In Squaring the Circle in Descartes’ Meditations, Stephen Wagner aims to show that Descartes’ project in the Meditations is best understood as a ‘strong validation of reason’ i.e., as proving in a non-circular way that human reason is a reliable, truth-conducive faculty. For such an enterprise to qualify as a ‘strong’ validation, Wagner contends, skeptical doubt must be given its strongest force. The most stringent doubt available in the Meditations is the deceiving God. To rule out the possibility (...) that an omnipotent God created humans so that their best functioning cognitive faculties provide misleading information about what the world is like, Descartes must prove that a non-deceiving God exists. Furthermore, only a non-circular proof will count as a ‘validation.’ Wagner spells out the requirements of non-circularity as involving a proof for God’s existence that is not deductive, does not simply achieve a clear and distinct perception of God’s existence, and proceeds on the basis of perceptions that remain true even when the reasons underlying them are not attended to any longer by the meditator. (shrink)

Development has been themain strategy in addressing the problemof sustainability since at least the mid-1980s. The results of this strategy have been mixed, if not disappointing. In their objections to this approach, critics frequently invoke constraints imposed by physical reality of which the most important one is entropy production. They question the belief that technological innovations are capable of solving the problem of sustainability. Is development the right response to this problem and is the current course capable of attaining sustainability? (...) The article examines closely and critiques the principal theoretical objection to sustainable development that emphasizes physical constraints, and more specifically entropy production. It also offers a critique of the current approach to sustainable development. The article advocates a systems approach as a way to anchor a broad consensus in the ongoing sustainability debates. (shrink)

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)

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)

Given quasi-realism, the claim is that any attempt to naturalise modal epistemology would leave out absolute necessity. The reason, according to Simon Blackburn, is that we cannot offer an empirical psychological explanation for why we take any truth to be absolutely necessary, lest we lose any right to regard it as absolutely necessary. In this paper, I argue that not only can we offer such an explanation, but also that the explanation won’t come with a forfeiture of the involved necessity. (...) Using ‘squaring the circle’ as evidence, I show that, contrary to quasi-realism, absolute necessity won’t be left out in attempts to naturalise modal epistemology. (shrink)

Is drastic action against global warming essential to avoid impoverishing our descendants? Or does it mean robbing the poor to give to the rich? We do not yet know. Yet most of us can agree on the importance of minimising expected deprivation. Because of the vast number of future generations, if there is any significant risk of catastrophe, this implies drastic and expensive carbon abatement unless we discount the future. I argue that we should not discount. Instead, the rich countries (...) should stump up the funds to support abatement both for themselves and the poor states of the world. Yet to ask the present generation to assume all the costs of drastic mitigation.is unfair.Worse still, it is politically unrealistic.We can square the circle by shifting part of the burden to our descendants. Even if we divert investment from other parts of the economy or increase public debt, future people should be richer, so long as we avert catastrophe. If so, it is fair for them to assume much of the cost of abatement.What we must not do is to expose them to the threat of disaster by not doing enough. (shrink)

Pre-emption cases have been taken by almost everyone to imply the unviability of the simple counterfactual theory of causation. Yet there is ample motivation from scientific practice to endorse a simple version of the theory if we can. There is a way in which a simple counterfactual theory, at least if understood contrastively, can be supported even while acknowledging that intuition goes firmly against it in pre-emption cases—or rather, only in some of those cases. For I present several new pre-emption (...) cases in which causal intuition does not go against the counterfactual theory, a fact that has been verified experimentally. I suggest an account of framing effects that can square the circle. Crucially, this account offers hope of theoretical salvation—but only to the counterfactual theory of causation, not to others. Again, there is (admittedly only preliminary) experimental support for this account. (shrink)

