Towards Open mathematics: the Transformation of the Practice of Mathematical Proof from Individual to Socio-Digital (in Russian, 2019) / На пути к открытой математике: трансформация практики математического доказательства от индивидуальной к социоцифровой (original) (raw)
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Epistemology & Philosophy of Science, 2018, vol. 55, No. 4, pp. 160-173
This paper attempts to look at contemporary mathematical practise through the lenses of the distributed cognition approach. The ubiquitous use of personal computers and the internet as a key attribute of the digital society is interpreted here as a means to achieve a more effective distribution of human cognitive activity. The major challenge that determines the transformation of mathematical practice is identified as ‘the problem of complexity'. The computer-assisted complete formalization of mathematical proofs as a current tendency is viewed as one of the strands along which the mathematical community responds to the challenge. It is shown that this tendency gives life to the project calling to revisit and rebuild the very foundations of mathematics to secure more effective communication and thus guarantee the reliability of contemporary mathematics. Keywords: distributed cognition, communication, digital society, mathematical practice, formal proof, foundations of mathematics.
The relevance of the topic is due to the emergence of the so-called digital skeptics who challenge the need for total digitalization of education. The object of the study is the values of digital transformation, the subject — their actual implementation in the system of higher education. The author has chosen an axiological approach to the study of the problem, involving the consideration of the digitalization of education in the socio-philosophical aspect. According to the author, the bonuses of Reality 2.0 are predominantly of an entertainment nature, which has nothing to do with research activities. In addition, most of the materials on the digital world in one way or another raise the topic of salesmanship. This means that the key direction of technology development is purely commercial, a priori consumer-oriented. In the spirit of concreteness and pragmatics, the vector of simplification is declared the only correct and universally applicable. The most dangerous simplifications are: 1) identifying knowledge with information and information with data; 2) identifying creativity with creativity; 3) identifying reality with reality. The author is confident: it is superfluous to argue that constructive criticism of digitalization has nothing to do with obscurantism. Protest is not so much against the numbers themselves, as against the neo-Lysenkovism (show pedagogy and other forms of profanation), zealously promoted by the adherents of the IT breakthrough. By defending the principles of classical pedagogy, digital skeptics defend culture from dogmatism and utilitarian primitivization.
Digitalization of Society and the Future of Christianity, 2021
The 7th International Scientific Conference "Digitalization of Society and the Future of Christianity. To the Question of Transformation the Value and Regulatory System of Society” was held at the Saint-Tikhon Orthodox University of Humanities (STOUH) on February 18-19, 2021. Foremost scientists from such countries as Russia, Italy, Germany, France, Taiwan, China, India, Nigeria, Ukraine and Belarus made their presentations at this scientific event. In their reports, they looked from a Christian point of view at the problems, challenges and welfares that the process of digitalizing society brings to modern people's lives. Particular accent was placed on the changes in the values and norms of the people he carries. Keywords: Digitalization, Christianity, society, virtualization, value-regulatory system. 18-19 февраля 2021 г. в Православном Свято-Тихоновском гуманитарном университете прошла VII международная научная конференция «Цифровизация общества и будущее христианства. К вопросу о трансформации ценностно-нормативной системы общества». На этом научном мероприятии со своими докладами выступили крупные учёные из таких стран как Россия, Италия, Германия, Франция, Тайвань, Китай, Индия, Нигерия, Украина, Белоруссия. В своих докладах они с христианской точки зрения рассмотрели те проблемы, вызовы и преимущества, которые привносит в современную жизнь людей процесс цифровизации общества. Особенный акцент был сделан на тех изменениях в ценностях и нормах людей, которые он за собой несёт. Ключевые слова: цифровизация, христианство, общество, виртуализация, ценностно-нормативная система.
