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.

Emilie Du Chatelet and Christian Wolff both argue, from the principle of sufficient reason, that extended objects and composite objects simpliciter must ultimately be composed of simple beings (monads). Leonhard Euler, who makes extended use of the principle of sufficient reason in his works on mechanics and natural science, argues the contrary: Every extended object is composed of other, composite, extended objects. In this chapter I attempt to locate the differences between these figures that drive them to disparate (...) conclusions. I argue that the difference comes, not from their different applications of the principle of sufficient reason, but from two other sources. First, they endorse different explicability principles which do not themselves follow from the principle of sufficient reasons; and second, they differ with respect to the kinds of explanations (what I call that-explanations and how-explanations) that the question of the composition of extension requires. (shrink)

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)

John Venn has the “uneasy suspicion” that the stagnation in mathematical logic between J. H. Lambert and George Boole was due to Kant’s “disastrous effect on logical method,” namely the “strictest preservation [of logic] from mathematical encroachment.” Kant’s actual position is more nuanced, however. In this chapter, I tease out the nuances by examining his use of Leonhard Euler’s circles and comparing it with Euler’s own use. I do so in light of the developments in logical calculus (...) from G. W. Leibniz to Lambert and Gottfried Ploucquet. While Kant is evidently open to using mathematical tools in logic, his main concern is to clarify what mathematical tools can be used to achieve. For without such clarification, all efforts at introducing mathematical tools into logic would be blind if not complete waste of time. In the end, Kant would stress, the means provided by formal logic at best help us to express and order what we already know in some sense. No matter how much mathematical notations may enhance the precision of this function of formal logic, it does not change the fact that no truths can, strictly speaking, be revealed or established by means of those notations. (shrink)

In the last two decades, blame has become a core topic in ethics, philosophical moral psychology and, more recently, epistemology. This chapter aims at clarifying the complex state of the debate and at making a suggestion for how we should proceed from here. The core idea is that accounts of blame are often motivated by very different background goals. One standard goal is to provide a unifying account of our everyday blame practices. The chapter argues that there is reason to (...) think that this goal is not achievable. Another goal is to provide the tools for solving or clarifying important social or philosophical problems. The chapter suggests that this is what theories of blame should focus on. (shrink)

For a long time the dominant view on the nature of blame was that to blame someone is to have an emotion toward her, such as anger, resentment or indignation in the case of blaming someone else and guilt in the case of self-blame. Even though this view is still widely held, it has recently come under heavy attack. The aim of this paper is to elaborate the idea that to blame is to have an emotion and to defend the (...) resulting emotion account of blame. (shrink)

Even though the idea that privacy is some kind of control is often presented as the standard view on privacy, there are powerful objections against it. The aim of this paper is to defend the control account of privacy against some particularly pressing challenges by proposing a new way to understand the relevant kind of control. The main thesis is that privacy should be analyzed in terms of source control, a notion that is adopted from discussions about moral responsibility.

Many philosophers characterize a particularly important sense of free will and responsibility by referring to basically deserved blame. But what is basically deserved blame? The aim of this paper is to identify the appraisal entailed by basic desert claims. It presents three desiderata for an account of desert appraisals and it argues that important recent theories fail to meet them. Then, the paper presents and defends a promising alternative. The basic idea is that claims about basically deserved blame entail that (...) the targets have forfeited their claims that others not blame them and that there is positive reason to blame them. The paper shows how this view frames the discussion about skepticism about free will and responsibility. (shrink)

Blame skeptics argue that we have strong reason to revise our blame practices because humans do not fulfill all the conditions for it being appropriate to blame them. This paper presents a new challenge for this view. Many have objected that blame plays valuable roles such that we have strong reason to hold on to our blame practices. Skeptics typically reply that non-blaming responses to objectionable conduct, like forms of disappointment, can serve the positive functions of blame. The new challenge (...) is that skeptics need to show that it can be appropriate (or less inappropriate) to respond with this kind of disappointment to people’s conduct if it is inappropriate to respond with blame. The paper argues that current blame-skeptical views fail to meet this challenge. (shrink)