The traditional Lewis–Stalnaker semantics treats all counterfactuals with an impossible antecedent as trivially or vacuously true. Many have regarded this as a serious defect of the semantics. For intuitively, it seems, counterfactuals with impossible antecedents—counterpossibles—can be non-trivially true and non-trivially false. Whereas the counterpossible "If Hobbes had squared the circle, then the mathematical community at the time would have been surprised" seems true, "If Hobbes had squared the circle, then sick children in the mountains of Afghanistan at the (...) time would have been thrilled" seems false. Many have proposed to extend the Lewis–Stalnaker semantics with impossible worlds to make room for a non-trivial or non-vacuous treatment of counterpossibles. Roughly, on the extended Lewis–Stalnaker semantics, we evaluate a counterfactual of the form "If A had been true, then C would have been true" by going to closest world—whether possible or impossible—in which A is true and check whether C is also true in that world. If the answer is "yes", the counterfactual is true; otherwise it is false. Since there are impossible worlds in which the mathematically impossible happens, there are impossible worlds in which Hobbes manages to square the circle. And intuitively, in the closest such impossible worlds, sick children in the mountains of Afghanistan are not thrilled—they remain sick and unmoved by the mathematical developments in Europe. If so, the counterpossible "If Hobbes had squared the circle, then sick children in the mountains of Afghanistan at the time would have been thrilled" comes out false, as desired. In this paper, I will critically investigate the extended Lewis–Stalnaker semantics for counterpossibles. I will argue that the standard version of the extended semantics, in which impossible worlds correspond to maximal, logically inconsistent entities, fails to give the correct semantic verdicts for many counterpossibles. In light of the negative arguments, I will then outline a new version of the extended Lewis–Stalnaker semantics that can avoid these problems. (shrink)

This paper attempts to clarify the nature and the importance of a third kind of sophistic argument that is not always found in the classification of those arguments in the secondary literature. An argument of the third kind not only is a valid one, but is also constituted of true propositions. What makes it a sophistic argument is the fact that it produces a false semblance of scientific explanation: its explanation seems to be appropriate to the explanandum without being so. (...) Evidence from this kind of argument comes from Sophistic Refutations 11, and Brison’s attempt to square the circle should be counted as one of its instances. (shrink)

The content of the manuscript represents a bold idea system, it is beyond the boundaries of all existing knowledge but the method of reasoning and logic is also very strict and scientific. The purpose of the manuscript is to unify the natural categories (natural philosophy, natural geometry, quantum mechanics, astronomy,…), and to open a new direction for most other sciences. Abstract of the manuscript: About Philosophy: • Proved the existence of time and non-dilation. • Proved that matter is always motionless (...) in space. • Conclusion that space is energy. • … About Mathematics: • Solved the squaring the circle problem(a millennium problem). • Using the equation to calculate speed of light is 471.000.000 m/s • … About Physics : • Explained the nature of gravity. • Explained dark energy, spin value of Nucleon. • Explained matter and antimatter. • …. (shrink)

