A case study of multimodal systems and a new interpretation of Charles S. Peirce's theory of reasoning and signs based on an analysis of his system of ...

Logic, the discipline that explores valid reasoning, does not need to be limited to a specific form of representation but should include any form as long as it allows us to draw sound conclusions from given information. The use of diagrams has a long but unequal history in logic: The golden age of diagrammatic logic of the 19th century thanks to Euler and Venn diagrams was followed by the early 20th century's symbolization of modern logic by Frege and Russell. Recently, (...) we have been witnessing a revival of interest in diagrams from various disciplines - mathematics, logic, philosophy, cognitive science, and computer science. This book aims to provide a space for this newly debated topic - the logical status of diagrams - in order to advance the goal of universal logic by exploring common and/or unique features of visual reasoning. (shrink)

Parallelism has been drawn between modes of representation and problem-sloving processes: Diagrams are more useful for brainstorming while symbolic representation is more welcomed in a formal proof. The paper gets to the root of this clear-cut dualistic picture and argues that the strength of diagrammatic reasoning in the brainstorming process does not have to be abandoned at the stage of proof, but instead should be appreciated and could be preserved in mathematical proofs.

The evolution of Euler diagrams is examined from Euler's original system through the modifications made by Venn and Peirce. It is shown that these modifications were motivated by an attempt to increase the expressivity of the diagrams, but that a side effect of these modifications was a loss of the visual clarity of Euler's original system. Euler's original system is reconstructed from a modern, logical point of view. Formal semantics and rules of inference are provided for this reconstruction of Euler's (...) system, and basic logical properties are proved. (shrink)

Research-oriented universities are known for prolific research activity that is often supported by students in faculty-guided research. To maintain ethical standards, universities require on-going training of both faculty and students to ensure Responsible Conduct of Research (RCR). However, previous research has indicated RCR-based training is insufficient to address the ethical dilemmas that are prevalent within academic settings: navigating issues of authorship, modeling relationships between faculty and students, minimization of risk, and adequate informed consent. U.S. universities must explore ways to identify (...) and improve RCR concerns for current (faculty) and future researchers (students). This article reports the findings of a self-study (_N_ = 50) of research stakeholders (students and faculty) at a top tier research institution. First, we report on their perceived importance of applying RCR principles. Second, we explore relationships between stakeholder backgrounds (e.g., prior training, field, and position) and how they ranked the degree of ethical concerns in fictitious vignettes that presented different unethical issues university students could encounter when conducting research. Vignette rankings suggested concerns of inappropriate relationships, predatory authorship and IRB violations which were judged as most unethical, which was dissimilar to what sampled researchers reported in practice as the most important RCR elements to understand and adhere to for successful research. Regression models indicated there was no significant relationship between individuals’ vignette ethics scores and backgrounds, affirming previous literature suggesting that training can be ineffectual in shifting researcher judgments of ethical dilemmas. Recommendations for training are discussed. (shrink)

Let me start by saying that I had the privilege of witnessing the birth of Jon Barwise's new research on heterogeneous logic and its subsequent developments. I entered the Stanford philosophy graduate program in the Fall of 1987, became Barwise and Etchemendy's first research assistant on the project of diagrammatic/heterogeneous reasoning during summer of 1989, and under their guidance completed my thesis, “Valid reasoning and visual representation,” in August, 1991. With this experience I would like to focus on the more (...) personal and informal aspects of Jon's research on heterogeneous logic which may not be conveyed by his articles. (Accordingly, I have written this paper without footnotes or other references except to Jon's work.) The present article can only hint at the depth and the influence of Jon's work in this area.In the first section, I single out an important feature of the project on heterogeneous logic Jon founded together with John Etchemendy about 15 years ago. I title it “resolving conflicts” since the research, I strongly believe, grew out of Jon's personal attitude toward how to resolve a tension between opposite extremes.The second section focuses on how teaching logic itself was shaped as part of Barwise and Etchemendy's research agenda. It is worthwhile noting that their textbookLanguage, Proof, and Logicconstitutes part of their research and, hence, the success of the book vindicates the goal of the overall project. (shrink)