ABSTRACT Recently, many authors have argued that claims about determinism and free will are situated on different levels of description and that determinism on one level does not rule out free will on another. This paper focuses on Christian List’s version of this basic idea. It will be argued for the negative thesis that List’s account does not rule out the most plausible version of incompatibilism about free will and determinism and, more constructively, that a level-based approach to free will (...) has better chances to meet skeptical challenges if it is guided by reasoning at the moral level – a level that has not been seriously considered so far by proponents of this approach. (shrink)

The Top-Down Argument for the ability to do otherwise aims at stablishing that humans can do otherwise in the sense that is relevant for debates about free will. It consists of two premises: first, we always need to answer the question of whether some phenomenon (such as the ability to do otherwise) exists by consulting our best scientific theories of the domain at issue. Second, our best scientific theories of human action presuppose that humans can do otherwise. This paper argues (...) that this is not enough to establish the conclusion. The Top-Down Argument supports that humans can do otherwise in some sense. But it does not show that humans can do otherwise in the sense that is relevant for debates about free will. The paper then shows that the apparently best way to make the argument valid does not work. (shrink)

Skepticism about blameworthiness says that there is good reason to doubt that, in our world, humans are ever blameworthy for their deeds. A significant problem for the discussion of this view is that it is unclear how to understand the kind of blame that should be at issue. This paper makes a new proposal. The basic idea is that the kind of blame skeptics should be skeptical about is constituted by responses that can violate the targets’ claims and by the (...) responders’ thought that the targets have forfeited this claim because of their morally objectionable actions and because of how they were when they performed them. This view identifies an important part of our everyday lives and frames discussions about skepticism about blameworthiness in a new way. (shrink)

A standard account of privacy says that it is essentially a kind of control over personal information. Many privacy scholars have argued against this claim by relying on so-called threatened loss cases. In these cases, personal information about an agent is easily available to another person, but not accessed. Critics contend that control accounts have the implausible implication that the privacy of the relevant agent is diminished in threatened loss cases. Recently, threatened loss cases have become important because Edward Snowden’s (...) revelation of how the NSA and GCHQ collected Internet and mobile phone data presents us with a gigantic, real-life threatened loss case. In this paper, I will defend the control account of privacy against the argument that is based on threatened loss cases. I will do so by developing a new version of the control account that implies that the agents’ privacy is not diminished in threatened loss cases. (shrink)

When confronted with the question of why it is appropriate to morally blame a person for some bad action, it may seem plausible to reply that she is morally responsible for it. Some authors, inspired by Peter Strawson's "Freedom and Resentment," argue, however, that thinking this way is backwards. They believe that a person is morally responsible for some bad action because it would be appropriate to blame her for it. The aims of this paper are to present this account, (...) to highlight some of its important but often overlooked features, and to defend it against pressing objections. (shrink)

This paper discusses the idea that the concept of privacy should be understood in terms of control. Three different attempts to spell out this idea will be critically discussed. The conclusion will be that the Source Control View on privacy is the most promising version of the idea that privacy is to be understood in terms of control.

How do the fact that an agent is morally responsible for a certain morally objectionable action and the fact that she is an appropriate target of blame for it relate to each other? Many authors inspired by Peter Strawson say that they necessarily co‐occur. Standard answers to the question of why they co‐occur say that the occurrence of one of the facts explains that the other obtains. This article presents a third option: that they are one and the same fact. (...) There is no difference between the fact that a person is an appropriate target of blame for an objectionable action and the fact that she is morally responsible for it. This view has the advantage of being metaphysically more parsimonious and of answering, in an elegant and plausible way, an interesting question about which many standard theories of responsibility keep silent: what is it to be morally responsible simpliciter? (shrink)

