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)

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)

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)

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)

We present a novel approach to defining the mathematical constant π through the infinite den- sification of a sweeping net, which approximates a circle as the net becomes infinitely dense. By developing and enhancing notation related to sweeping nets and saddle maps, we establish a rigor- ous framework for expressing π in terms of the densification process using reverse integration. This method, inspired by the concept that numbers ”come from infinity,” leverages a reverse integral approach to model the transition from (...) infinite densification to the finite circle. Our work not only offers a new perspective on the geometric interpretation of π but also provides insights into reverse integration techniques and their applications in mathematical analysis. (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)

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.

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)

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.

Moral circles help define the boundaries of one’s moral consideration. One’s moral circle may provide insight into how one perceives or treats other entities. A data-driven model exploration was conducted to explore predictors and prediction models. Candidate predictors were built upon past research using moral foundations and political orientation. Moreover, we also employed additional moral psychological indicators, i.e., moral reasoning, moral identity, and empathy, based on prior research in moral development and education. We used model exploration methods, i.e., Bayesian (...) model exploration, Bayesian model averaging, and elastic-net regression. The study successfully replicated past research supporting the relationship between moral foundations, political orientation, and the moral circle. Additional moral psychological constructs, such as post-conventional moral reasoning and moral identity, significantly predicted the moral circle width. The identified components of the moral circle were conceptually related to phronesis, i.e., practical wisdom. We discussed the educational implications of the findings, particularly those related to moral education focusing on phronesis cultivation, multiculturalism and global citizenship, and climate justice. (shrink)

Roughly put, explanatory circles — if any exist — would be propositions such that (i) each explains the next, and (ii) the last explains the first. In this paper, I give two arguments for the view that there are explanatory circles. The first argument appeals to general relativistic worlds in which time is circular. The second argument appeals to special science theories that describe feedback loops. In addition, I show that three standard arguments against explanatory circles are (...) unsuccessful. (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)

Hermeneutic studies of science locate a circle at the heart of scientific practice: scientists only gain knowledge of what they, in some sense, already know. This may seem to threaten the rational validity of science, but one can argue that this circle is a virtuous rather than a vicious one. A virtuous circle is one in which research conclusions are already present in the premises, but only in an indeterminate and underdeveloped way. In order to defend the validity of science, (...) the hermeneuticist must describe a method by which a vague and confused initial knowledge of nature gets transformed into a clear and determinate knowledge of nature. I consider three such methods. The first is regressus demonstrativa, favoured by the physicians of Padua during the fifteenth and sixteenth centuries. The second is mathēsis, introduced by Martin Heidegger in his discussion of seventeenth-century science. The third is Denkstil, a key concept in Ludwik Fleck’s history of syphilology. I conclude by listing three desiderata for a hermeneutic science studies: that it be anti-metaphysical, historical, and sociological. --- Reprinted in: Erich Otto Graf, Martin Schmid & Johannes Fehr (eds.), Fleck and the Hermeneutics of Science (Collegium Helveticum Heft 14) (Zürich, 2016), pp. 85-93. (shrink)

This article is intended as a contribution to the current debates about the relationship between politics and the philosophy of science in the Vienna Circle. I reconsider this issue by shifting the focus from philosophy of science as theory to philosophy of science as practice. From this perspective I take as a starting point the Vienna Circle’s scientific world-conception and emphasize its practical nature: I reinterpret its tenets as a set of recommendations that express the particular epistemological attitude in which (...) both the Vienna Circle’s (doing) philosophy of science and its political engagement were rooted. -/- Regarding politics, and referring to new primary sources, I reconstruct how the scientific world-conception placed the Vienna Circle within a neoliberal-socialist political network that pursued concrete political aims. In light of my reconstruction I shall argue that neither the Vienna Circle’s alleged ethical noncognitivism nor its alleged adhesion to the Weberian ideal of a value-free science rules out the possibility of ascribing to the Vienna Circle a politically engaged philosophy of science: the case of the Vienna Circle shows how philosophy of science, as a public activity, can itself become a form of political engagement, even without necessarily entailing a theory of objective values. (shrink)