The second volume of “Advancing Uncertain Combinatorics through Graphization, Hyperization, and Uncertainization: Fuzzy, Neutrosophic, Soft, Rough, and Beyond” presents a deep exploration of the progress in uncertain combinatorics through innovative methodologies like graphization, hyperization, and uncertainization. This volume integrates foundational concepts from fuzzy, neutrosophic, soft, and rough set theory, among others, to further advance the field. Combinatorics and set theory, two central pillars of mathematics, focus on counting, arrangement, and the study of collections under defined rules. Combinatorics excels in handling (...) uncertainty, while set theory has evolved with concepts such as fuzzy and neutrosophic sets, which enable the modeling of complex real-world uncertainties by addressing truth, indeterminacy, and falsehood. These advancements, when combined with graph theory, give rise to novel forms of uncertain sets in "graphized" structures, including hypergraphs and superhypergraphs. Innovations such as Neutrosophic Oversets, Undersets, and Offsets, as well as the Nonstandard Real Set, build upon traditional graph concepts, pushing both theoretical and practical boundaries. The synthesis of combinatorics, set theory, and graph theory in this volume provides a robust framework for addressing the complexities and uncertainties inherent in both mathematical and real-world systems, paving the way for future research and application. In the first chapter, “A Review of the Hierarchy of Plithogenic, Neutrosophic, and Fuzzy Graphs: Survey and Applications”, the authors investigate the interrelationships among various graph classes, including Plithogenic graphs, and explore other related structures. Graph theory, a fundamental branch of mathematics, focuses on networks of nodes and edges, studying their paths, structures, and properties. A Fuzzy Graph extends this concept by assigning a membership degree between 0 and 1 to each edge and vertex, representing the level of uncertainty. The Turiyam Neutrosophic Graph is introduced as an extension of both Neutrosophic and Fuzzy Graphs, while Plithogenic graphs offer a potent method for managing uncertainty. The second chapter, “Review of Some Superhypergraph Classes: Directed, Bidirected, Soft, and Rough”, examines advanced graph structures such as directed superhypergraphs, bidirected hypergraphs, soft superhypergraphs, and rough superhypergraphs. Classical graph classes include undirected graphs, where edges lack orientation, and directed graphs, where edges have specific directions. Recent innovations, including bidirected graphs, have sparked ongoing research and significant advancements in the field. Soft Sets and their extension to Soft Graphs provide a flexible framework for managing uncertainty, while Rough Sets and Rough Graphs address uncertainty by using lower and upper approximations to handle imprecise data. Hypergraphs generalize traditional graphs by allowing edges, or hyperedges, to connect more than two vertices. Superhypergraphs further extend this by allowing both vertices and edges to represent subsets, facilitating the modeling of hierarchical and group-based relationships. The third chapter, “Survey of Intersection Graphs, Fuzzy Graphs, and Neutrosophic Graphs”, explores the intersection graph models within the realms of Fuzzy Graphs, Intuitionistic Fuzzy Graphs, Neutrosophic Graphs, Turiyam Neutrosophic Graphs, and Plithogenic Graphs. The chapter highlights their mathematical properties and interrelationships, reflecting the growing number of graph classes being developed in these areas. Intersection graphs, such as Unit Square Graphs, Circle Graphs, and Ray Intersection Graphs, are crucial for understanding complex graph structures in uncertain environments. The fourth chapter, “Fundamental Computational Problems and Algorithms for SuperHyperGraphs”, addresses optimization problems within the SuperHypergraph framework, such as the SuperHypergraph Partition Problem, Reachability, and Minimum Spanning SuperHypertree. The chapter also adapts classical problems like the Traveling Salesman Problem and the Chinese Postman Problem to the SuperHypergraph context, exploring how hypergraphs, which allow hyperedges to connect more than two vertices, can be used to solve complex hierarchical and relational problems. The fifth chapter, “A Short Note on the Basic Graph Construction Algorithm for Plithogenic Graphs”, delves into algorithms designed for Plithogenic Graphs and Intuitionistic Plithogenic Graphs, analyzing their complexity and validity. Plithogenic Graphs model multi-valued attributes by incorporating membership and contradiction functions, offering a nuanced representation of complex relationships. The sixth chapter, “Short Note of Bunch Graph in Fuzzy, Neutrosophic, and Plithogenic Graphs”, generalizes traditional graph theory by representing nodes as groups (bunches) rather than individual entities. This approach enables the modeling of both competition and collaboration within a network. The chapter explores various uncertain models of bunch graphs, including Fuzzy Graphs, Neutrosophic Graphs, Turiyam Neutrosophic Graphs, and Plithogenic Graphs. In the seventh chapter, “A Reconsideration of Advanced Concepts in Neutrosophic Graphs: Smart, Zero Divisor, Layered, Weak, Semi, and Chemical Graphs”, the authors extend several fuzzy graph classes to Neutrosophic graphs and analyze their properties. Neutrosophic Graphs, a generalization of fuzzy graphs, incorporate degrees of truth, indeterminacy, and falsity to model uncertainty more effectively. The eighth chapter, “Short Note of Even-Hole-Graph for Uncertain Graph”, focuses on Even-Hole-Free and Meyniel Graphs analyzed within the frameworks of Fuzzy, Neutrosophic, Turiyam Neutrosophic, and Plithogenic Graphs. The study investigates the structure of these graphs, with an emphasis on their implications for uncertainty modeling. The ninth chapter, “Survey of Planar and Outerplanar Graphs in Fuzzy and Neutrosophic Graphs”, explores planar and outerplanar graphs, as well as apex graphs, within the contexts of fuzzy, neutrosophic, Turiyam Neutrosophic, and plithogenic graphs. The chapter examines how these types of graphs are used to model uncertain parameters and relationships in mathematical and real-world systems. The tenth chapter, “General Plithogenic Soft Rough Graphs and Some Related Graph Classes”, introduces and explores new concepts such as Turiyam Neutrosophic Soft Graphs and General Plithogenic Soft Graphs. The chapter also examines models of uncertain graphs, including Fuzzy, Intuitionistic Fuzzy, Neutrosophic, and Plithogenic Graphs, all designed to handle uncertainty in diverse contexts. The eleventh chapter, “Survey of Trees, Forests, and Paths in Fuzzy and Neutrosophic Graphs”, provides a comprehensive study of Trees, Forests, and Paths within the framework of Fuzzy and Neutrosophic Graphs. This chapter focuses on classifying and analyzing graph structures like trees and paths in uncertain environments, contributing to the ongoing development of graph theory in the context of uncertainty. (shrink)