This paper reconstructs the Peircean interpretation of Kant's doctrine on the syntheticity of mathematics. Peirce correctly locates Kant's distinction in two different sources: Kant's lack of access to polyadic logic and, more interestingly, Kant's insight into the role of ingenious experiments required in theorem-proving. In this second respect, Kant's analytic/synthetic distinction is identical with the distinction Peirce discovered among types of mathematical reasoning. I contrast this Peircean theory with two other prominent views on Kant's syntheticity, i.e. the Russellian and the (...) Beckian views, and show how Peirce's interpretation of Kant solves the dilemma that each of these two views faces. I also show that Hintikka's criterion for Kant's synthetic judgments, i.e. a new individual introduced by the -instantiation rule, does not capture the most important characteristic of Peirce's theorematic reasoning, i.e. the process of choosing a correct individual. (shrink)

In contrast to Clarke and Beck's claim that that the approximate number system represents rational numbers, we argue for a more modest alternative: The ANS represents natural numbers, and there are separate, non-numeric processes that can be used to represent ratios across a wide range of domains, including natural numbers.

Deduction is decisive but nonetheless mysterious, as I argue in the introduction. I identify the mystery of deduction as surprise-effect and demonstration-difficulty. The first section delves into how the mystery of deduction is connected with the representation of information and lays the groundwork for our further discussions of various kinds of representation. The second and third sections, respectively, present a case study for the comparison between symbolic and diagrammatic representation systems in terms of how two aspects of the mystery of (...) deduction – surprise-effect and demonstration-difficulty – are handled. The fourth section illustrates several well-known examples to show how diagrammatic representation suggests more clues to the mystery of deduction than symbolic representation and suggests some conjectures and further work. (shrink)

Many do not doubt that Peirce's Existential Graphs are diagrammatic, as opposed to symbolic. However, when we are pressured to draw a distinction between the two different forms of representation, we find ourselves at a loss and our intuition quite vague. In this paper, I locate fundamental differences between two logically equivalent systems, Peirce's Alpha system and propositional languages. Suppose we have only two sentential connectives, ¬ and ^. In spite of its truth-functional completeness, we don't want to use this (...) language for the translation of English sentences or as a deductive calculus. We would adopt this language only when we intend to develop logical theories. That is, it is convenient to have fewer connectives for a meta-theory, but not for practical use. So, there seems to be a trade-off between a language with fewer connectives and a language with more connectives. This view has been accepted without question. In this paper, I will argue that this trade-off is limited to linear symbolic systems and that we could have a diagrammatic system with fewer operations but no need to suffer from problems like those of a sentential language with fewer connectives. How is that possible? A comparison between Peirce's Alpha system and a propositional language is presented to answer this question. The case study identifies the following unique property of a non-linear diagrammatic system as a main source of the discrepancy between two different types of representation: One and the same diagram can be read off in more than one way by carving it up in many ways, but without ambiguity. (shrink)

Logicians have strongly preferred first-order natural deductive systems over Peirce's Beta Graphs even though both are equivalent to each other. One of the main reasons for this preference, I claim, is that inference rules for Beta Graphs are hard to understand, and, therefore, hard to apply for deductions. This paper reformulates the Beta rules to show more fine-grained symmetries built around visual features of the Beta system, which makes the rules more natural and easier to use and understand. Noting that (...) the rules of a natural deductive system are natural in a different sense, this case study shows that the naturalness and the intuitiveness of rules depends on the type of representation system to which they belong. In a diagrammatic system, when visual features are discovered and fully used, we have a more efficacious deductive system. I will also show that this project not only helps us to apply these rules more easily but to understand the validity of the system at a more intuitive level. (shrink)

In this paper, I aim to identify Peirce?s great contribution to logical diagrams and its limit.Peirce is the first person who believed that the same logical status can be given to diagrams as to symbolic systems.Even though this belief led him to invent his own graphical system, Existential Graphs, the success or failure of this system does not determine the value of Peirce?s general insights about logical diagrams.In order to make this point clear, I will show that Peirce?s revolutionary ideas (...) about diagrams not only overcame some important defects of Venn diagrams but opened a new horizon for logical diagrams.Finally, I will point out where Peirce?s new horizon for logical diagrams stopped and will claim that this limit is mainly responsible for the discrepancy between Peirce?s and others? estimates of his contribution to logical diagrams. (shrink)

