We introduce Kripke models for propositional substructural logics with strong negation, and show the completeness theorems for these logics using an extended Ishihara's canonical model construction method. The framework presented can deal with a broad range of substructural logics with strong negation, including a modified version of Nelson's logic N$^-$, Wansing's logic COSPL, and extended versions of Visser's basic propositional logic, positive relevant logics, Corsi's logics and M\'endez's logics.

Dual-intuitionistic logics are logics proposed by Czermak , Goodman and Urbas . It is shown in this paper that there is a correspondence between Goodman's dual-intuitionistic logic and Nelson's constructive logic N−.

A new combined temporal logic called synchronized linear-time temporal logic (SLTL) is introduced as a Gentzen-type sequent calculus. SLTL can represent the n -Cartesian product of the set of natural numbers. The cut-elimination and completeness theorems for SLTL are proved. Moreover, a display sequent calculus δ SLTL is defined.

N. Kamide introduced a pair of classical and constructive logics, each with a peculiar type of negation: its double negation behaves as classical and intuitionistic negation, respectively. A consequence of this is that the systems prove contradictions but are non-trivial. The present paper aims at giving insights into this phenomenon by investigating subsystems of Kamide’s logics, with a focus on a system in which the double negation behaves as the negation of minimal logic. We establish the negation inconsistency (...) of the system and embeddability of contradictions from other systems. In addition, we attempt at an informational interpretation of the negation using the dimathematical framework of H. Wansing. (shrink)

The definitions of disease proffered by philosophers and medical actors typically require that a state of ill health be linked to some known bodily dysfunction before it is classified as a disease. I argue that such definitions of disease are not fully implementable in current medical discourse and practice. Adhering to the definitions would require that medical actors keep close track of the current state of knowledge on the causes and mechanisms of particular illnesses. Yet, unaddressed problems in medical terminology (...) can make this difficult to do. I show that unrecognized misuse of “heterogeneous,” “biomarker,” and other important health terms—which I call index terms—can misrepresent the current empirical evidence on illness pathophysiology, such that unvalidated illness constructs become mistaken for diseases. Thus, implementing common definitions of disease would require closing this “loophole” in medical discourse. I offer a simple rule that, if followed, could help do just that. (shrink)

The ongoing debate within neuroethics concerning the degree to which neuromodulation such as deep brain stimulation (DBS) changes the personality, identity, and agency (PIA) of patients has paid relatively little attention to the perspectives of prospective patients. Even less attention has been given to pediatric populations. To understand patients’ views about identity changes due to DBS in obsessive-compulsive disorder (OCD), the authors conducted and analyzed semistructured interviews with adolescent patients with OCD and their parents/caregivers. Patients were asked about projected impacts (...) to PIA generally due to DBS. All patient respondents and half of caregivers reported that DBS would impact patient self-identity in significant ways. For example, many patients expressed how DBS could positively impact identity by allowing them to explore their identities free from OCD. Others voiced concerns that DBS-related resolution of OCD might negatively impact patient agency and authenticity. Half of patients expressed that DBS may positively facilitate social access through relieving symptoms, while half indicated that DBS could increase social stigma. These views give insights into how to approach decision-making and informed consent if DBS for OCD becomes available for adolescents. They also offer insights into adolescent experiences of disability identity and “normalcy” in the context of OCD. (shrink)

Noise in behavior is often viewed as a nuisance: while the mind aims to take the best possible action, it is let down by unreliability in the sensory and response systems. How researchers study cognition reflects this viewpoint – averaging over trials and participants to discover the deterministic relationships between experimental manipulations and their behavioral consequences, with noise represented as additive, often Gaussian, and independent. Yet a careful look at behavioral noise reveals rich structure that defies easy explanation. First, both (...) perceptual and preferential judgments show that sensory and response noise may potentially only play minor roles, with most noise arising in the cognitive computations. Second, the functional form of the noise is both non-Gaussian and non-independent, with the distribution of noise being better characterized as heavy-tailed and as having substantial long-range autocorrelations. It is possible that this structure results from brains that are, for some reason, bedeviled by a fundamental design flaw, albeit one with intriguingly distinctive characteristics. Alternatively, noise might not be a bug but a feature: indeed, we suggest that noise is fundamental to how cognition works. Specifically, we propose that the brain approximates probabilistic inference with a local sampling algorithm, one that uses randomness to drive its exploration of alternative hypotheses. Reframing cognition in this way explains the rich structure of noise and leads to a surprising conclusion: that noise is not a symptom of cognitive malfunction but plays a central role in underpinning human intelligence. (shrink)

