Chapter 3: A Constraints-Based Philosophy of Mathematical Practice

2017 ◽  
pp. 59-99
Keyword(s):  
Mathematical Practice ◽  
Philosophy Of Mathematical Practice

scholarly journals On the centenary of Zygmunt Janiszewski (1888-1920): ideals of mathematical practice and the constitution of continuum theory

2020 ◽  
Vol 8 (18) ◽  
pp. 431-453
Author(s):  
Luis Carlos Arboleda ◽  
Andrés Chaves
Keyword(s):  
Mathematical Practice ◽  
Continuum Theory ◽  
Axiomatic System ◽  
Intellectual Character ◽  
The Social ◽  
Polish School ◽  
The Aesthetic ◽  
Aesthetic Values ◽  
Philosophy Of Mathematical Practice ◽  
Scientific Life

This paper shows the importance of applying a certain approach to the history and philosophy of mathematical practice to the study of Zygmunt Janiszewski's contribution to the topological foundations of Continuum theory. In the first part, a biography of Janiszewski is presented. It emphasizes his role as one of the founders of the Polish School of Mathematics, and the social, political and military facets in which his intellectual character was revealed, as well as the values that guided his academic and scientific life. Kitcher's view of mathematical practice is then adopted to examine the philosophical conceptions and epistemological style of Janiszewski in relation to the construction of the formal axiomatic system of knowledge about the continua. Finally, it is shown the convenience of differentiating in Kitcher's approach, the methods, procedures, techniques and strategies of practice, and the aesthetic values of mathematics. Keywords: Zygmunt Janiszewski; Continuum theory; Philosophy of mathematical practice; Polish school of mathematics.

scholarly journals Showing Mathematical Flies the Way Out of Foundational Bottles: The Later Wittgenstein as a Forerunner of Lakatos and the Philosophy of Mathematical Practice

2022 ◽  
Vol 0 (0) ◽  
Author(s):  
José Antonio Pérez-Escobar
Keyword(s):  
Philosophy Of Mathematics ◽  
Mathematical Practice ◽  
History Of ◽  
Philosophy Of Mathematical Practice ◽  
The Way

Abstract This work explores the later Wittgenstein’s philosophy of mathematics in relation to Lakatos’ philosophy of mathematics and the philosophy of mathematical practice. I argue that, while the philosophy of mathematical practice typically identifies Lakatos as its earliest of predecessors, the later Wittgenstein already developed key ideas for this community a few decades before. However, for a variety of reasons, most of this work on philosophy of mathematics has gone relatively unnoticed. Some of these ideas and their significance as precursors for the philosophy of mathematical practice will be presented here, including a brief reconstruction of Lakatos’ considerations on Euler’s conjecture for polyhedra from the lens of late Wittgensteinian philosophy. Overall, this article aims to challenge the received view of the history of the philosophy of mathematical practice and inspire further work in this community drawing from Wittgenstein’s late philosophy.

A Constraints-Based Philosophy of Mathematical Practice

2017 ◽  
Author(s):  
Roi Wagner
Keyword(s):  
Philosophy Of Mathematics ◽  
Mathematical Practice ◽  
Philosophical Approach ◽  
Integrative Framework ◽  
Philosophy Of Mathematical Practice ◽  
Mathematical Interpretation

This chapter describes a constraints-based philosophy of mathematical practice and shows that mathematics can be so many different things, even if we look at a particular branch of mathematics in a particular time and place. It introduces a philosophical approach to mathematics that can serve as an integrative framework for the insights of the various philosophies of mathematics and demonstrates what kind of plurality the philosophy of mathematics must embrace, if it is to be faithful to the phenomenon that it seeks to explicate. The chapter reflects on the function of mathematical statements, consensus in mathematics, and mathematical interpretation and semiosis. It also considers various constraints that apply to mathematical practice and how they are negotiated by different mathematical cultures. Finally, it examines more mainstream notions of reality and truth of mathematical entities and statements and suggests how a takeoff on Hilary Putnam's notion of relevance might relativize them.

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