In this reflection, I respond to Anthony Reddie's reflections and assertions about the sacramentality of black flesh in a world shaped by white supremacy. I locate myself as Korean American and refer to my experience of ministering to university students during the rise of Black Lives Matter in the US. Instead of offering cognate claims for the sacramentality of Asian flesh, I ask what theological repentance should look like in light of the historical profaning of the black body. Using the (...) work of two black American artists, jazz musician Robert Glasper and painter Titus Kaphar, I offer beginning reflections on how our liturgies and practices need to change as part of theological repentance—including lament. (shrink)

This thesis challenges a general prejudice against visualization in the history of logic and mathematics, by providing a semantic analysis of two graphical representation systems--a traditional Venn diagram representation system and an extension of it. While Venn diagrams have been used to solve problems in set theory and to test the validity of syllogisms in logic, they have not been considered valid proofs but heuristic tools for finding valid formal proofs. ;I present Venn diagrams which have been used in logic (...) as a formal system of representation equipped with its own syntax and semantics. I also show that Venn-I, with the rules of transformation that I specify, is sound and complete. The soundness of Venn-I refutes a worry that mathematicians and logicians have about graphical representation: Fallacies often have arisen from the misuse of diagrams in mathematical proofs, especially in geometry. However, the validity of the transformation rules assures us that the correct application of these rules will not lead to fallacies. ;I extend Venn-I so that this new system has a general way to convey disjunctive information. A new formation rule is introduced and new transformation rules are added. I call this extended system Venn-II. The semantics of Venn-II is formalized as an extension of the semantics of Venn-I. The soundness and completeness of Venn-II are also proven. I then show that Venn-II and a monadic first-order language are equivalent in their expressiveness. ;The analysis of Venn-I and Venn-II leads to interesting issues which have their analogues in other deductive systems. I conclude the thesis with a discussion of some fundamental differences between graphical systems and linguistic systems. (shrink)

In lieu of an abstract, here is a brief excerpt of the content:Global Health Careers:Serving the Navajo CommunityMaricruz Merino, Jonathan Iralu, and Sonya ShinGallup Indian Medical Center (GIMC) sits on a hilltop in Gallup, New Mexico, a town of 20,000 in the four corners region of the Southwestern United States. From its third story windows one can see the red cliffs of the nearby Navajo Nation, a 27,000 square mile reservation that reaches into Arizona, northern New Mexico, and the southern (...) edges of Utah. It is a vast, rural landscape that houses more than 350,000 Navajos. For many on the reservation, healthcare is provided by Indian Health Service hospitals such as GIMC."Are you going to stay?" is a common question for new doctors at GIMC. The Navajo know that their geographic location, while beautiful and attractive to many young providers, will also be the reason they leave. It is hard for doctors to be away from their own homelands. Aging parents get sick, [End Page 86] educational opportunities arise, and children who need to be near extended family are born. But to the Navajo, the story of an individual provider is not so important or memorable. All they know is that providers come and go."Are you here to experiment on us?" is yet another question. Years of exploitation and efforts to destroy traditional ways and language have made many Navajo wary of healthcare providers, no matter how genuine their intentions. Many are so fearful of the hospital—they regard it as "the place to go die."Yet despite this initial suspicion, the Navajo are welcoming people at heart, and tend to develop relationships of trust with their providers. Parents will begin to talk about their grief over a son that has committed suicide or a daughter who died from alcoholic cirrhosis. The elderly will tell you how they care for their five orphaned grandchildren while they can barely take care of their own diabetes. A carpenter tells you he has not worked in a year and feels worthless. An HIV-positive woman will tell you she has been sleeping in a dry river bed because she has no place to go. It quickly becomes apparent that as a physician you will be treating patients with enormous social challenges in addition to complex medical conditions.The origins of the Federal Government's involvement in the healthcare of American Indians and Alaskan Natives (AI/ANs) in the 19th century arose out of both legal obligation and concern for self- preservation. Health services were promised to AI/ ANs in exchange for land, settlements, and agreements. In addition, infectious diseases endemic on reservations as a consequence of crowding and abject poverty, including smallpox and tuberculosis, were seen as a major public health concern. The responsibility of Native American health was first granted to the War Department, then to the Bureau of Indian Affairs, and finally to the Public Health Service in 1955 under the heading of the IHS, or Indian Health Service (U.S. Commission on Civil Rights, 2004; National Library of Medicine, 1994).Since then, the IHS has had many successes. Vaccination rates have gone up, and rates of pneumonia and tuberculosis have gone down significantly. Maternal and infant mortality have declined, and life expectancy has increased (Indian Health Services, 1999). Nonetheless, these improvements remain overshadowed by glaring health disparities among AI/ANs across a broad spectrum of diseases, both communicable and non-communicable, acute and chronic. Native Americans experience higher rates of obesity, diabetes, and cardiovascular disease than the general United States population. They are also more likely to die from alcohol-related causes and in accidents. Life expectancy remains more than five years less than that of the general U.S. population (U.S. Commission on Civil Rights, 2004; U.S. Department of Health and Human Services, 2000).Underlying these health indicators is the continued impoverished status of most AI/ANs. In Navajo, almost half of the population lives below the poverty line. According to the Navajo Nation, the current unemployment rate is 42% (Navajo Nation Department of Economic Development, 2011). Many Navajo on the reservation do not have running water or electricity. They heat with wood, which they chop and haul themselves—regardless... (shrink)