The introduction of normothermic regional perfusion (NRP) in controlled donation after circulatory determination of death (cDCDD) protocols is by some regarded as controversial and ethically troublesome. One of the main concerns that opponents have about introducing NRP in cDCDD protocols is that reestablishing circulation will negate the determination of death by circulatory criteria, potentially resuscitating the donor. In this article, I argue that this is not the case. If we take a closer look at the concept of death underlying the (...) circulatory criterion for determination of death, we find that the purpose of the criterion is to show whether the organism as a whole has died. I argue that this purpose is fulfilled by the circulatory criterion in cDCDD protocols, and that applying NRP does not negate the determination of death or resuscitate the donor. (shrink)

Kesselheim proposes doubling the NIH’s budget to promote clinically meaningful pharmaceutical innovation. Since the effects of a previous doubling (from 1998-2003) were mixed, I argue that policymakers should couple future budget growth with investments in experimentation and evaluation.

A series of structural constitutional arguments lodged in multiple cases against Centers for Medicare and Medicaid Services’ (CMS) authorities to negotiate prescription drug prices via the 2022 Inflation Reduction Act threaten the legitimacy of CMS program and federal agency powers.

El presente artículo presenta las grandes líneas de la hermenéutica agustiniana de Is 10,23 LXX en sermones ad populum de Agustín de Hipona. En su predicación aparece este locus exegético de la Patrística que se remonta a autores como Ireneo de Lyon y Orígenes de Alejandría. Brevemente veremos cómo aparece la mención y exégesis del texto de Isaías a lo largo de la producción agustiniana, para luego detenernos en la utilización del texto por parte de Agustín en contexto homilético. Nociones (...) de retórica clásica y elementos teológicos mostrarán la finalidad y la riqueza de la ratio interpretandi agustiniana. (shrink)

The use of sound to systematically communicate data has been with us for a long time, and has received considerable research, albeit in a broad range of distinct fields of inquiry. Sonification is uniquely capable of conveying series and patterns, trends and outliers…and effortlessly carries affect and emotion related to those data. And sound-either by itself or in conjunction with visual, tactile, or even olfactory representations-can make data exploration more compelling and more accessible to a broader range of individuals. Nevertheless, (...) sonification and auditory displays still occupy only a sliver of popular mindshare: most people have never thought about using non-speech sound in this manner, even though they are certainly very familiar with other intentional uses of sound to convey status, notifications, and warnings. This article provides a brief history of sonification, introduces terms, quickly surveys a range of examples, and discusses the past, present, and as-yet unrealized future promise of using sound to expand the way we can communicate about data, broaden the use of auditory displays in society, and make science more engaging and more accessible. (shrink)

Este artigo tem por objetivo relatar a experiência com o Projeto de educação filosófica denominado Ética e Educação para o Pensar a partir da Literatura Infantil, abordando a história da sua criação, algumas referências teóricas e metodológicas, a estrutura do projeto e o desenvolvimento através de parceria entre o Instituto Sadia, Fundação Sidónio Muralha, Instituto de Filosofia e Educação para o Pensar e seis secretarias de educação. O foco do projeto é a educação ética através da comunidade de investigação, enfatizando (...) a abordagem dialógica dos valores, procurando trabalhar na direção da autonomia moral e cognitiva das crianças. O projeto foi desenvolvido com professores e alunos da Educação Infantil e Ensino Fundamental I. No final do artigo são apresentadas algumas produções dos alunos desenvolvidas como parte do projeto e depoimentos dos professores sobre o mesmo. (shrink)

Ivancovsky et al. explore the relationship between curiosity and creativity, by suggesting they align through novelty-seeking mechanisms. We argue that a general mechanism linking both capacities together is question-asking: Curiosity drives question-asking that leads to creative problem solving. Yet, current findings from our lab suggest that question complexity relates to creativity, but not necessarily to curiosity, warranting further investigation.

