The Web may critically transform the way we understand the activity of proving. The Web as a collaborative medium allows the active participation of people with different backgrounds, interests, viewpoints, and styles. Mathematical formal proofs are inadequate for capturing Web‐based proofs. This article claims that Web provings can be studied as a particular type of Goguen's proof‐events. Web‐based proof‐events have a social component, communication medium, prover‐interpreter interaction, interpretation process, understanding and validation, historical component, and styles. To demonstrate its claim, the (...) article discusses the Kumo and Polymath projects, both of which employ Web‐based communication as part of proving. Web proving is a novel type of proving activity that may have a serious impact on the change in mathematical practices, despite the fact that it is not currently a universally acceptable methodology. (shrink)

In this paper, we explore certain exemplifications of transgression in the history and philosophy of mathematics. We recognize transgressive acts in the transition from a “real” to an “imaginary” world. Further, we suggest the concept of proof-events that transgress traditional concepts of mathematical proof. The theory of proof-events provides us with means to identify transgressive acts in the development of a discovery proof-event. These concern the creative understanding of a purported mathematical proof by reconstructing the meaning conveyed by it, eventually (...) supplementing it, surpassing stylistic hindrances in the narrative formulated by a prover, exceeding the boundaries of the (local) logic of a prover, etc. Finally, we identify transgressive acts with discontinuous points of change in the development of proof-events and suggest formal measures for their recognition. (shrink)