This research explores the relationships between business students’ academic misconduct and their attitudes toward professional ethics, specifically credential embellishment and business unethicality. Based on 135 survey responses from business students in a northwestern university, we tested hypothesized relationships using multiple regression analyses. We found that students’ attitudes toward academic misconduct, especially illicit collaboration and exam cheating, were positively correlated with their attitudes toward credential embellishment, unethical business operations, and unethical employee practices. In addition, gender yielded meaningful differences related to perceptions (...) of both dimensions of business unethicality. We emphasize the importance of ethics education, and suggest actionable remedies including placement of strict policies, promotions of shared norms and cultures, and curriculum redesign guidelines for business educators and administrators. (shrink)

In the mid-nineteenth century, Karl Marx issued several critiques of political economy writings stressing the exclusive duality of states and the national economies. He argued that capitalism had characteristic features quite apart from those shaped by the idiosyncrasies of national economies. In the first part of this article, we critique the contemporary state-centered explanations for the industrialization of East Asia on same grounds. We claim that most political economists misinterpret or entirely ignore the significance of export-led industrialization, which is a (...) characteristic feature of East Asian capitalism. In the second part of the article, we demonstrate the importance of the retail revolution in the US and Europe on Asian industrialization. In particular, we show that the development of the sequential ordering system that is an inherent feature of Western-based contract manufacturing differentially shaped the industrial organization of East Asian economies. The resulting path-dependent trajectories of development, in turn, encouraged government policy-makers to ‘buy into’ trends of global capitalism in different ways. The trajectories also led business people to privilege and adapt some social institutions and cultural patterns over other ones. (shrink)

This paper expands the current business ethics research area by empirically testing the relationships between students’ misconduct including academic dishonesty (i.e., plagiarism/fabrication and/or exam cheating) and undesirable academic behaviors (i.e., disrespectful behaviors and/or slacker behaviors) and their perception of business ethics. Based on 133 surveys from the students in a northwestern regional comprehensive university business program, this study reveals that students who have reported higher frequencies of engaging in exam cheating, disrespectful behavior, or slacker behavior have perceived the given questionable, (...) unethical employee practices as more acceptable conducts than the students who have reported lower frequencies. Students who have more frequently engaged in plagiarism/fabrication are found to be more accepting of both questionable, unethical business operations and employee practices. Gender, age, and cumulative GPA have been additionally explored and found to have correlations with business ethics perception. For ethically-sensitive future practitioners, this paper calls for institutions of higher education (IHEs) to provide clear guidelines on academic conduct/misconduct along with business ethics education in curriculum. (shrink)