Chronic pain is a common disorder with enormous sociomedical importance. A major part of primary and secondary costs of illness is caused by the various pain syndromes. Nociception – the sensory perception of a painful stimulus – is a complex process relying on an intricate system of anatomical, neurophysiological and biochemical networks. This applies even more so to pain – the state of experiencing a nociceptive event, of interpreting it in terms of meaning for the affected individual and of suffering (...) a range of emotions it elicits. This intricacy renders it obvious, that the empirical medical sciences alone cannot explain all aspects of pain. Hence, it has also become a focus of phenomenological research. One aspect of these investigations is the interaction of pain and the perception of the lived body’s spatiality. The focus of this article will build on these concepts to develop a construct of the alteration of temporality caused by chronic pain and the effects this spells out for the affected subject. To this end, I will primarily draw on Merleau-Ponty’s ideas of the lived body as well as on theories of enactivism and embodiment. I will also point out parallels to neuroscientific data, thereby demonstrating the proximity of phenomenology and neuroscience. A possible partial solution to the pain dilemma may be derived from psychology: techniques relying on cognitive behavioural intervention, awareness training, and existential analysis may provide alleviation to patients suffering from chronic pain. (shrink)

First Professor of Logic and Metaphysics at Main Pedagogical Institute and then also St. Petersburg University, Carpatho-Rusyn P. D. Lodij spent a quarter of a century teaching philosophy and law in the Russian Empire in the first third of the 19th century. His knowledge of Kant’s philosophy and his attitude to Kant’s criticism are estimated diametrically opposed in the research literature. An analysis of his main philosophical work, “Logical Precepts which Lead to Cognition and the Distinction of the True from (...) the False” (1815), convincingly proves that Lodij was an excellent scholar of Kant’s philosophy. In Russia, he was the first thinker who spoke about the differences between the first and second editions of the “Critique of Pure Reason”. Lodij also was the first who noted both the revolutionary role of Kant’s Copernican turn, and the importance of Humeʼs causality problem for the formation of critical philosophy. In Russia, Lodij was the first who proposed a detailed description of Kant’s transcendental idealism. At the same time, Lodij’s general attitude to Kant was rather skeptical. In his own logic, he does not follow Kant’s division of logic into pure and applied, but he returns to pre-Kant’s split into theoretical and practical logics. Lodij disputes with the basic conclusions about the space derived from the transcendental aesthetic, denies synthetic judgments a priori and the rooting of the cognizing reason in illusions. Despite his unequivocal claims regarding Kant’s philosophy, “Logical Precepts” and its author were persecuted during the so-called “professorsʼ affair” of the 1820s. As a result, Lodij was suspended from teaching philosophy, and his logic textbook was withdrawn from teaching for both “disgrace” and imaginary Kantianism. (shrink)

This note examines the significance of Gylippus at Aen. 12.271–83 and argues that Virgil's narrative is an epitaphic gesture alluding to Nicander of Colophon, Anth. Pal. 7.435 and other epigrams from Anth. Pal. 7. Virgil's bilingual reader would participate in the Hellenistic Ergänzungsspiel and supplement further meaning to this otherwise generic scene.

The relevance of the problem under study is due to the need to improve the practical skills and competencies of students in the course of training in order to prepare them for competition with other job seekers in employment. In this regard, this article is aimed at identifying the expediency of students’ participation in competitive selections and grants as a factor that creates conditions for effective practice-oriented learning. The leading method for the study of this problem is a pedagogical experiment, (...) which allows us to comprehensively consider the relationship between students’ participation in competitions and their further self-realization and development as young professionals. The article presents the results of monitoring the behavior of students who received an offer to participate in the university-wide competitive selection of student projects, implemented as part of the Program for Supporting Applied Research and Development of Students and Postgraduates of Petrozavodsk State University. The materials of the article can be useful for teaching staff in building a scheme for teaching students and services involved in the recruitment of personnel for large and medium-sized companies that require young professionals to have practical work skills, teamwork skills and creativity. (shrink)

Many have interpreted symbolic material culture in the deep past as evidencing the origins sophisticated, modern cognition. Scholars from across the behavioural and cognitive sciences, including linguists, psychologists, philosophers, neuroscientists, primatologists, archaeologists and paleoanthropologists have used such artefacts to assess the capacities of extinct human species, and to set benchmarks, milestones or otherwise chart the course of human cognitive evolution. To better calibrate our expectations, the present paper instead explores the material culture of three contemporary African forager groups. Results show (...) that, while these groups are unequivocally behaviourally modern, they would leave scant long-lasting evidence of symbolic behaviour. Artefact-sets are typically small, perhaps as consequence of residential mobility. When excluding traded materials, few artefacts have components with moderate-strong taphonomic signatures. Present analyses show that artefact function influences preservation probability, such that utilitarian tools for the processing of materials and the preparation of food are disproportionately likely to contain archaeologically traceable components. There are substantial differences in material-use between populations, which create important population-level variation preservation probability independent of cognitive differences. I discuss the factors — cultural, ecological and practical — that influence material choice. In so doing, I highlight the difficulties of using past material culture as an evolutionary or cognitive yardstick. (shrink)