The volume starts with the paper of Lynn Maurice Ferguson Arnold, former Premier of South Australia and former Minister of Education of Australia, concerning the Exposition Internationale des Arts et Techniques dans la Vie Moderne (International Exposition of Art and Technology in Modern Life) that was held from 25 May to 25 November 1937 in Paris, France. The organization of the world exhibition had placed the Nazi German and the Soviet pavilions directly across from each other. Many papers are devoted (...) to the interpretation of this opposition. Arnold’s paper considers the differences in the two totalitarian states’ architectural and design discourse styles. Although each of them communicated a totalitarian language of purposes, permissions, and boundaries, they essentially differed in the styles of discourse represented by the architecture and design of their respective pavilions. They were opposites of each other and the liberal ideals they contested. The internationalist viewpoint reflecting the multi-ethnic mix of the USSR is contrasted to the ein Volk homogeneity represented in the German pavilion. The Soviet pavilion opted for a utopian future to be arrived at by “benign” leadership, whereas the German pavilion anchored itself in the myth of Teutonic history with the nostalgic pride protected by the swastika-bearing eagle. Jean-Yves Béziau is best known as a logician and founder of Universal Logic. However, in this paper, he poses a new philosophical question: why philosophical discourse does not use images? The paper begins with a general analysis of different types of philosophical discourses. Then, he focuses on why images have been and are still rejected in philosophical discourse. He explains various ways to use images in a fruitful way to develop philosophical thinking and discourse and illustrates his view by providing several examples. He concludes with a promising programmatic declaration about founding a new journal entitled World Journal of Pictorial Philosophy to stimulate the usage of images for developing philosophical thinking. Although complaints about the obscurity of many philosophers’ discourse are widespread, Tatiana Denisova, ex-professor of the Surgut University and a research associate of the University of the Aegean undertakes a positive attitude to this problem. She explains that the reasons for the obscurity of philosophical texts, the subsequent complexity in communicating philosophers’ meanings and their eventual incomplete understanding is not a sign of their inferiority. On the contrary, it is a sign of the fruitfulness of philosophical discourse, which can generate new meanings. Thus, the darkness of philosophical discourse is like the life-giving chaos, and the obscurity that it inevitably contains can be the keeper of implicit meanings and even their generator. Katarzyna Gan-Krzywoszyńska and Piotr Leśniewski, authors of a monograph on Polish philosopher Kazimierz Ajdukiewicz (1890 – 1963), make a comparative analysis of his educational style with that of Paulo Reglus Neves Freire (1921 – 1997). The authors highlight that these scholars have distinctly different backgrounds. The former was an educator, philosopher and a leading advocate of critical pedagogy connected with the dialogical Latin-American tradition. The latter was a philosopher and logician, a notable representative of the Lwów–Warsaw school of logic with significant contributions to semantics, model theory and the philosophy of science. Despite their apparent difference, the authors identify some striking similarities regarding their attitudes towards education; notably, their approaches are essentially dialogical. Gilah Yelin Hirsch is a multidisciplinary artist who works as a painter, writer, curator, educator, and filmmaker. In her experiential paper, he explains how and why she uses four channels of communication in her creative expression: writing, painting, filmmaking, and teaching, as dialogic inquiry. She considers that these channels compose a continuum of discourse styles, each reaching a different facet of kaleidoscopic consciousness. She claims that her choice of medium is prompted by a need to communicate her insights profoundly. Thus, for instance, she created painted allegories to express narratives based on dreams and visions emerging from her subconscious. Art and healing is another Tibetan-rooted type of discourse practised by the author. Creating and observing a healing image produces a positive psychophysiological change in both the artist and the viewer. The discourse here is tripartite between creator, image, and viewer. Filmmaking is another type of discourse she practices between the filmmaker/artist as shaman or healer and the viewer as respondent or participant. These films are meant to be experienced frame by frame, physically and emotionally in both the body and mind. Jocelyn Ireson-Paine is a cartoonist and programmer. His paper offers an original attempt to use category theory in cartooning. Category theory is a branch of mathematics that provides concepts and methods to describe general abstract structures in terms of a labelled directed graph called category, whose nodes are called objects, and whose labelled directed edges are called arrows (or morphisms or transformations or mappings). The author explores different ways to define “style” in art using category theory and a relational view of art. Moreover, he examines how “translation” (transformation) between styles could be defined and reveals the difficulties of how it could be implemented in a computer using special software. Jens Lemanski is a philosopher who has revived research in Arthur Schopenhauer’s legacy by exploring his work on mathematical evidence, logic diagrams, and problems of semantics. In this paper, he advances a new approach to eristic as an art of protecting oneself from the one who deliberately violates norms of discourse ethics to win an argument. The author attributes the origins of this view to Schopenhauer, suggesting a new reading of his work. According to the author, eristic is a prohibitive technique that takes effect when the norms of discourse ethics are transgressed and violated. Thus, eristic is viewed as a discipline of Enlightenment philosophy and a correlate of discourse ethics. Roshdi Rashed is an authority on the history of Arabic mathematical sciences. Proceeding from Gilles-Gaston Granger’s definition of mathematical style, he studies the question of whether a mathematical work can be characterized by a single style or by a multitude of styles. This question is explored within the style of a single work, namely Menelaus’s Sphaerica, and through the study of the development of a single problem over time, namely the isoperimetric problem. He indicates Menelaus’s divergence from the Euclidean style of (plane and stereometric) geometry caused by the drop of the Parallel Postulate, which associated it with hyperbolic geometry. Hence, the author concludes that Menelaus’s Sphaerica incorporates the well-known Euclidean style with a variation of the non-Euclidean one. On the other hand, examining the isoperimetric problem reveals another interesting historical picture. A succession of different styles (cosmological, geometric, infinitesimalistic, style of the calculus of variations, of synthetic geometry) can be observed due to the transformation of the research object over time. Boris Shalyutin, a Russian social philosopher, and Ombudsman for Human Rights in the Kurgan Region, explores the origins of discourse in combination with the birth of society and law. He claims that legal discourse marks the historical emergence of discourse in general. Homo Juridicus generated Homo Sapiens, which have created new spheres of discourse, notably moral discourse and further philosophical, political, and scientific discourse. Petros Stefaneas, a logician, computer scientist and novelist, suggests an alternative to the traditional narratology approach for studying (interactive) social media discourse. He claims that style describes how the parts of a narrative are blended into a whole. The author relies upon Goguen’s and Harrel’s concept of style as a choice of blending principles and transfers to the study of the social media narratives elements from the methodology of studying Web-based collaborative search for mathematical proofs like those implemented within the Polymath project. The last paper belongs to Ghil‘ad Zuckermann, a linguist, language revivalist, and proponent of a model of the emergence of Israeli Hebrew, according to which Hebrew and Yiddish were the primary sources of Modern Hebrew. This paper explores the fascinating and multifaceted Yiddish language and its survival in Israeli. Yiddish is characterized by a unique style that embeds psycho-ostensive expressions throughout its discourse. The author highlights the cross-fertilization between Hebrew and Yiddish as it manifests itself in any aspect of the Israeli language. He claims that Yiddish survives beneath Israeli phonetics, phonology, discourse, syntax, semantics, lexis, and even morphology, although traditional and institutional linguists have been most reluctant to admit it. (shrink)

