Periodic Reporting for period 2 - TOKMAT (TOKMAT: Truth, Objectivity, and Knowledge: rethinking the social construction of MAThematics)
Período documentado: 2024-09-01 hasta 2025-08-31
The project TOKMAT aims to use the mathematical school of intuitionism in order to shed light on how society and science interact. The project focuses on the cultural, personal, and social dimensions of mathematical knowledge in order to better understand how mathematical ideas develop. It combines historical examinations of primary and secondary sources (the Significs Dialogues, 1922-1926) with methods from philosophy of science (Perspectival Realism) and philosophy of mathematics (mathematical pluralism) to provide new ways of understanding the nature of mathematics as situated, on the one hand, in realism, and on the other, in social reality. In doing so, it aims to reconcile realism about mathematics with mathematical pluralism and can shed new light on some of the contemporary more standard readings of intuitionism. But more than that, it is a necessary first step towards a large-scale, socially oriented account of the history of mathematics, one that comprises the complex and profound connections between individual mathematicians and the communities they inhabit.
The following key milestones were successfully achieved:
1. Skill Development and Analytical Expertise:
• The project facilitated the enhancement of my ability to identify, analyze, and articulate complex issues at the intersection of science, technology, and public policy. I deepened my understanding of major analytic frameworks within the field of Science, Technology, and Society (STS), which has been crucial for advancing my research and academic contributions.
2. Networking and Professional Growth:
• I significantly expanded my professional network by engaging with international members and visiting scholars associated with the MIT STS program. Additionally, I networked with researchers across various international conferences, exploring new academic domains such as social theory and cultural history. My active participation in the HASTS seminar sessions and MIT’s Teaching and Learning Lab workshops contributed to the enhancement of my communication skills and opened up new career opportunities.
3. Academic Contributions and Ongoing Research:
• I deepened my expertise in intuitionistic mathematics and logic by regularly participating in Carl Posy’s intuitionism group. This engagement not only enriched my knowledge but also supported the development of my research output. Notably, I submitted a paper to Studies in History and Philosophy of Science that is now in its second round of revisions. This paper provides a socially-oriented analysis of Brouwer’s engagement with the Significs circle. Furthermore, I successfully secured a book contract with Springer to publish a manuscript based on this project and my dissertation.
Project Objectives:
1. Social Aspects of Brouwer’s Intuitionism: Submitted a paper focusing on the social dimensions of Brouwer’s intuitionism, particularly as they relate to the Significs Dialogues and his perspectives on the relationship between society and mathematics. This paper is currently under review in Studies in History and Philosophy of Science
2. Book Proposal Submission: Successfully wrote and submitted a book proposal based on my dissertation. The manuscript investigates the community's diverse responses to Brouwer's intuitionism and introduces a novel historiographical framework centered on intergroup relations. The proposal was accepted, and a book contract was signed with Springer
3. Further Development of Intuitionistic Expertise: Continued to enhance my knowledge in the foundations of intuitionism through ongoing participation in the “intuitionism working group”.
4. Advancement of Research Methodology: Attended various workshops and seminars organized by MIT’s STS, history, and philosophy departments, as well as Harvard’s history of science program. These activities advanced my research methodology in the history and sociology of science.
5. Expertise in Academic Writing: Acquired further expertise in academic writing by attending two workshops and two certificate programs offered by MIT’s Teaching and Learning Lab on scientific writing
1. Skill Development and Analytical Expertise:
• The project facilitated the enhancement of my ability to identify, analyze, and articulate complex issues at the intersection of science, technology, and public policy. I deepened my understanding of major analytic frameworks within the field of Science, Technology, and Society (STS), which has been crucial for advancing my research and academic contributions.
2. Networking and Professional Growth:
• I significantly expanded my professional network by engaging with international members and visiting scholars associated with the MIT STS program. Additionally, I networked with researchers across various international conferences, exploring new academic domains such as social theory and cultural history. My active participation in the HASTS seminar sessions and MIT’s Teaching and Learning Lab workshops contributed to the enhancement of my communication skills and opened up new career opportunities.
3. Academic Contributions and Ongoing Research:
• I deepened my expertise in intuitionistic mathematics and logic by regularly participating in Carl Posy’s intuitionism group. This engagement not only enriched my knowledge but also supported the development of my research output. Notably, I submitted a paper to Studies in History and Philosophy of Science that is now in its second round of revisions. This paper provides a socially-oriented analysis of Brouwer’s engagement with the Significs circle. Furthermore, I successfully secured a book contract with Springer to publish a manuscript based on this project and my dissertation.
Project Objectives:
1. Social Aspects of Brouwer’s Intuitionism: Submitted a paper focusing on the social dimensions of Brouwer’s intuitionism, particularly as they relate to the Significs Dialogues and his perspectives on the relationship between society and mathematics. This paper is currently under review in Studies in History and Philosophy of Science
2. Book Proposal Submission: Successfully wrote and submitted a book proposal based on my dissertation. The manuscript investigates the community's diverse responses to Brouwer's intuitionism and introduces a novel historiographical framework centered on intergroup relations. The proposal was accepted, and a book contract was signed with Springer
3. Further Development of Intuitionistic Expertise: Continued to enhance my knowledge in the foundations of intuitionism through ongoing participation in the “intuitionism working group”.