This article presents an ontological proof that God is impossible.I define an ‘impossibility’ as a condition which is inconceivable due to its a priori characteristics (e.g. a ‘square circle’). Accordingly, said conditions will not ever become conceivable, as they could in instances of a posteriori inconceivability (e.g. the notion that someone could touch a star without being burned). As the basis of this argument, I refer to an a priori observation (Primus, 2019) regarding our inability to imagine inconsistency (difference) (...) within any point of space. This observation renders the notion of absolute power to be inconceivable, a priori.I briefly discuss the moral implications of religious faith in the context of Purism: a moral rationalist paradigm. I conclude that whilst belief in God can be aesthetically expressed it should not be possessed as a material purpose, due to the illogicality of the latter category of belief and/or expression. With this article I provide conceptual delineation between harmless religious belief and expression—which, I argue, should be protected from persecution, as per any other artistic expression— and religious belief and expression which is materially harmful to society. Whilst I aim to protect religious freedom of expression on one hand, I duly aim to reduce instances of material faith in God(s) on the other. Finally, I aim to bring hope in the possibility for human salvation via technology—such that they should exist indefinitely as ‘demigods,’ defined by conditional, relative power over their environment. (shrink)

This article investigates the specific cultural and collaborative nature of China’s public spaces and how they are formed through performative appropriations. Collective cultural practices as political participation were encouraged during the Mao era when cultural activities played a key role in workers’ education and participation. Since the opening-up period, performance in public space has become widespread in China and creates alternative community spaces that constitute alternatives to capitalist spaces of consumption. Using Habermas’s theory of communicative action, we argue that cultural (...) practices performed in public space create a proletariat public sphere that plays a wider role in governance and China’s democratization. Further, the article examines performative practices in public space. It traces the popular activity of public square dancing through history and counters this research with a parallel study of a much younger skateboarding practice. The two practices are very differently rooted. Yet both practices appear to move through cycles of disruption and appropriation, followed by an affirmation of governmental rule. The studies reveal that western ideas of citizenship and individual leisure are less applicable. Public spaces are largely managed through collaborative practices, whereas contemporary scholarship reaffirms Fei Xiaotong’s description of Chinese society as individuals positioned within a complex network of concentric circles. (shrink)

It seems certain to me that I will die and stay dead. By “I”, I mean me, Greg Nixon, this person, this self-identity. I am so intertwined with the chiasmus of lives, bodies, ecosystems, symbolic intersubjectivity, and life on this particular planet that I cannot imagine this identity continuing alone without them. However, one may survive one’s life by believing in universal awareness, perfection, and the peace that passes all understanding. Perhaps, we bring this back with us to the Source (...) from which we began, changing it, enriching it. Once we have lived – if we don’t choose the eternal silence of oblivion by life denial, vanity, indifference, or simple weariness – the Source learns and we awaken within it. Awareness, consciousness, is universal – it comes with the territory – so maybe you will be one of the few prepared to become unexpectedly enlightened after the loss of body and self. You may discover your own apotheosis – something you always were, but after a lifetime of primate experience, now much more. Since you are of the Source and since you have changed from life experience and yet retained the dream of ultimate awakening, plus you have brought those chaotic emotions and memories back to the Source with you (though no longer yours), your life & memories will have mattered. Those who awaken beyond the death of self will have changed Reality. (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)