Proof requires a dialogue between agents to clarify obscure inference steps, fill gaps, or reveal implicit assumptions in a purported proof. Hence, argumentation is an integral component of the discovery process for mathematical proofs. This work presents how argumentation theories can be applied to describe specific informal features in the development of proof-events. The concept of proof-event was coined by Goguen who described mathematical proof as a public social event that takes place in space and time. This new meta-methodological concept (...) is designed to cover not only “traditional” formal proofs but all kinds of proofs and inference steps, including incomplete or purported proofs. Our approach attempts to make proof-events more comprehensive to express the complete trajectory of a mathematical proof-event until the ultimate validation of the proving outcome. Thus, we advance an extended version of proof-event calculus which is built on argumentation theories designed to capture the internal and external structure of collaborative mathematical practice and highlight the relationship between proof, human reasoning, and cognitive processes. In addition, another area in which argumentation can make a significant contribution is dealing with the defeasible knowledge of the Web which is a product of its open and ubiquitous nature. This approach seems to be sufficient for the presentation of Web-based proving processes as manifested in the case of the Mini-Polymath 4 project. (shrink)

The theory of the square of opposition has been studied for over 2,000 years and has seen a resurgence in new theories and research since the second half of the twentieth century. This volume collects papers presented at the Sixth World Congress on the Square of Opposition, held in Crete in 2018, developing an interdisciplinary exploration of the theory. Chapter authors explore subjects such as Aristotle’s ontological square, logical oppositions in Avicenna’s hypothetical logic, and the power of the square of (...) opposition to solve theological problems regarding predestination and theodicy. Other topics covered include: Hegel’s opposition to diagrams De Morgan’s unpublished octagon of opposition turnstile figures of opposition institutional model-theoretic treatment of oppositions Lacan’s four formulas of sexuation the theory of oppositional poly-simplexes The Exoteric Square of Opposition will appeal to pure logicians, historians of logic, semioticians, philosophers, theologians, mathematicians, and psychoanalysts. (shrink)

The gradual crowding out of singleton and small team science by large team endeavors is challenging key features of research culture. It is therefore important for the future of scientific practice to reflect upon the individual scientist’s ethical responsibilities within teams. To facilitate this reflection we show labor force trends in the US revealing a skewed growth in academic ranks and increased levels of competition for promotion within the system; we analyze teaming trends across disciplines and national borders demonstrating why (...) it is becoming difficult to distribute credit and to avoid conflicts of interest; and we use more than a century of Nobel prize data to show how science is outgrowing its old institutions of singleton awards. Of particular concern within the large team environment is the weakening of the mentor–mentee relation, which undermines the cultivation of virtue ethics across scientific generations. These trends and emerging organizational complexities call for a universal set of behavioral norms that transcend team heterogeneity and hierarchy. To this end, our expository analysis provides a survey of ethical issues in team settings to inform science ethics education and science policy. (shrink)

Deep brain stimulation of the subthalamic nucleus or the globus pallidus is an established treatment for Parkinson’s disease that yields a marked and lasting improvement of motor symptoms. Yet, DBS benefit on gait disturbances in PD is still debated and can be a source of dissatisfaction and poor quality of life. Gait disturbances in PD encompass a variety of clinical manifestations and rely on different pathophysiological bases. While gait disturbances arising years after DBS surgery can be related to disease progression, (...) early impairment of gait may be secondary to treatable causes and benefits from DBS reprogramming. In this review, we tackle the issue of gait disturbances in PD patients with DBS by discussing their neurophysiological basis, providing a detailed clinical characterization, and proposing a pragmatic programming approach to support their management. (shrink)

This paper counters an objection raised against one of Bertrand Russell’s lesser-known epistemological views, viz. ‘‘structural realism’’ (SR). In short, SR holds that at most we have knowledge of the structure of the external (i.e., physical) world. M. H. A. Newman’s allegedly fatal objection is that SR is either trivial or false. I argue that the accusation of triviality is itself empty since it fails to establish that SR knowledge claims are uninformative. Moreover, appealing to Quine’s notion of ontological relativity, (...) I suggest that far from being false, SR knowledge claims seem to be the most that we can hope for. (shrink)