4. Advancement of Research Methodology: Attended various workshops and seminars organized by MIT’s STS, history, and philosophy departments, as well as Harvard’s history of science program. These activities advanced my research methodology in the history and sociology of science.
5. Expertise in Academic Writing: Acquired further expertise in academic writing by attending two workshops and two certificate programs offered by MIT’s Teaching and Learning Lab on scientific writing
1. Scientific Achievements and Contributions to the State of the Art:
The TOKMAT project has made significant strides in advancing the scientific discourse on the social constructions of mathematics. The project introduces a novel twofold perspective of truth, which differentiates between truth as a mentally constructed subjective claim and truth as a socially constructed objective knowledge-claim. This dual perspective provides a foundational framework for exploring objectivity in mathematics and contributes to broader discussions on how social factors influence scientific knowledge and standards of certainty.
By presenting an original analysis of both historical and contemporary intuitionistic positions through a socially-oriented lens, the project enriches philosophical, historical, and sociological discussions about the nature, development, and creation of mathematical knowledge. It offers a fresh perspective on intuitionistic concepts, such as Brouwer’s ‘creating subject’ and the development of choice sequences, contributing to ongoing debates in the philosophy of mathematics and the foundations of mathematics. Should the paper currently under review be accepted, its socio-philosophical approach could provide insights into transnational and conceptual questions about the nature of truth, objectivity, and the social dynamics surrounding these concepts.
2. Innovation Outputs:
While the project primarily focuses on theoretical contributions, its innovative approach to understanding mathematical knowledge through a socially-oriented prism has the potential to influence related scientific fields. For instance, disciplines like biology that engage in discussions about science, values, and objectivity might find the project’s twofold approach to truth relevant and applicable to their own conceptual frameworks. The project has also raised interest among psychologists and anthropologists researching the development of human concepts and values.
3. Societal Impact and Social Relevance:
The TOKMAT project addresses crucial questions about the influence of marginalized groups on the development and social constitution of mathematical knowledge. By investigating the social and psychological dynamics behind the visibility and marginalization of certain forms of mathematical knowledge, the project contributes to a deeper understanding of collective behavior and its role in shaping socially constructed concepts. This research is socially relevant as it sheds light on how conformity, norm-following, and other collective behaviors influence the creation and evolution of knowledge within scientific communities.
Overall, the TOKMAT project is making significant progress towards delivering scientific impact by contributing to the state of the art in multiple disciplines and raising important questions with societal implications. Its focus on the intersection of social and philosophical perspectives in mathematics has the potential to influence both academic discourse and broader societal understandings of truth and objectivity.
The TOKMAT project has made significant strides in advancing the scientific discourse on the social constructions of mathematics. The project introduces a novel twofold perspective of truth, which differentiates between truth as a mentally constructed subjective claim and truth as a socially constructed objective knowledge-claim. This dual perspective provides a foundational framework for exploring objectivity in mathematics and contributes to broader discussions on how social factors influence scientific knowledge and standards of certainty.
By presenting an original analysis of both historical and contemporary intuitionistic positions through a socially-oriented lens, the project enriches philosophical, historical, and sociological discussions about the nature, development, and creation of mathematical knowledge. It offers a fresh perspective on intuitionistic concepts, such as Brouwer’s ‘creating subject’ and the development of choice sequences, contributing to ongoing debates in the philosophy of mathematics and the foundations of mathematics. Should the paper currently under review be accepted, its socio-philosophical approach could provide insights into transnational and conceptual questions about the nature of truth, objectivity, and the social dynamics surrounding these concepts.
2. Innovation Outputs:
While the project primarily focuses on theoretical contributions, its innovative approach to understanding mathematical knowledge through a socially-oriented prism has the potential to influence related scientific fields. For instance, disciplines like biology that engage in discussions about science, values, and objectivity might find the project’s twofold approach to truth relevant and applicable to their own conceptual frameworks. The project has also raised interest among psychologists and anthropologists researching the development of human concepts and values.
3. Societal Impact and Social Relevance:
The TOKMAT project addresses crucial questions about the influence of marginalized groups on the development and social constitution of mathematical knowledge. By investigating the social and psychological dynamics behind the visibility and marginalization of certain forms of mathematical knowledge, the project contributes to a deeper understanding of collective behavior and its role in shaping socially constructed concepts. This research is socially relevant as it sheds light on how conformity, norm-following, and other collective behaviors influence the creation and evolution of knowledge within scientific communities.
Overall, the TOKMAT project is making significant progress towards delivering scientific impact by contributing to the state of the art in multiple disciplines and raising important questions with societal implications. Its focus on the intersection of social and philosophical perspectives in mathematics has the potential to influence both academic discourse and broader societal understandings of truth and objectivity.