Cerebellar Purkinje cells generate two distinct types of spikes, complex and simple spikes, both of which have conventionally been considered to be highly irregular, suggestive of certain types of stochastic processes as underlying mechanisms. Interestingly, however, the interspike interval structures of complex spikes have not been carefully studied so far. We showed in a previous study that simple spike trains are actually composed of regular patterns and single interspike intervals, a mixture that could not be explained by a simple rate-modulated (...) Poisson process. In the present study, we systematically investigated the interspike interval structures of separated complex and simple spike trains recorded in anaesthetized rats, and derived an appropriate stochastic model. We found that: (i) complex spike trains do not exhibit any serial correlations, so they can effectively be generated by a renewal process, (ii) the distribution of intervals between complex spikes exhibits two narrow bands, possibly caused by two oscillatory bands (0.5–1 and 4–8 Hz) in the input to Purkinje cells and (iii) the regularity of regular patterns and single interspike intervals in simple spike trains can be represented by gamma processes of orders, which themselves are drawn from gamma distributions, suggesting that multiple sources modulate the regularity of simple spike trains. (shrink)

Though their biographies vastly differ, Karl Barth's long-term extra-marital relationship with Charlotte von Kirschbaum and John H. Yoder's sexual crimes have been the focus of a range of reactions and proposed approaches on how to read the theology of the two theologians given their biographies. This article will examine those critical responses using an analytical framework appropriated from Sameer Yadav's work on cognate conversations about locating and remedying the causes of white supremacy in the church: are the problems due to (...) problematic theology, problematic institutional practice, or both? A correct diagnosis helps the theologian to then propose the right remedy. This adapted framework will be applied to the cases of Barth and Yoder to critically examine how Steven Plant and Rachel Muers respond to Barth's biography and how Stanley Hauerwas and Hilary Scarsella respond to Yoder's biography. After demonstrating how the different respondents address the issue as one primarily of problematic theology or problematic institutional practices, I will argue that it is both theology and practice that must be addressed in order to satisfactorily deal with the reality and scale of infection when it comes to influential theologians. Sample treatments will be offered for responding to Barth's and Yoder's biographies. (shrink)

Background: An association between gaming disorder and the symptoms of common mental disorders is unraveled yet. In this preregistered study, we quantitatively synthesized reliability, convergent and discriminant validity of GD scales to examine association between GD and other constructs.Methods: Five representative GD instruments were chosen based on recommendations by the previous systematic review study to conduct correlation meta-analyses and reliability generalization. A systematic literature search was conducted through Pubmed, Proquest, Embase, and Google Scholar to identify studies that reported information on (...) either reliability or correlation with related variables. 2,124 studies were full-text assessed as of October 2020, and 184 were quantitatively synthesized. Conventional Hedges two-level meta-analytic method was utilized.Results: The result of reliability generalization reported a mean coefficient alpha of 0.86 and a mean test-retest estimate of 0.86. Estimated effect sizes of correlation between GD and the variables were as follows: 0.33 with depression, 0.29 with anxiety, 0.30 with aggression, –0.22 with quality of life, 0.29 with loneliness, 0.56 with internet addiction, and 0.40 with game playtime, respectively. The result of moderator analyses, funnel and forest plots, and publication bias analyses were also presented.Discussion and Conclusion: All five GD instruments have good internal consistency and test-retest reliability. Relatively few studies reported the test-retest reliability. The result of correlation meta-analysis revealed that GD scores were only moderately associated with game playtime. Common psychological problems such as depression and anxiety were found to have a slightly smaller association with GD than the gaming behavior. GD scores were strongly correlated with internet addiction. Further studies should adopt a rigorous methodological procedure to unravel the bidirectional relationship between GD and other psychopathologies.Limitations: The current study did not include gray literature. The representativeness of the five tools included in the current study could be questioned. High heterogeneity is another limitation of the study.Systematic Review Registration: [https://www.crd.york.ac.uk/PROSPERO/], identifier [CRD42020219781]. (shrink)