Der einzige aus Byzanz erhaltene (fast) vollständig illustrierte Historikertext ist nun endlich durch eine Facsimile-Ausgabe in Originalgröße der Forschung zugänglich, während das Original leider für immer dem Tresor anvertraut wurde. So war es dem Rezensenten auch nicht möglich, die farbliche Qualität der Ausgabe mit dem Original zu vergleichen. Auf diese Weise stehen nun auch alle Textteile und die verschiedenen Randscholien (die in der Ausgabe von Thurn nicht vermerkt sind) der paläographischen und kodikologischen Forschung zur Verfügung. Ein Rückgriff auf die Illustrationen (...) bei S. Cirac Estopañan (Barcelona-Madrid 1965) und A. Grabar – M. Manoussacas (L'Illustration du manuscrit de Skylitzès de la Bibliothèque Nationale de Madrid, Venedig 1979) und die in der Literatur fast gänzlich vergessene Teilausgabe von A. Božkov (Miniatjuri ot Madridskija rŭkopis na Ioan Skylica, Sofia 1972) sind nicht mehr nötig, sofern die mehr als 400 € teure Ausgabe erreichbar ist. (shrink)

Is God's foreknowledge compatible with human freedom? One of the most attractive attempts to reconcile the two is the Ockhamistic view, which subscribes not only to human freedom and divine omniscience, but retains our most fundamental intuitions concerning God and time: that the past is immutable, that God exists and acts in time, and that there is no backward causation. In order to achieve all that, Ockhamists distinguish ‘hard facts’ about the past which cannot possibly be altered from ‘soft facts’ (...) about the past which are alterable, and argue that God's prior beliefs about human actions are soft facts about the past. (shrink)

This article looks at some of the salient analyses of moderation in the ancient Greek and the Islamic traditions and uses them to develop a contemporary view of the matter. Greek ethics played a huge role in shaping the ethical views of the Muslim philosophers and theologians, and thus the article starts with an overview of the revival of contemporary western virtue ethics--in many ways an extension of Platonic-Aristotelian ethics--and then looks at the place of moderation or temperance in Platonic-Aristotelian (...) ethics. This sets the stage for an exposition of the position taken by Ibn Miskawayh and al-Ghazali, which is then used as a backdrop for suggesting a revival of the Quran's virtue ethics. After outlining a basis for its virtue ethics, the Quranic view of wasatiyya or moderation is discussed briefly. (shrink)

In “Imposing Risks,” Judith Thomson gives a case in which, by turning on her stove, she accidentally causes her neighbor’s death. She claims that both the following are true: (1) she ought not to have caused her neighbor’s death; (2) it was permissible for her to turn her stove on. In this paper it is argued that it cannot be that both (1) and (2) are true, that (2) is true, and that therefore (1) is false. How this is so (...) is explained, and the implications of this position regarding the relation between rights and duties is explored. (shrink)

Plato's Timaeus contains a powerful and influential myth, of the construction of the universe by a divine craftsman. A god imposes reason on necessity, to bring order from a primeval 'receptacle' of disordered matter. There results the 'child' that is the cosmos - a copy of an eternally-existing perfect model. Here eight new essays from a distinguished international cast, explore aspects of this challenging work: the principles of the mythical narrative, how the world soul and human body are formed, implications (...) for illness - mental and physical, the importance of music and harmonious proportion. Later developments are also treated: Aristotle's theory of generation, the commentary of Proclus and elements of modern evolutionary theory. (shrink)

This is the first of two companion articles drawn from a larger project, provisionally entitled Undisciplining Moral Epistemology. The overall goal is to understand how moral claims may be rationally justified in a world characterized by cultural diversity and social inequality. To show why a new approach to moral justification is needed, it is argued that several currently influential philosophical accounts of moral justification lend themselves to rationalizing the moral claims of those with more social power. The present article explains (...) how discourse ethics is flawed just in this way. The article begins by identifying several conditions of adequacy for assessing reasoning practices designed to achieve moral justification and shows that, when used in contexts of cultural diversity and social inequality, discourse ethics fails these conditions. It goes on to argue that the failure of discourse ethics is rooted in its reliance on a broader conception of moral epistemology that is invidiously idealized. It concludes by pointing to the need to rethink both the mission and the method of moral epistemology. (shrink)