Most people, including those in academia and the media, view Darwin's theory of evolution as a fact, a concept so thoroughly established as to be beyond serious challenge. Yet almost no one today bothers to read what Darwin wrote, nor are they aware of the pseudo-scientific racism and eugenics that arose from his theories. More than that, Darwin's motivation in writing The Origin of the Species was not entirely "scientific." After his young daughter's death, he deliberately moved away from an (...) essentially Christian worldview and aimed to find an explanation for life that did not require anything Divine. Yet, in his last months of life, Darwin's atheism failed him and he evidently returned to faith in God. (shrink)

This work has been selected by scholars as being culturally important, and is part of the knowledge base of civilization as we know it. This work was reproduced from the original artifact, and remains as true to the original work as possible. Therefore, you will see the original copyright references, library stamps (as most of these works have been housed in our most important libraries around the world), and other notations in the work. This work is in the public domain (...) in the United States of America, and possibly other nations. Within the United States, you may freely copy and distribute this work, as no entity (individual or corporate) has a copyright on the body of the work. As a reproduction of a historical artifact, this work may contain missing or blurred pages, poor pictures, errant marks, etc. Scholars believe, and we concur, that this work is important enough to be preserved, reproduced, and made generally available to the public. We appreciate your support of the preservation process, and thank you for being an important part of keeping this knowledge alive and relevant. (shrink)

단국대 학생들의 교책과목으로 집필된 책.단국대학교의 역사와 한민족의 가치관,미래부터 교육과 인간화까지 전체 15장에 엮었다.

In lieu of an abstract, here is a brief excerpt of the content:Reviewed by:WisCon 46Laurie Fuller, Jenna N. Hanchey, and E. OrnelasExistence as Resistance, WisCon 46, May 26–29, 2023, Madison, Wisconsin, United StatesIn a world that seems structured to kill most of its occupants, there is a utopian impulse in the act of existence itself. WisCon 46 represented a prefigurative utopian impulse through centering continued marginalized existence as resistance.1 Leah Lakshmi Piepzna-Samarasinha calls “prefigurative politics” the “fancy term for the idea (...) of imagining and building the world we want to see now,” particularly in terms of access needs.2 The structure as well as the content of the convention itself created a space in which to set the groundwork for utopia: the ways that we live and act to resist structures of oppression in order to prefigure a better world.Since WisCon’s founding in 1977, its intended audience has been fans, authors, and academics interested in the intersection between feminism and “science fiction, fantasy, and speculative literature of all sorts.”3 While neither feminism nor speculative fiction could be solely defined as utopian, both do explore utopian impulses that inspire change for the better. Therein lies the hope of Alessa Johns’s proposal that “the utopian imagination has been crucial for feminists.”4 Lisa Yaszek agrees: “for nearly 200 years writers have used speculative fiction consciously and collectively to dramatize the political issues most central to women living in a technocultural world and to create a sense of wonder about the interrelated possibilities of social and scientific change.”5 Envisioning a liberatory world is a feminist imperative, and speculative fiction offers a unique venue to do so. This imperative informed WisCon this year, as participants collectively worked to imagine and enact a better future for marginalized folks, in and beyond the space of the conference. [End Page 618]Enabling Existence through Con StructuresWisCon is unique in attuning its organizational structure to the creation of liberatory futures in the here and now. WisCon is strongly attentive to disability access of all kinds, COVID safety, antiracist/anti-oppression principles, and safety and anti-abuse support for all these areas. In the contemporary US context—where COVID-19 remains a major barrier to disabled people wishing to participate in conventions, where racist violence continues to threaten BIPOC (Black, Indigenous, and People of Color) life, where queer and trans folks are under exacerbated legal attacks—creating a convention space that protects and enables marginalized participation becomes a means of prefiguring utopian potential through embodied praxis. As mask, capacity, and vaccination mandates disappear (despite these ongoing pandemic times), and as bigotry of all forms continues relatively unabated, WisCon 46 remains steadfast in its commitment to safety. In short, the conference itself aims to become a utopian space.WisCon organizers are also keenly aware of the challenges that many different bodyminds might encounter in large group settings.6 Trained monitors oversee in-person and online programming in an effort to discourage harmful words and actions as well as ensure the fullest participation for those most impacted. Hence, disability justice lies at the center of the Con’s policies and practices. The event is made as accessible as possible through careful attention to venue selection, including the availability of gender-neutral bathrooms, scent-free spaces, and quiet rooms, as well as the use of color communication badges.This year’s event followed strict masking and testing protocols: individually packaged rapid COVID-19 tests were available without cost at registration, as were KN95 masks. The Con kept an anonymized record of self-reported positive COVID-19 tests, in case of possible exposure. This mutual responsibility reflects the kind of utopianism inherent to disability politics; that is, disability “allows for reformulation of in/dependence and community,” a way of rethinking how we share space and produce knowledge together.7The conference’s decidedly feminist approach “to creating a space for feminism and its consideration within the science fiction community” is applied at every level. The Con’s general organization and procedures are structured as nonhierarchically as possible. There is a board of directors as well as co-chairs, but these are rotating positions. This “commitment to feminism” is [End Page 619] reflected... (shrink)