Friedrich Nietzsche was among the figures from the history of nineteenth century philosophy that, perhaps surprisingly, some of the Vienna Circle’s members had presented as one of their predecessors. While, primarily for political reasons, most Anglophone figures in the history of analytic philosophy had taken a dim view of Nietzsche, the Vienna Circle’s leader Moritz Schlick admired and praised Nietzsche, rejecting what he saw as a misinterpretation of Nietzsche as a militarist or proto-fascist. Schlick, Frank, Neurath, and Carnap were in (...) different ways committed to the view that Nietzsche made a significant contribution to the overcoming of metaphysics. Some of these philosophers praised the intimate connection Nietzsche drew between his philosophical outlook and empirical studies in psychology and physiology. In his 1912 lectures on Nietzsche, Schlick maintained that Nietzsche overcame an initial Schopenhauerian metaphysical-artistic phase in his thinking, and subsequently remained a positivist until his last writings. Frank and Neurath made the weaker claim that Nietzsche contributed to the development of a positivistic or scientific conception of the world. Schlick and Frank took a further step in seeing the mature Nietzsche as an Enlightenment thinker. (shrink)

The history of early analytic philosophy, and especially the work of the logical empiricists, has often been seen as involving antagonisms with rival schools. Though recent scholarship has interrogated the Vienna Circle’s relations with e.g. phenomenology and Neo-Kantianism, important works by some of its leading members are involved in responding to the rising tide of Lebensphilosophie. This paper will explore Carnap’s configuration of the relation between Lebensphilosophie and the overcoming of metaphysics, Schlick’s responses to Schopenhauer and Nietzsche, and Neurath’s reaction (...) against Spengler. (shrink)

The apparently circular arguments in Descartes’s Meditations should be read as analytic arguments, as Descartes himself suggested. This both explains and excuses the appearance of circularity. Analysis “digs out” what is already present in the meditator’s mind but not yet “expressly known”. Once this is achieved, the meditator may take the result of analysis as an epistemic starting point independent of the original argument. That is, analytic arguments may be reversed to yield demonstrative proofs that follow an already worked-out order (...) of ideas. The “Cartesian Circle,” for example, is circular only when Descartes’s original analytic argument is mistaken for the demonstration that it enables. This approach to Cartesian Circles is unlike the standard approach, which attempts to show that Descartes’s original arguments do work as demonstrations after all. (shrink)

In two recent papers, Michael Della Rocca accuses Descartes of reasoning circularly in the Fourth Meditation. This alleged new circle is distinct from, and more vicious than, the traditional Cartesian Circle arising in the Third Meditation. We explain Della Rocca’s reasons for this accusation, showing that his argument is invalid.

What is attention? On one influential position, attention constitutively is the selection of some stimulus for coupling with a response. Wayne Wu has proposed a master argument for this position that relies on the claim that cognitive science commits to an empirical sufficient condition (ESC), according to which, if a subject S perceptually selects (or response-couples) X to guide performance of some experimental task T, she therein attends to X. In this paper I show that this claim about cognitive science (...) is false. Cognitive science allows for inattentive selection-for-task, or inattentive response-coupling. This means that Wu’s account is without independent support. (shrink)

What might it mean to say that there is such a thing as a hermeneutic circle in the social sciences? A consideration of some remarks by Charles Taylor and others and an interpretive reconstruction, and assessment, of the idea of such a circle.

In this paper I attempt to trace some entanglements of an event documented in my PhD research, which contests dominant modes of enquiry. This research takes place with a group of Grade 2 learners in a government school in Cape Town, South Africa. It is experimental research which resists the human subject as the most important aspect of research, the only one with agency or intentionality. In particular, the analysis focuses on the process of the making of the circle, and (...) how integral it is in contributing to building the Community of Enquiry, the pedagogy of Philosophy with Children. A critical posthuman analysis is offered which engages with the material-discursive entanglements of the making of the circle. Also, how this making of a circle can be a democratising practice, by including in the concept of democracy, the more-than-human. The analysis also focuses on the placing of the chairs by the children, as a deliberate pedagogical practice, and how this works to disrupt the adult /child binary. There is a move beyond the linguistic turn by paying attention to not only the discursive in the transcriptions but also the intra-actions in between human and more-than-human, the circle, the chairs and the materiality of place. (shrink)

