. According to P. Bernhard, the appreciation of logic diagrams had not started prior to the 1960s, therefore the fact that logic diagrams become an end the point of research arose very late. The paper will focus on the question whether logic resp. analytical diagrams were just means in the history of (early) modern logic or not. In contrast to Gardner, I will argue that logic diagrams were not only used as a tool for “dull-witted students”, but rather as a tool used by didactic reformers in early modern logic. In predating Bernhard’s thesis, I will argue that in the 1820s logic diagrams had already become a value in themselves in Arthur Schopenhauer’s lectures on logic, especially in proof theory. (shrink)

Transformed RAVAL NOTATION solves Syllogism problems very quickly and accurately. This method solves any categorical syllogism problem with same ease and is as simple as ABC… In Transformed RAVAL NOTATION, each premise and conclusion is written in abbreviated form, and then conclusion is reached simply by connecting abbreviated premises.NOTATION: Statements (both premises and conclusions) are represented as follows: Statement Notation a) All S are P, SS-P b) Some S are P, S-P c) Some S are not P, S / PP (...) d) No S is P, SS / PP (- implies are and / implies are not) All is represented by double letters; Some is represented by single letter. No S is P implies No P is S so its notation contains double letters on both sides. -/- RULES: (1) Conclusions are reached by connecting Notations. Two notations can be linked only through common linking terms. When the common linking term multiplies (becomes double from single), divides (becomes single from double) or remains double then conclusion is arrived between terminal terms. (Aristotle’s rule: the middle term must be distributed at least once) -/- (2)If both statements linked are having – signs, resulting conclusion carries – sign (Aristotle’s rule: two affirmatives imply an affirmative) -/- (3) Whenever statements having – and / signs are linked, resulting conclusion carries / sign. (Aristotle’s rule: if one premise is negative, then the conclusion must be negative) -/- (4)Statement having / sign cannot be linked with another statement having / sign to derive any conclusion. (Aristotle’s rule: Two negative premises imply no valid conclusion) Syllogism conclusion by Tranformed Raval’s Notation is in accordance with Aristotle’s rules for the same. It is visually very transparent and conclusions can be deduced at a glance, moreover it solves syllogism problems with any number of statements and it is quickest of all available methods. By new Raval method for solving categorical syllogism, solving categorical syllogism is as simple as pronouncing ABC and it is just continuance of Aristotle work on categorical syllogism. It’s believed that Boole's system could handle multi-term propositions and arguments, whereas Aristotle could handle only two-termed subject-predicate propositions and arguments. For example, it’s claimed that Aristotle's system could not deduce: "No quadrangle that is a square is a rectangle that is a rhombus" from "No square that is a quadrangle is a rhombus that is a rectangle" or from "No rhombus that is a rectangle is a square that is a quadrangle". Above conclusion is reached at a glance with Raval's Notations (Symbolic Aristotle’s syllogism rules). Premise: "No (square that is a quadrangle) is a (rhombus that is a rectangle)" Raval's Representations: S – Q, S – Q / Rh – Re, Rh – Re Premise: "No (rhombus that is a rectangle) is a (square that is a quadrangle)". Raval's Representations: Rh – Re, Rh – Re / S – Q, S - Q Conclusion: "No (quadrangle that is a square) is a (rectangle that is a rhombus)" Raval’s Representations: Q – S, Q – S / Re – Rh, Re – Rh As “ Q – S” follows from “S – Q” and “Re – Rh” from “Rh – Re”. Given conclusion follows from the given premises. Author disregards existential fallacy, as subset of a null set has to be a null set. -/- . (shrink)