This article represents the author’s reflections on the book by Karl Sigmund “Exact Thinking in Demented Times. The Vienna Circle and the Epic Quest for the Foundations of Science” and the fate of the Vienna Circle. Sigmund paints a vivid portrait of the Vienna Circle against the background of the difficult historical period in which its members lived and worked. The Vienna Circle established the tradition of liberating consciousness and science from metaphysics. But the participants of the Vienna Circle and (...) their entourage did not manage to get rid of the humanistic issues, despite the declaration of strict scientific character. The author of the article draws attention to the internal contradiction between strict scientific topics and the existential-humanistic perception of this topic by the Vienna Circle’s authors and their likeminded people, and by Sigmund himself. The author concludes that it was thanks to this contradiction the Vienna Circle became not only a stage in the development of philosophical science, but also had a broad cultural influence on art, politics, architecture, museums, etc. The historical and philosophical tradition connects the activities of the Vienna Circle with the beginning of the divergence between the philosophical scientific and humanistic traditions in the understanding of philosophy, and the controversy between R. Carnap and M. Heidegger is an important point in this process. But Sigmund’s book gives the impression that this is not the divergence strictly scientific and humanistic traditions, but the difference between two humanistic traditions, one of them tends to express its thoughts strictly analytically. (shrink)

Background Scientific and technological advancements in mapping and understanding the interrelated pathways through which biological and environmental exposures affect disease development create new possibilities for detecting disease risk factors. Early detection of such risk factors may help prevent disease onset or moderate the disease course, thereby decreasing associated disease burden, morbidity, and mortality. However, the ethical implications of screening for disease risk factors are unclear and the current literature provides a fragmented and case-by-case picture. Methods To identify key ethical considerations (...) arising from the early detection of disease risk factors, we performed a systematic scoping review. The Scopus, Embase, and Philosopher’s Index databases were searched for peer-reviewed, academic records, which were included if they were written in English or Dutch and concerned the ethics of (1) early detection of (2) disease risk factors for (3) disease caused by environmental factors or gene-environment interactions. All records were reviewed independently by at least two researchers. Results After screening 2034 titles and abstracts, and 112 full papers, 55 articles were included in the thematic synthesis of the results. We identified eight common ethical themes: (1) Reliability and uncertainty in early detection, (2) autonomy, (3) privacy, (4) beneficence and non-maleficence, (5) downstream burdens on others, (6) responsibility, (7) justice, and (8) medicalization and conceptual disruption. We identified several gaps in the literature, including a relative scarcity of research on ethical considerations associated with environmental preventive health interventions, a dearth of practical suggestions on how to address expressed concerns about overestimating health capacities, and a lack of insights into preventing undue attribution of health responsibility to individuals. Conclusions The ethical concerns arising with the early detection of risk factors are often interrelated and complex. Comprehensive ethical analyses are needed that are better embedded in normative frameworks and also assess and weigh the expected benefits of early risk factor detection. Such research is necessary for developing and implementing responsible and fair preventive health policies. (shrink)