Aristotle’s points about circle and vicious circle are as follows: 1. Aristotle criticizes some thinkers because ‘they see no difficulty in holding that all truths are demonstrated, on the ground that demonstration may be circular and reciprocal.’ (PsA., A, 3, 72b16-18) 2. ‘Not all knowledge is demonstrative’ and ‘knowledge of the immediate premises is independent of demonstration.’ Aristotle brings two reasons for this: ‘Since we must know the prior premises from which the demonstration is drawn, and since the regress must (...) end in immediate truths, those truths must be indemonstrable.’ (PsA., A, 3, 72b18-22) 3. Demonstration in the unqualified sense cannot be circular: ‘Demonstration must be based on premises prior to and better known than the conclusion; and the same things cannot simultaneously be both prior and posterior to one another: so circular demonstration is clearly not possible in the unqualified sense of demonstration, but only possible if ‘demonstration be extended to include that other method of argument which rests on a distinction between truths prior to us and truths without qualification prior, i.e. the method by which induction produces knowledge. But if we accept this extension of meaning, our definition of unqualified knowledge will prove faulty; for there seem to be two kinds of it. Perhaps, however, the second form of demonstration, that which proceeds from truths better known to us, is not demonstration in the unqualified sense of the term.’ (PsA., A, 3, 72b23-32) 4. The theory of circular demonstration ‘reduces to the mere statement that if a thing exists, then it does exist- an easy way of providing anything.’ (psA., A, 3, 72b32-34) 5. ‘To constitute the circle it makes no difference whether many terms or few or even only one is taken. Thus by direct proof, if A is, B must be; if B is, C must be; therefore, if A is, C must be. Since then- by the circular proof- if A is, B must be, and if B is, A must be. A may be substituted for C above. Then ‘if B is, A must be’ = ‘if B is, C must be.’ But C and A have been identified. Consequently, the upholders of circular demonstration are in the position of saying that if A is, A must be- a simple way of proving anything. Moreover, even such circular demonstration is impossible except in the case of attributes that imply one another, viz. ‘peculiar’ properties.’ (PsA, A, 3, 72b34-73a7) . (shrink)

How can a business institution function as an ethical institution within a wider system if the context of the wider system is inherently unethical? If the primary goal of an institution, no matter how ethical it sets out to be, is to function successfully within a market system, how can it reconcile making a profit and keeping its ethical goals intact? While it has been argued that some ethical businesses do exist, e.g., Johnson and Johnson, the argument I would like (...) to put forth is that no matter how ethical a business institution is, or how ethical its goals are, its capacity to act in an ethical manner is restricted by the wider system in which it must operate, the market system. Unless there is a fundamental change in the notion of the market system itself, the capacity for individual businesses to act in an ethical manner will always be restricted. My argument is divided into two parts. The first part is to show the inherent bias towards unethical outcomes that is inherent in the market system. The second part is to suggest how to reorient the general economic framework in order to make ethical institutions more possible. The question then becomes, how to define economic behavior in terms other than competition for profit. (shrink)

Consequentialism is a state of affairs centered moral theory that finds support in state of affairs centered views of value, reason, action, and desire/preference. Together these views form a mutually reinforcing circle. I map an exit route out of this circle by distinguishing between two different senses in which actions can be understood as bringing about states of affairs. All actions, reasons, desires, and values involve bringing about in the first, deflationary sense, but only some appear to involve bringing about (...) in a second, rationalizing sense. I demonstrate that the views making up this circle hold, implausibly, that all reasons, values, desires, and actions involve bringing about in both senses, and that failure to distinguish these senses obscures the implausibility of these views as a set. I demonstrate, in addition, that the distinction blocks two common arguments that otherwise threaten to leverage us back in to the consequentialist circle. (shrink)

This chapter explores the opportunities and limitations of the ideal of transparency in responsible innovation, by consulting the virtual case of "The Circle", a company which appears in Dave Eggers' novel The Circle. The Circle is a high-tech company with the main purpose of being responsive to societal needs. They want to eradicate unethical behaviour in society, enhance public health and make a positive impact on the environment. The ultimate goal of The Circle is to reach 100% full transparency in (...) the world, which is impossible without any societal desirability. In first instance, it is free choice of people to accept and embrace the products and services of The Circle, who invest resources in keeping customers happy and in raising awareness about the dangers of privacy. The chapter concludes that The Circle meets the requirements regarding the outcomes of responsible innovation, at least to a certain extent, while at the same time, one feels unease about certain activities they undertake. (shrink)

Descartes has been accused of reasoning in a circle since the publication of the Meditations. The Circle is easy to point out: it seems that Descartes employs clear and distinct perceptions to demonstrate God’s existence and benevolence, and the latter, in turn, validates the use of clear and distinct perceptions. But is Descartes really guilty of fallacious argument, or can we break the arc somehow?