Recent work on the imagination has stressed the epistemic significance of imaginative experiences, notably in justifying modal beliefs. An immediate problem with this is that modal beliefs appear to admit of justification through the mere exercise of rational capacities. For instance, mastery of the concepts of square, circle, and possibility should suffice to form the justified belief that a square circle is not possible, and mastery of the concepts of pig, flying, and possibility should suffice to form a (...) justified belief that a flying pig is possible. It is thus unnecessary to try to imagine a square circle or a flying pig to justify these beliefs. In this paper, I consider three ways to defend the epistemic role of imagination in modal epistemology against this challenge. One claims that modal beliefs simply admit of justification by two separate sources: rational capacities and imaginative experience. Another holds that while beliefs about logical or conceptual modality can be justified entirely by rational capacities, beliefs about metaphysical modality require imaginative experiences. The third, which I defend, is the idea that imagination is relevant in the first instance not to modal knowledge but to modal understanding: even where imaginative experience is unnecessary for the justification of modal beliefs, it is indispensable for directly grasping certain modal propositions. (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)

Conservation of the Circle is the only dynamic in Nature.

What’s wrong with begging the question? Some philosophers believe that question-begging arguments are inevitably fallacious and that their fallaciousness stems from a shared “formal” deficiency. In contrast, some philosophers, like Robinson deny that begging the question is fallacious at all. And others characterize begging the question as an “informal” fallacy of reasoning that can only be understood with the aid of epistemic notions. Sorensen joins this last camp by offering a powerful argument against both Robinson’s skepticism and fully formal approaches (...) to the phenomenon. According to Sorensen’s view, question-begging is fallacious because it compromises the rationality of the question-beggar’s position. Though his argument forces Robinson into a peculiar dialectical position, it does little to elucidate the reasons why Robinson’s position is unstable and it fails to embody Sorensen’s own conception of rationally persuasive argumentation. I utilize this conception to show how Robinson is left with no easily identifiable grounds on which to deny the fallaciousness of begging the question. By advancing the dialectic between Sorensen and Robinson, I aim to show that our argumentative practices must take the perspectives of others seriously, whether or not those perspectives are rational. (shrink)

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

A review of the recent exhibition of Wassily Kandinsky's artworks at the Guggenheim Museum, with interest in Kandinsky's career-wide separation of form from content.

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 line connecting everything to everything is both diameter and circumference of a circle. Thus, complementarity is the basis for identity (duplicity is the basis for a unit). See, also, The Singularity and Object-Oriented Reality (also on PhilPapers).

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)

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 fear of the other is the main focus of this paper, which analyse Tehran protest squares as inside-out spaces where the state attempts to maintain some form of control, and where the public attempts to occupy it. The fear of ‘others’ can lead to exclusion from the public space of those who are seen as threatening. This process of ‘otherness’ renders fear as an arena of conflict and highlights the political utility of fear by particular groups and individuals.

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)