The mid-fourth-century c.e.Cento Vergilianus de laudibus Christi retells the biblical story using cento technique (recombining excerpted lines and partial lines from Virgil into a new poem). Its author, the Christian poet Faltonia Betitia Proba, states that her aim in writing the Cento is to demonstrate that Virgil ‘sang the pious deeds of Christ’ (Vergilium cecinisse … pia munera Christi). Her compositional strategy reflects the exegetical method of typology, as explored in detail by Cullhed: by reusing particular Virgilian verses for biblical (...) characters, Proba creates an implicit typological relationship whereby a Virgilian type both prefigures and is fulfilled by a biblical antitype. This paper first presents an extended model of typology, whereby the type not only prefigures the antitype but also enfigures it, providing the reader with a novel conceptual paradigm through which to understand a particular supernatural reality. The paper then turns to a case study: the baptism scene (380–414), the only passage in the Cento depicting all three members of the Trinity. For each, Proba reuses passages which in the Aeneid describe female characters, hinting at a feminine typological Trinity, one which highlights often-overlooked aspects of the three Christian antitypes. In so doing, she convincingly advances her thesis that Virgil's poetic works reflect typological correspondences to the Christian narrative in a similar way to Old Testament prophecy. (shrink)

The legacy of apartheid spatial planning can still be seen in the dynamics of spaces in South Africa today. The elite (according to research is racialised and mostly white people) lives in well-located city areas, close to economic activity and rule social life that defines cities as stated in 2016 by the Socio Economic Rights Institute of South Africa (SERI). Alternatively, mostly black South Africans are confined to urban margins in densified and poorly serviced areas, with low rates of home (...) ownership. The effects of these policies extend beyond the urban nature, as spaces on the margin by design tend to have fewer opportunities for education compared to urban areas, and there are spatial limits to black business ownership. This article seeks to discuss a case study on a church’s use of space during coronavirus disease 2019 (COVID-19), to show an inclusionary spatial dynamic that may be used in South African spaces. Firstly, it presents an overview of the unequal spatial dynamics in South Africa, particularly Cape Town, and dynamics during COVID-19. Secondly, it provides a historical overview of the Church of the Nazarene and its foundational beliefs. Moreover, it discusses a case study of renewed spatial dynamic in church using the Church of the Nazarene in Khayelitsha. Furthermore, the case study will be used to show the innovative way they reached their community during this time. The final part will discuss how this inclusive spatial dynamic reveals an innovative dynamic in the concept of the missional church, one that goes beyond the going out contextually, but allowing the outside in as well. Contribution: This article discusses the new spatial dynamic of the missional church which inspires inclusivity. The article uses literature around space, COVID-19, mission studies and church history. Furthermore, a semi-structured interview with a church leader at the Church of the Nazarene in Khayelitsha is used for a contextual case study. (shrink)

The article analyzes the implementation of an online educational module and its impact on the organization of the classroom’s interaction order. The latter is institutionally constrained by the presence of a goal and the distribution of roles between teacher and students. The introduction of a digital learning platform adds a technological context to the institutional setting. The article considers technologies as possessing communicative affordances — opportunities for action made possible or delimited through their use. Technologies bring new interactive resources to (...) the process of ed­ucation and can affect the organization of the classroom’s interaction order. Using multimodal conversation analysis, we analyzed video recordings of the telemediated interaction of Russia-based students and teachers within a gamified online educational module. We investigate a case in which a student’s correct answer is nevertheless corrected by the teacher. We dem­onstrate that the teacher initiates the correction because they are guided by the ordering of the game elements within the interface. Based on a detailed analysis of the teacher’s mouse movement in relation to ongoing turns-at-talk, we show that this orientation is sustained by all participants. The work contributes to classroom interaction studies and affordance theory and develops the methodology of multimodal transcription for mediated contexts. The primary result of the study is an empirical demonstration that the relevance of technological affordances for interactants is situation­ally produced, and that this process is associated with the interweaving of the institutional and technical context of interaction. The conclusion discusses the relationship between affordances and institutional norms. (shrink)

This very short introduction will first outline how ontological investigations and questions of practice go together. The second section will bring in the next pole of this entire book, history of mathematics. How do ontology, practice, and history go together? Is this a forced marriage or one born in true love? That is, do these three belong together in some very basic way? One chapter in the section argues that the philosophy of mathematical practice intersects with the history of mathematics (...) essentially. If the first section of this introduction is persuasive that will also show that the history of mathematics intersects with ontological questions as well, specifically, that historical questions are very much about the ontological commitments of past mathematicians. The last section will take up what might seem a very different theme, namely, how these things matter to mathematics education. This section is connected closely to the second section since mathematics education has taken an interest in the role of history of mathematics in mathematics education, and much insight can be gained by seeing the issues in relation to the ontology-practice-history triad. The question of education is also important since teachers must consider what it is exactly that they are teaching, or, to adapt the title of Reuben Hersh’s well-known book, “What is mathematics really about?” And the “aboutness” of mathematics is really the ontological question. (shrink)