According to the standard analysis of degree questions, the logical form of a degree question contains a variable that ranges over individual degrees and is bound by the degree question operator how. In contrast with this, we claim that the variable bound by the degree question operator how does not range over individual degrees but over intervals of degrees, by analogy with Schwarzschild and Wilkinson's proposal regarding the semantics of comparative clauses. Not only does the interval-based semantics predict the existence (...) of certain readings that are not predicted under the standard view, it is also able, together with other natural assumptions, to account for the sensitivity of degree questions to negative islands, as well as for the fact, uncovered by Fox and Hackl, that negative islands can be obviated by some properly placed modals. Like Fox and Hackl, we characterize negative island effects as arising from the fact that the relevant question, due to its meaning alone, can never have a maximally informative answer. Contrary to Fox and Hackl, however, we do not need to assume that scales are universally dense, nor that the notion of maximal informativity responsible for negative islands is blind to contextual parameters. (shrink)

Scott Soames argues that interpreted in the light of Quine's holistic verificationism, Quine's thesis of underdetermination leads to a contradiction. It is contended here that if we pay proper attention to the evolution of Quine's thinking on the subject, particularly his criterion of theory individuation, Quine's thesis of underdetermination escapes Soames' charge of paradoxicality.

This article is focused on some conditions in today’s world of globalized media, which are producing either an uncritical acquiescence or fright in Muslim societies as a result of the interaction between these societies and the contemporary Western powers that represent modernity and postmodernity on the global stage. The rise of fundamentalism, a tendency toward returning to the roots and stringently insisting upon some pure and literal interpretation of them, in almost all the religions of the world is a manifestation (...) of this fright. The central concern of this article is to suggest that fundamentalism is neither the only nor the most reasonable response for Muslim societies in the face of contemporary modernity. Muslims need to adopt an independent and critical attitude toward modernity and reshape their societies in the light of the ethics of the Qur’an, keeping in view the historical link between Islam and science in as much as Islamic culture paved the way for emergence of modern science during European Renaissance. The necessity of a pluralistic or contextualized modernization of Muslim societies is discussed along with the need for the removal of cultural duplicity in the role of the West in relation to Muslim societies. All this leads to an overall proposal for modernization which is given towards the end. (shrink)

In the General Psychopathology Jaspers famously draws a distinction between the understandable and explainable. Meaningful connections between psychic events, he argues, can only be understood empathetically and cannot be explained causally. The idea behind this distinction, according to some interpreters at least, seems to be that psychic events do not fall under any general causal rules whereas ordinary events do fall under such rules. Also Jaspers distinguishes empathetic understanding of the connection between two psychic events from a mere interpretation of (...) it, which may turn out to be false. Hence, understanding seems to be able to give us the truth about the connection and is factive as well as self-evident in nature. Contemporary epistemologists, such as Linda Zagzebsky, Duncan Pritchard, and Jonathan Kvanvig, for example, distinguish three varieties: propositional, objectual or holistic, and atomistic understanding. They do not agree on factivity and transparency of understanding. What then is the difference between their views and that of Jaspers? This essay compares recent epistemological views of understanding with those of Jaspers and critiques his claims about empathetic understanding as being both factive and self-evident or transparent; to show that empathetic understanding of connections between psychic events needs a public criterion for its individuation. (shrink)

Considerable methodological difficulties abound in neuroimaging, and several philosophers of science have recently called into question the potential of neuroimaging studies to contribute to our knowledge of human cognition. These skeptical accounts suggest that functional hypotheses are underdetermined by neuroimaging data. I apply Mayo’s error-statistical account to clarify the evidential import of neuroimaging data and the kinds of inferences it can reliably support. Thus, we can answer the question “What can we reliably learn from neuroimaging?” and make sense of how (...) this knowledge can contribute to novel construals of cognition. (shrink)

The use of platelet rich plasma as a novel treatment is discussed in the context of a qualitative research study comprising 38 interviews with sports medicine practitioners and other stakeholders working within the English Premier League during the 2013–16 seasons. Analysis of the data produced several overarching themes: conservatism versus experimentalism in medical attitudes; therapy perspectives divergence; conflicting versions of appropriate evidence; subcultures; community beliefs/practices; and negotiation of medical decision-making. The contested evidence base for the efficacy of PRP is presented (...) in the context of a broader professional shift towards evidence based medicine within sports medicine. Many of the participants while accepting this shift are still committed to casuistic practices where clinical judgment is flexible and does not recognize a context-free hierarchy of evidentiary standards to ethically justifiable practice. We also discuss a tendency in the data collected to consider the use of deceptive, placebo-like, practices among the clinician participants that challenge dominant understandings of informed consent in medical ethics. We conclude that the complex relation between evidence and ethics requires greater critical scrutiny for this emerging specialism within the medical community. (shrink)