Philosophy of Science and Technology 2019, vol. 24, no. 2, pp. 70–81
The 1970s to 1990s constitute a crucial period in the history of the philosophy of mathematics for it was the time when the philosophy of mathematical practice movement took shape. One of its most notable episodes arguably was the debate concerning the existence and meaning of revolutions in the history of mathematics which was triggered by the question whether T.S. Kuhn’s extremely influential theory of science applies to mathematics or not. The paper attempts at revisiting that debate in search of its outcome and possible significance for the philosophy of mathematics nowadays. The debate was initiated by a Crowe – Dauben controversy: while M. Crowe claimed that revolutions never occur in mathematics, J. Dauben objected that revolutions do occur within it. Tracking the course of the debate during the three decades in question, in this paper, I have concluded that only the nominal victory was Dauben’s while the real one was Crowe’s. The existence of “revolutions” in the history of mathematics was generally accepted, but for the most part not in the Kuhnian sense of the word for that acceptance was combined with the ubiquitous presence of the belief in the strictly progressive accumulation of the results throughout the history of mathematics. In contradistinction to the scholarly works that assert the fruitlessness of the debate on revolutions in mathematics, in my paper, some intellectual trends brought to the fore by it are recognised. These trends are still highly relevant to the philosophy of mathematical practice; the positive ones call for further scrutiny while the negative ones for conscious opposition. Keywords: philosophy of mathematics, philosophy of mathematical practice, revolutions in mathematics, cumulativity of the development of mathematics, T.S. Kuhn
Philosophy of Science and Technology, 2020, vol. 25, no. 1, pp. 5–17
This paper is the second (and final) part of a study of the debate concerning the existence and meaning of revolutions in the history of mathematics. The discussion in question has emerged in the 1970s and was inspired by T.S. Kuhn’s hugely influential theory of science. In the previous part of this study, an initial Crowe – Dauben controversy is considered. M.J. Crowe put forward ten “laws” concerning the evolution of mathematics with the final one stating that revolutions never occur in mathematics. At the same time, J.W. Dauben tried to support the occurrence of revolutions in mathematics. The story of the debate − which was famously summed up in D. Gillies’s 1992 edited collection “Revolutions in Mathematics” − apparently suggested that Dauben’s position entirely predominates over Crowe’s among the scholars; even Crowe was finally forced to acknowledge the occurrence of revolutions in mathematics. In 2000 B. Pourciau disputed such a view of the debate’s outcome, stressing that the overwhelming majority of the scholars who took part in the 1992 collection, happily married the recognition of revolutions in the history of mathematics with the strictly cumulative character of mathematics as far as mathematical results are concerned. In other words, they were talking about “revolutions” that cannot be called “Kuhnian”. It means that only the nominal victory is Dauben’s while the real one is Crowe’s. In this part of the study, a lot of additional material belonging to the debate is analyzed. This analysis corroborates Pourciau’s thesis and takes a closer look at the varieties of the “compromise” position accepting revolutions in mathematics on one level while rejecting them on the other. Some reviewers consider the debate on the revolutions in mathematics futile. Still, this study shows it to be highly instructive in bringing to light some ambivalent trends in the philosophy of mathematical practice. Keywords: philosophy of mathematics, philosophy of mathematical practice, revolutions in mathematics, cumulativity of the development of mathematics, T.S. Kuhn
2019
В работе рассматриваются возможности применения в России новых цифровых инструментов самоорганизации ученых и управления наукой. С учетом международной практики авторы выработали четыре экспериментальные модели децентрализованного самоуправления и группового принятия решений в науке, предположительно применимые для имплементации принципов цифрового управления (e-governance) в отечественной академической среде, и предложили их к обсуждению российским ученым в формате фокус-групп. Основным результатом обсуждения стала концептуализация системы отношений между членами научного сообщества в России при помощи социально-антропологической метафоры трайба. Авторы приходят к выводу, что предпосылками любых форм цифровизации отечественной науки должно стать как понимание партизанских практик ученых, так и установление в отношениях науки, общества и государства базового уровня видимости (понимания, кто что делает), подотчетности и делиберативности (обсуждаемости решений).