It is a received view that Kant’s formal logic (or what he calls “pure general logic”) is thoroughly intensional. On this view, even the notion of logical extension must be understood solely in terms of the concepts that are subordinate to a given concept. I grant that the subordination relation among concepts is an important theme in Kant’s logical doctrine of concepts. But I argue that it is both possible and important to ascribe to Kant an objectual notion of logical (...) extension according to which the extension of a concept is the multitude of objects falling under it. I begin by defending this ascription in response to three reasons that are commonly invoked against it. First, I explain that this ascription is compatible with Kant’s philosophical reflections on the nature and boundary of a formal logic. Second, I show that the objectual notion of extension I ascribe to Kant can be traced back to many of the early modern works of logic with which he was more or less familiar. Third, I argue that such a notion of extension makes perfect sense of a pivotal principle in Kant’s logic, namely the principle that the quantity of a concept’s extension is inversely proportional to that of its intension. In the process, I tease out two important features of the Kantian objectual notion of logical extension in terms of which it markedly differs from the modern one. First, on the modern notion the extension of a concept is the sum of the objects actually falling under it; on the Kantian notion, by contrast, the extension of a concept consists of the multitude of possible objects—not in the metaphysical sense of possibility, though—to which a concept applies in virtue of being a general representation. While the quantity of the former extension is finite, that of the latter is infinite—as is reflected in Kant’s use of a plane-geometrical figure (e.g., circle, square), which is continuum as opposed to discretum, to represent the extension in question. Second, on the modern notion of extension, a concept that signifies exactly one object has a one-member extension; on the Kantian notion, however, such a concept has no extension at all—for a concept is taken to have extension only if it signifies a multitude of things. This feature of logical extension is manifested in Kant’s claim that a singular concept (or a concept in its singular use) can, for lack of extension, be figuratively represented only by a point—as opposed to an extended figure like circle, which is reserved for a general concept (or a concept in its general use). Precisely on account of these two features, the Kantian objectual extension proves vital to Kant’s theory of logical quantification (in universal, particular and singular judgments, respectively) and to his view regarding the formal truth of analytic judgments. (shrink)

Two weeks after reports came to light that singer Chris Brown had physically assaulted and abandoned his girlfriend, famous Barbadian pop star Rihanna, the celebrity blog TMZ released a close-up photo of Rihanna’s face taken by the Los Angeles Police Department the night she was beaten. The news and the photo sparked fierce online debates about domestic violence and culpability. The locus of accountability in many of these debates seemed to circle back to Rihanna, rather than land squarely on (...) Chris Brown. The question repeatedly raised was, as a survivor of domestic violence, what did Rihanna owe to others? This paper explores several of these online debates, engages the question of survivor accountability, and discusses how Internet-based discourse can act as a temperature read for our unspoken, but very present expectations of survivors of domestic violence. (shrink)

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 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)

We offer a novel interpretation of the argumentative role that Meditation IV plays within the whole of the Meditations. This new interpretation clarifies several otherwise head-scratching claims that Descartes makes about Meditation IV, and it fully exonerates the Fourth Meditation from either raising or exacerbating Descartes’ circularity problems.

In this work we consider the problem of the approximate hedging of a contingent claim in the minimum mean square deviation criterion. A theorem on martingale representation in case of discrete time and an application of the result for semi-continuous market model are also given.

Lack of physical activity is one of the main cause of obesity. Currently, scientists proposed that teenagers and women are overweight or obese than men in Bangladesh. Furthermore, non-communicable diseases (NCDs) are becoming more prevalent in Bangladesh. By 2050, the illness burden of non-communicable diseases will have a significant impact on the health budget. To reduce non-communicable diseases, physical activity is one of the options. However, the lack of public facilities for physical activities in each community is a concern. According (...) to the Department of Military Estate Administration, Central Circle, DOHS (Defense Officers' Housing Scheme) has a total of 2966 plots and 396.6327 acres of area (640 acres =1 square mile) including 5 DOSH in Bangladesh. However, each DOHS has all the public facilities including structures streets, parks, walking paths, squares, gyms, cultural and sports grounds, walkways, waterfronts, lakes, mosques, cafeterias, public toilets, sitting areas for elderly or passersby, etc for physical activities specially for women, children, and the disabled people. Gulshan, Baridhara, Banani, and Dhanmondi areas are other good examples from Bangladesh where dwellers specially, women and children have facilities for physical activities. Sangmoo Kim, urban specialist said, “it is not over-ambitious thinking to have public facilities; it is a basic need for each city dweller for a healthy life”. This report aims to explore what are the policy drawbacks of the Government of Bangladesh not providing public facilities to perform physical activities in each area. (shrink)

