scholarly journals The constitution of physics and the certainty of mathematics in the 16th century scholastic philosophy

2020 ◽  
Vol 14 (1) ◽  
pp. 143-163
Author(s):  
Vitaly Ivanov
Keyword(s):  
Scientific Knowledge ◽  
Mathematical Knowledge ◽  
Mathematical Object ◽  
16Th Century ◽  
New Science ◽  
Mathematical Demonstration ◽  
The Status ◽  
Operational Art ◽  
Early Modern Times ◽  
And Mathematics

Traditionally, it is believed that one of the most important phenomena in the history of "new" science, i.e. the science of Early Modern times, is the emergence of mathematical natural science. However, in the 16th century the status of physics and mathematics within the framework of scientific knowledge was far from being so unambiguous. In this article, we consider and analyze the arguments of the late Peripatetic author of the late 16th century – the learned Jesuit Benedict Pereira – in favor of his thesis about "non-scientific character" of mathematical disciplines. These arguments focus not on the weaker (less perfect) status of the reality of the mathematical object, but on the nature of mathematical demonstration and mathematical knowledge as such. Pereira shows in detail that mathematics does not meet the criteria of scientific knowledge (in the sense of "Second Analytics"), because the middle terms in its demonstrations are non-proper, general and accidental, and mathematics itself is not a knowledge of the real causes. In sum, in Pereira's consideration mathematics turns out to be some sort of “operational art” rather than a necessary knowledge of the truth from real causes. A comparison of the scientific status of physical and mathematical knowledge in Pereira makes it possible to clarify the conditions for the emergence of modern mathematical physics.

scholarly journals The development of cognitive interest at pupils of senior profile classes in polydisciplinary teaching

2021 ◽  
Author(s):  
Н.В. Протасова
Keyword(s):  
Foreign Language ◽  
Present Article ◽  
Scientific Knowledge ◽  
Mathematical Knowledge ◽  
Research Work ◽  
Knowledge And Skills ◽  
New Approaches ◽  
Subject Categories ◽  
Different Types ◽  
And Mathematics

Актуальность настоящей статьи обусловлена происходящими изменениями в научном знании. Формирующиеся новые отрасли знания, в том числе стыке наук, вносят изменения в содержание образования, исследователи осуществляют поиск новых подходов обучения. Предложено использование полипредметного подхода в обучении иностранным языкам обучающихся старших классов негуманитарного профиля с целью сформировать целостное представление о предметах и явлениях окружающего мира. Данная статья посвящена развитию познавательного интереса у обучающихся старших классов негуманитарного профиля в полипредметном обучении. Особый акцент в полипредметном обучении делается на приобретение новых знаний, умений и навыков по предметам естественно-математического цикла средствами иностранного языка. Полипредметность расширяет и углубляет предметные знания обучающихся, улучшает их лингвистическую подготовку. Составляющими полипредметного обучения являются проектная и исследовательская деятельность, которые в рамках полипредметного обучения позволяют приобретать знания по проблеме исследования из разных предметных областей. Разработка проектов и проведение исследовательской работы в полипредметном обучении активизирует мыслительную деятельность, развивает разные типы мышления, познавательный интерес. The actuality of present article is occasioned by changes in scientific knowledge. New branches of knowledge, forming at the junction of sciences make changes in syllabus, investigators search new approaches in teaching. This article is devoted to the development of cognitive interest at pupils of non-humanitarian profile in polydisciplinary education. Special accent is made on getting knowledge and skills on the subjects of science and mathematics using a foreign language. Polydisciplinary spreads and deeps science and mathematical knowledge and improves the linguistic education. Being a part of polydisciplinary teaching, project and research work help to get knowledge on the problem of investigation from different subject categories. Preparing a project or a research work in a polydisciplinary education makes thinking active, develops different types of thinking, cognitive interest.

scholarly journals Intensionality: From Philosophical Logic to Metamathematics

2020 ◽  
pp. 85-89
Author(s):  
Vitaly V. Tselishchev ◽  
◽  
Keyword(s):  
Mathematical Knowledge ◽  
Research Area ◽  
Mathematical Discourse ◽  
Foundations Of Mathematics ◽  
Philosophical Logic ◽  
David Hilbert ◽  
The Status ◽  
And Mathematics ◽  
Theoretical Apparatus