The Vienna Circle was an influential group of philosophers in the early 20th century. Its members were dedicated to do philosophy and to conduct research in accordance with the guidelines of the scientific world-conception. For some of them, Oswald Spengler was a dangerous antagonist due to the success and influence of his metaphysical philosophy of history in Der Untergang des Abendlandes and other works. In this paper, I will explore systematically the Circle’s critical reception of Spengler regarding his methodological approaches, (...) ontological positions, and political philosophy. I will, thereby, also evaluate the criticism brought forth against Spengler. (shrink)

I consider recent strategies proposed by econometricians for extrapolating causal effects from experimental to target populations. I argue that these strategies fall prey to the extrapolator’s circle: they require so much knowledge about the target population that the causal effects to be extrapolated can be identified from information about the target alone. I then consider comparative process tracing as a potential remedy. Although specifically designed to evade the extrapolator’s circle, I argue that CPT is unlikely to facilitate extrapolation in typical (...) econometrics and evidence-based policy applications. To argue this, I offer a distinction between two kinds of extrapolation, attributive and predictive, the latter being prevalent in econometrics and evidence-based policy. I argue that CPT is not helpful for predictive extrapolation when using the kinds of evidence that econometricians and evidence-based policy researchers prefer. I suggest that econometricians may need to consider qualitative evidence to overcome this problem. (shrink)

In theological sources, many symbols are used to explain the transcendent truths of existence. Among the shapes, the circle has the most use of a symbol which is important for Religious, philosophers, and mystics. However, what is refer mostly to the shape of a circle is the rotation of a circular line that begins at a point on a surface and ends at the same point; then, the most superficial and intermediate symbols of facts are explained with it. Contrary, the (...) present article proposes a novel way of drawing a circle, and with this approach, examines some philosophical concepts. We call this drawing "Boiling Circle", because, the rays are coming out boiling from the center. We also have analyzed and introduced a unique example of a mystical-philosophical-religious Architectural building, during which a circular spring has been built. Its water comes out boiling of the center and fills the five circles within itself and twelve eyes around it. This article begins with the drawing of a boiling circle, continues with explaining the philosophical symbols of the boiling circle and boiling spring according to Islamic mysticism, and ends with comparing and expressing the differences between the symbols of the two circles. (shrink)

Zero and one is circumference and diameter. Literally. And, figuratively.

Conservation of a circle explains (the human) mind.

The Berlin Group was an equal partner with the Vienna Circle as a school of scientific philosophy, albeit one that pursued an itinerary of its own. But while the latter presented its defining projects in readily discernible terms and became immediately popular, the Berlin Group, whose project was at least as sig-nificant as that of its Austrian counterpart, remained largely unrecognized. The task of this chapter is to distinguish the Berliners’ work from that of the Vienna Circle and to bring (...) to light its impact in the history of scientific philosophy. (shrink)

The hermeneutic circle serves as a standard argument for all those who raise a claim to the autonomy of the human sciences. The proponents of an alternative methodology for the human sciences present the hermeneutic circle either as an ontological problem or as a specific methodological problem in the social sciences and the humanities. This paper checks the soundness of the argument by sketching out three variations of the problem and critically discussing them.

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)

Tscha Hung was a member of the Vienna Circle who achieved high international academic recognition. He dedicated his entire life to spreading the philosophy of the Circle to China and developed deep insights in his criticisms to that philosophy. Hung was a witness to the encounter of Western and Chinese philosophy in the twentieth century. His debate with Fung You-lan on metaphysics reflects different understandings of the nature of philosophy and metaphysics as well as different perspectives. Hung defended the position (...) of metaphysics in Chinese philosophy in his own way and engaged in a contemporary reconstruction of Chinese philosophy. (shrink)

A widespread assumption in current philosophy of mind is that a conscious state’s phenomenal properties vary with its representational contents. In this paper, I present (rather dogmatically) an alternative picture that recognizes two kinds of phenomenal properties that do not vary concomitantly with content. First, it admits phenomenal properties that vary rather with attitude: what it is like for me to see rain is phenomenally different from what it is like for me to remember (indistinguishable) rain, which is different again (...) from what it is like for me to visualize (indistinguishable) rain – where these differences cannot be traced back to variations in content. Secondly, there is a kind of phenomenal property that varies neither with content nor with attitude but is altogether invariant across all conscious states: a substantive phenomenal commonality among what it is like for me to see, remember, and visualize rain, cats, or dogs. This substantive commonality, I will suggest, is the for-me-ness component of what it is like for me to have any of these experiences. I will close by discussing the interrelations among these three concentric layers of phenomenality: content-based, attitude-based, and for-me-ness. (shrink)