We re-examine the problem of existential import by using classical predicate logic. Our problem is: How to distribute the existential import among the quantified propositions in order for all the relations of the logical square to be valid? After defining existential import and scrutinizing the available solutions, we distinguish between three possible cases: explicit import, implicit non-import, explicit negative import and formalize the propositions accordingly. Then, we examine the 16 combinations between the 8 propositions having the first two kinds of (...) import, the third one being trivial and rule out the squares where at least one relation does not hold. This leads to the following results: (1) three squares are valid when the domain is non-empty; (2) one of them is valid even in the empty domain: the square can thus be saved in arbitrary domains and (3) the aforementioned eight propositions give rise to a cube, which contains two more (non-classical) valid squares and several hexagons. A classical solution to the problem of existential import is thus possible, without resorting to deviant systems and merely relying upon the symbolism of First-order Logic (FOL). Aristotle’s system appears then as a fragment of a broader system which can be developed by using FOL. (shrink)

The aim of the paper is to analyze the expressive power of the square operator of Łukasiewicz logic: ∗x=x⊙x⁠, where ⊙ is the strong Łukasiewicz conjunction. In particular, we aim at understanding and characterizing those cases in which the square operator is enough to construct a finite MV-chain from a finite totally ordered set endowed with an involutive negation. The first of our main results shows that, indeed, the whole structure of MV-chain can be reconstructed from the involution and the (...) Łukasiewicz square operator if and only if the obtained structure has only trivial subalgebras and, equivalently, if and only if the cardinality of the starting chain is of the form n+1 where n belongs to a class of prime numbers that we fully characterize. Secondly, we axiomatize the algebraizable matrix logic whose semantics is given by the variety generated by a finite totally ordered set endowed with an involutive negation and Łukasiewicz square operator. Finally, we propose an alternative way to account for Łukasiewicz square operator on involutive Gödel chains. In this setting, we show that such an operator can be captured by a rather intuitive set of equations. (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)

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.

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)

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)

. Each predicate of the Aristotelian square of opposition includes the word “is”. Through a twofold interpretation of this word the square includes both classical logic and non-classical logic. All theses embodied by the square of opposition are preserved by the new interpretation, except for contradictories, which are substituted by incommensurabilities. Indeed, the new interpretation of the square of opposition concerns the relationships among entire theories, each represented by means of a characteristic predicate. A generalization of the square of opposition (...) is achieved by not adjoining, according to two Leibniz’ suggestions about human mind, one more choice about the kind of infinity; i.e., a choice which was unknown by Greek’s culture, but which played a decisive role for the birth and then the development of modern science. This essential innovation of modern scientific culture explains why in modern times the Aristotelian square of opposition was disregarded. (shrink)

An underappreciated fact in the history of analytic philosophy is that American pragmatism had an early and strong influence on the Vienna Circle. The path of that influence goes from Charles Peirce to Frank Ramsey to Ludwig Wittgenstein to Moritz Schlick. That path is traced in this paper, and along the way some standard understandings of Ramsey and Wittgenstein, especially, are radically altered.

In a previous issue of Philosophia Christi, Kirk MacGregor responded to an essay of mine in which I argued for a neo-Molinist account of open theism. The argument demonstrated how, given standard counterfactual semantics, one could derive an “open future square of opposition,” that is, a depiction of the logical relations that hold between future-tense statements from an open theistic standpoint. Conceding the validity of the argument, MacGregor nevertheless sought to deny its soundness by criticizing both its conclusion and the (...) Stalnaker-Lewis semantics on which the argument was based. In this paper, I argue that MacGregor’s reasons for rejecting the open future square, as well as his Molinist alternative to the Stalnaker-Lewis semantics, are uncompelling. (shrink)

In this work, we consider the problem of the approximate hedging of a contingent claim in the minimum mean square deviation criterion. A theorem on martingaỉe representation in the case of discrete time and an application of obtained result for semi-continous market model are given.

In this paper I propose a set-theoretical interpretation of the logical square of opposition, in the perspective opened by generalized quantifier theory. Generalized quantifiers allow us to account for the semantics of quantificational Noun Phrases, and of other natural language expressions, in a coherent and uniform way. I suggest that in the analysis of the meaning of Noun Phrases and Determiners the square of opposition may help representing some semantic features responsible to different logical properties of these expressions. I will (...) conclude with some consideration on scope interactions between quantifiers. (shrink)