The article is devoted to the study of the status of intensionality in the exact contexts of logical and mathematical theories. The emergence of intensionality in logical and mathematical discourse leads to significant obstacles in its formalization due to the appearance of indirect contexts, the uncertainty of its indication in the theoretical apparatus, as well as the presence of various kinds of difficult-to-account semantic distinctions. The refusal to consider intensionality in logic is connected with Bertrand Russell’s criticism of Alexius Meinong’s intensionality ontology, and with Willard Van Orman Quine’s criticism of the concept of meaning and quantification of modalities. It is shown that this criticism is based on a preference for the theory of indication over the theory of meaning, in terms of the distinction “Bedeutung” and “Sinn” introduced by Gottlob Frege. The extensionality thesis is explicated; by analogy with it the intensionality thesis is constructed. It is shown that complete parallelism is not possible here, and therefore we should proceed from finding cases of extensionality violation. Since the construction of formal logical systems is to a certain extent connected with the programs of the foundations of mathematics, the complex interweaving of philosophical and purely technical questions makes the question of the role of intensionality in mathematics quite confusing. However, there is one clue here: programs in the foundations of mathematics have given rise to metamathematics, which, although it stands alone, is considered a branch of mathematics. It is not by chance that, judging by the problems arising in connection with intensionality, there is a growing suspicion that intensionality can play a significant role in metamathematics. As for the question of the sense in which metamathematics results can be considered mathematical, in terms of the presence of intensional contexts in both disciplines, it is a matter of taste: for example, the autonomy of mathematical knowledge as a result of the desire of mathematicians to eliminate the influence of philosophy that took place in the case of David Hilbert may be worth considering in the context of mathematics. Thus, the rather vague concept of intensionality receives various explications in different contexts, whether it is philosophical logic or metamathematics. In any case, the detection of context intensionality is always associated with a clear narrowing of the research area. It is obvious that the creation of a more general theory of intensionality is possible within a more general framework, in which logic and mathematics must be combined. In this respect, we can hope for the resumption of a logical project, which would be a purely logical consideration made of the natural and the mathematical.

Field Experience and Prospective Teachers' Mathematical Knowledge and Beliefs

2017 ◽  
Vol 48 (2) ◽  
pp. 148-190 ◽  
Author(s):  
Erik D. Jacobson
Keyword(s):  
Prospective Teachers ◽  
Mathematical Knowledge ◽  
Field Experience ◽  
Mathematics Learning ◽  
Future Research ◽  
Prospective Elementary Teachers ◽  
Knowledge And Beliefs ◽  
And Mathematics ◽  
Education And Development ◽  
The Relationship

This study (n = 1,044) used data from the Teacher Education and Development Study in Mathematics (TEDS-M) to examine the relationship between field experience focus (instruction- or exploration-focused), duration, and timing (early or not) and prospective elementary teachers' intertwined knowledge and beliefs about mathematics and mathematics learning. Early instruction-focused field experience (i.e., leading directly to classroom instruction) was positively related to the study outcomes in programs with such field experience of median or shorter duration. Moreover, the duration of instruction-focused field experience was positively related to study outcomes in programs without early instruction-focused field experience. By contrast, the duration of exploration-focused field experience (e.g., observation) was not related to the study outcomes. These findings suggest that field experience has important but largely overlooked relationships with prospective teachers' mathematical knowledge and beliefs. Implications for future research are discussed.

Arguments for the Existence of God

2014 ◽  
pp. 700-716
Author(s):  
Brandon C. Look
Keyword(s):  
Mathematical Knowledge ◽  
Cosmological Argument ◽  
Existence Of God ◽  
Eternal Truths ◽  
The Status

This chapter critically discusses Leibniz’s arguments for the existence of God. It explores Leibniz’s improvements on the traditional ontological arguments of Anselm and Descartes, as well as his version of the cosmological argument and his argument from eternal truths. It is suggested that, while Leibniz’s arguments are unlikely to move a hardened atheist, they do offer important insights about the status of the existence predicate, the nature of modality, and the nature of mathematical knowledge.

Culturally-Connected Integrated STEM Instruction

2021 ◽  
pp. 751-769
Author(s):  
Tiffany S. Powell
Keyword(s):  
New York ◽  
Culturally Diverse ◽  
New York State ◽  
Integrative Approach ◽  
Culturally Diverse Students ◽  
Integrated Stem ◽  
The Status ◽  
Stem Instruction ◽  
And Mathematics ◽  
Culturally Connected

This chapter provides an overview of integrative STEM instruction through the lens of culturally connected practices as a foundation for elementary learners. The integrative STEM model can be a catalyst for increasing the number of culturally diverse, competent contributors to the STEM field. At the heart of an integrative approach to STEM instruction, students are exposed to rich science, technology, engineering, and mathematics content in ways that propel culturally diverse students to dive into these once exclusive bodies of knowledge with zeal and confidence. The only way this can occur is by having teachers whose belief systems 1) support the importance of rigorous learning, 2) are willing to challenge the status quo, and 3) who are adequately versed in culturally responsive teaching approaches. Additionally, this chapter highlights the implementation of Wheel Instruction for Integrative STEM through two professional development cycles within an urban school district in the New York State Capital Region.