A. J. Ayer’s Language, Truth, and Logic had been responsible for introducing the Vienna Circle’s ideas, developed within a Germanophone framework, to an Anglophone readership. Inevitably, this migration from one context to another resulted in the alteration of some of the concepts being transmitted. Such alterations have served to facilitate a number of false impressions of Logical Empiricism from which recent scholarship still tries to recover. In this paper, I will attempt to point to the ways in which LTL has (...) helped to foster the various mistaken stereotypes about Logical Empiricism which were combined into the received view. I will begin by examining Ayer’s all too brief presentation of an Anglocentric lineage for his ideas. This lineage, as we shall see, simply omits the major 19th century Germanophone influences on the rise of analytic philosophy. The Germanophone ideas he presents are selectively introduced into an Anglophone context, and directed towards various concerns that arose within that context. I will focus on the differences between Carnap’s version of the overcoming of metaphysics, and Ayer’s reconfiguration into what he calls the elimination of metaphysics. Having discussed the above, I will very briefly outline the consequences that Ayer’s radicalisation of the Vienna Circle’s doctrines had on the subsequent Anglophone reception of Logical Empiricism. (shrink)

This contribution aims at providing a more concrete and accurate understanding of Doughnut economics, its model, and its ideas. In doing so, it provides a comprehensive description of the Doughnut and its connection with the Sustainable Development Goals. Then, it inquires into the philosophical background of Doughnut economics, elucidating its existential rationale that relies on human dignity. Further, examples of four AI applications are used to showcase how the Doughnut model would address their use and challenges that arise thereof. From (...) this testing exercise transpires the understanding that another limitation is required in the Doughnut model, pursuant to its philosophical background. Therefore, besides economic activities that may breach the ecological ceiling or the social foundation, activities that infringe human dignity, without breaching any of the boundaries, are also incompatible with the Doughnut model. This complementing proposal is conceptually represented within the model of Doughnut economics. (shrink)

This paper explores the mathematical details behind the geometric transformation of folding a circle into a cone. It includes detailed theo- rems, proofs, and Python implementations for visualization, providing a thorough analysis of the transformation process.

In 1682, Leibniz published an essay containing his solution to the classic problem of squaring the circle: the alternating converg-ing series that now bears his name. Yet his attempts to disseminate his quadrature results began seven years earlier and included four distinct approaches: the conventional (journal article), the grand (treatise), the impostrous (pseudepigraphia), and the extravagant (medals). This paper examines Leibniz’s various attempts to disseminate his series formula. By examining oft-ignored writings, as well as unpublished manuscripts, this paper answers the (...) question of how one of the greatest mathematicians sought to introduce his first great geometrical discovery to the world. (shrink)

Much contemporary political philosophy claims to be Kant-inspired, but its aims and method differ from Kant's own. In his recent book, Force and Freedom, Arthur Ripstein advocates a more orthodox Kantian outlook, presenting it as superior to dominant (Kant-inspired) views. The most striking feature of this outlook is its attempt to ground the whole of political morality in one right: the right to freedom, understood as the right to be independent of others’ choices. Is Ripstein's Kantian project successful? In this (...) research note I argue that it is not. First, I suggest that Ripstein's notion of freedom is viciously circular. It is meant to ground all rights, but in fact it presupposes an account of those rights. Second, I show that—independently of its inability to ground a whole political morality—such a moralized understanding of freedom is normatively unappealing. (shrink)

Conservation of the Circle is the only dynamic in Nature.

This paper focuses on the early sixteenth-century epistemic logic developed by John Mair’s circle and discusses iterated epistemic modalities, epistemic closure and Bradwardinian semantics related to the logic of epistemic statements. These topics are addressed as part of setting up and solving epistemic sophisms based on traditional scenarios which can be traced back to fourteenth-century British epistemic logic. While the ultimate source for the debate appears to be the second chapter of William Heytesbury’s Regule solvendi sophismata, the immediate source is (...) the Italian editorial, commentarial and philosophical tradition, notably Paul of Venice and Cajetan of Thiene. (shrink)

Epicurean ethics has been subject to withering ancient and contemporary criticism for the supposed irreconcilability of Epicurus’s emphatic endorsement of friendship and his equally clear and striking ethical egoism. Recently, Matthew Evans (2004) has suggested that the key to a plausible Epicurean response to these criticisms must begin by understanding why friendship is valuable for Epicurus. In the first section of this paper I develop Evans’ suggestion further. I argue that a shared conception of the human telos and of what (...) is required to attain it structures the confidence that characterizes friendship. In the second part of the paper I return to two contemporary criticisms of Epicurean friendship. The first criticism focuses on the problem of free riders. The second criticism points to a seeming inconsistency in Epicurean doctrine. I suggest that both criticisms can be adequately addressed once we understand Epicurean friendship in greater depth. (shrink)