As Christian List (2021) has recently argued, the increasing arrival of powerful AI systems that operate autonomously in high-stakes contexts creates a need for “future-proofing” our regulatory frameworks, i.e., for reassessing them in the face of these developments. One core part of our regulatory frameworks that dominates our everyday moral interactions is blame. Therefore, “future-proofing” our extant regulatory frameworks in the face of the increasing arrival of powerful AI systems requires, among others things, that we ask whether it makes sense (...) to extend our blaming practices to these systems. In the paper, we argue for the admittedly surprising thesis that this question should be answered in the affirmative: contrary to what one might initially think, it can make a lot of sense to blame AI systems, since, as we furthermore argue, many of the important functions that are fulfilled by blaming humans can also be served by blaming AI systems. The paper concludes that this result gives us a good pro tanto reason to extend our blame practices to AI systems. (shrink)

Newton rested his theory of mechanics on distinct metaphysical and epistemological foundations. After Leibniz's death in 1716, the Principia ran into sharp philosophical opposition from Christian Wolff and his disciples, who sought to subvert Newton's foundations or replace them with Leibnizian ideas. In what follows, I chronicle some of the Wolffians' reactions to Newton's notion of absolute space, his dynamical laws of motion, and his general theory of gravitation. I also touch on arguments advanced by Newton's Continental followers, such as (...) Leonhard Euler, who made novel attempts to defend his mechanical foundations against the pro-Leibnizian attack. This examination grants us deeper insight into the fate of Newton's mechanics on the Continent during the early eighteenth century and, more specifically, sheds needed light on the conflicts and tensions that characterized the reception of Newton's philosophy of mechanics among the Leibnizians. (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)

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)

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)

Üblicherweise sind die Dinge kompliziert. Dies führt dazu, dass es eine Menge (unvereinbarer) Theorien gibt, die sich diesen Dingen widmen. Manche sind recht einfach gestrickt, andere sind komplexer. Die Existenz dieser unterschiedlichen Ideen sind ein Indiz dafür, dass die Dinge bisher letztlich unerklärt sind. Und sie sind eine Aufforderung, weiter zu denken. Manchmal sind sie aber auch eine Aufforderung, einmal aufzuräumen. Diese Aufgabe habe ich mir zu Herzen genommen und will deswegen in dieser Arbeit (sozusagen als kleiner Reiseführer) einige Theorien (...) zu Handlungsgründen beleuchten. (shrink)

The animal mindreading debate is coined with theoretical and practical problems which have lead some to believe that it has reached a stalemate. Since Premack and Woodruff have asked whether the chimpanzee has a theory of mind over 30 years ago, the question is still on the table. Even though a lot of evidence has been brought forward by both sides, proponents and opponents of the view that animals can be mindreaders, nothing is definitive. The essential problems remain unresolved.

In Being Realistic About Reasons,T.M. Scanlon develops a non-naturalistic realist account of normative reasons. A crucial part of that account is Scanlon’s contention that there is no deep epistemological problem for non-naturalistic realists, and that the method of reflective equilibrium suffices to explain the possibility of normative knowledge. In this critical notice we argue that this is not so: on a realist picture, normative knowledge presupposes a significant correlation between distinct entities, namely between normative beliefs and normative facts. This correlation (...) calls for an explanation. We show that Scanlon does not have the resources to offer such an explanation. (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)

Ein Beispiel für die Rezeption und Fortführung der schopenhauerschen Logik findet man in den Mathematiklehrbüchern Friedrich Adolph Wilhelm Diesterwegs (1790–1866), In diesem Aufsatz werden die historische und systematische Dimension dieser Anwendung von Logikdiagramme auf die Mathematik skizziert. In Kapitel 2 wird zunächst die frühe Rezeption der schopenhauerschen Logik und Philosophie der Mathematik vorgestellt. Dabei werden einige oftmals tradierte Vorurteile, die das Werk Schopenhauers betreffen, in Frage gestellt oder sogar ausgeräumt. In Kapitel 3 wird dann die Philosophie der Mathematik und der (...) Logik Schopenhauers vorgestellt. Es wird gezeigt, dass Schopenhauers Logikdiagramme auf Ideen der Mathematiker Leonhard Euler (1707–1783), Bernhard Friedrich Thibaut (1775–1832) und Franz Ferdinand Schweins (1780–1856) zurückgehen und dass Schopenhauer diese Logikdiagramme auch bereits zur Analyse mathematischer Begriffe verwendet. Kapitel 4 beschäftigt sich mit der Schopenhauer-Rezeption Diesterwegs. Es wird die Frage behandelt, inwieweit Diesterweg in der Mathematik von Schopenhauer beeinflusst war und welche Rolle dieser Einfluss auf sein Verständnis von Logik und Mathematik hatte. In Kapitel 5 wird schließlich gezeigt, dass Diesterweg die schopenhauersche Begriffsanalyse der Mathematik mit Hilfe von Logikdiagrammen aufgreift und weiterführt. Da Diesterweg einer der einflussreichsten Pädagogen und Mathematikdidaktiker des 20. Jahrhunderts war, ist anzunehmen, dass sich Spuren dieser Methode noch heute finden lassen. Inwiefern dies wahrscheinlich ist, wird in der Zusammenfassung (Kapitel 6) thematisiert. (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)