Cultural Contexts in Science and Mathematics Teaching to Young Children

2019 ◽  
Vol 15 (2) ◽  
Author(s):  
Gina C. Obiakor ◽  
Kristen E. Obiakor ◽  
Charles C. Obiakor ◽  
Festus E. Obiakor
Keyword(s):  
Teacher Preparation ◽  
Mathematics Teaching ◽  
Mathematical Knowledge ◽  
Teaching Science ◽  
National Origin ◽  
Innovative Teaching ◽  
Cultural Contexts ◽  
Language And Gender ◽  
And Gender ◽  
And Mathematics

AbstractScience and mathematics have international and global origins and impacts that are intertwined with national origin, race, culture, religion, language, and gender, to mention a few. This means that scientific and mathematical knowledge goes beyond myopic narrow confines. Put another way, teaching science and mathematics without explicating their phenomenal foundations and influences is tantamount to “scotching the snake, but not killing it.” In this article, we use cases to discuss cultural contexts in teaching science and mathematics. Embedded in our discussion are issues of teacher preparation, innovative teaching, and disparities in public health and environmental health.

scholarly journals The Function and Role in the IBAN Social Rank in their Communities

2018 ◽  
Vol 7 (2.29) ◽  
pp. 639
Author(s):  
Fujica Anak Anggo ◽  
Louis Laja
Keyword(s):  
Social Status ◽  
Social Rank ◽  
The State ◽  
16Th Century ◽  
Young Generation ◽  
General Knowledge ◽  
West Kalimantan ◽  
Traditional Belief ◽  
The Status

The Sea Dayaks, better known as the Ibans, inhabit nearly the whole of Sarawak. The Ibans belong to the Proto-Malay groups and historically, they were from the Kapuas Valley in West Kalimantan, Indonesia. They migrated to Sarawak about fifteen generations ago in the mid 16th century (the 1630s). They went to the state through the Kumpang Valley and inhabit Batang Ai and then split to several places in Sarawak (Morgan, 1968). Although the Ibans have a social status in their traditional belief, they do not have a hierarchy of social status such as the Orang Ulu. However, they have elevated the status so-called Pengulu, Tuai Rumah, Tuai Burung, Lemambang, Manang, Beliau, Tukang Sabak, dan Indu Takar. The era of modernization has led to changes to the knowledge of the young generation, especially the younger generation of the Ibans who lack knowledge about the function and role of each rank status in their communities. Therefore, this study was conducted qualitatively through an interview with expert informants, observation, and documentation. This research was hoped to contribute to the general knowledge of the Iban community and other communities in the preservation of the function and role of each social status in the Iban community.  

scholarly journals Plague, Practice, and Prescriptive Text

2020 ◽  
Vol 8 (2-3) ◽  
pp. 152-178
Author(s):  
Moshe Dovid Chechik ◽  
Tamara Morsel-Eisenberg
Keyword(s):  
Early Modern ◽  
Early Modern Period ◽  
16Th Century ◽  
15Th Century ◽  
Modern Period ◽  
The Status ◽  
Accepted Practice ◽  
At Home

Abstract This article studies the fate of a contradiction between practice and prescriptive text in 16th-century Ashkenaz. The practice was fleeing a plagued city, which contradicted a Talmudic passage requiring self-isolation at home when plague strikes. The emergence of this contradiction as a halakhic problem and its various forms of resolution are analyzed as a case study for the development of halakhic literature in early modern Ashkenaz. The Talmudic text was not considered a challenge to the accepted practice prior to the early modern period. The conflict between practice and Talmud gradually emerged as a halakhic problem in 15th-century rabbinic sources. These sources mixed legal and non-legal material, leaving the status of this contradiction ambiguous. The 16th century saw a variety of solutions to the problem in different halakhic writings, each with their own dynamics, type of authority, possibilities, and limitations. This variety reflects the crystallization of separate genres of halakhic literature.

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