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)

Christoph Andreas Leonhard Creuzer (1768-1844), che dedicherà la propria vita alIa carriera ecclesiastica e aIle attività benefiche, pubblica nel 1793 - ancora giovane ed entusiasta della filosofia - un'opera che suscita un certo scalpore, le Considerazioni scettiche sulla libertà del volere, sulla quale prendono posizione, polernicamente, anche Fichte e Schelling. Pur accogliendo i princlpi della filosofia critica, Creuzer sostiene che l'idea di libertà come autonornia della volontà, quale Kant l'ha definita, conduca nienterneno che alio spinozismo, ossia alia negazione dei (...) concetti di imputazione, merito e colpa. Mascherandosi dietro uno scetticismo di comodo, Creuzer mostra corne tale conclusione spinoziana, a cui Kant ha tentato inutilmente di sottrarsi, sia l'esito obbligato tanto della sua filosofia teoretica quanto di quella pratica, che pure mirava in prima istanza a salvaguardare la responsabilità morale. (shrink)

This paper aims at showing that Karl Leonhard Reinhold’s theory of representation and consciousness constitutes a link between Kantianism and the further developments of idealism. By retracing the presence of Reinhold in the young Hegel’s work, the author suggest that Reinhold may have influenced Hegel’s reading of Kant.

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)

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)

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.

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)

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)

This paper explains and defends Reinhold’s epistemology of disagreement. The concept of agreement is of central importance for Reinhold’s philosophy. He attempts to settle the most basic disputes among post-Kantian philosophers by offering intermediate positions that reconcile the seemingly incompatible views. Moreover, Reinhold argues for epistemic objectivism, that is, the thesis that a group of philosophers sharing the same information and respecting each other’s opinion may not reasonably disagree. If the members of such a group search for truth then they (...) must converge toward consensus. Disagreement is irrational. (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.

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)

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)

This paper traces the ancestry of a familiar historiographical narrative, according to which early modern philosophy was marked by the development of empiricism, rationalism, and their synthesis by Immanuel Kant. It is often claimed that this narrative became standard in the nineteenth century, due to the influence of Thomas Reid, Kant and his disciples, or German Hegelians and British Idealists. The paper argues that the narrative became standard only at the turn of the twentieth century. This was not due to (...) the influence of Reid, German Hegelians, or British Idealists as they did not endorse the narrative, although Thomas Hill Green may have facilitated its uptake. The narrative is based on Kant’s historiographical sketches, as corrected and integrated by Karl Leonhard Reinhold. It was first fleshed out into full-fledged histories by two Kantians, Wilhelm Gottlieb Tennemann and Johann Gottlieb Buhle. Numerous historians, several of whom were not Kantians, spread it in the English-speaking world. They include Kuno Fischer, Friedrich Ueberweg, Richard Falckenberg, and Wilhelm Windelband. However, the wide availability of their works did not suffice to make the narrative standard because, until the 1890s, the Hegelian account was at least as popular as theirs. Among the factors that allowed the narrative to become standard are its aptness to be adopted by philosophers of the most diverse persuasions, its simplicity and suitability for teaching. (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)

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)

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)

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)