The Sociology of Mathematical Knowledge
Studies of mathematical practice and quasi-empiricism in mathematics are also rightly part of the sociology of knowledge, since they focus on the community of those who practice mathematics and their common assumptions. Since Eugene Wigner raised the issue in 1960 and Hilary Putnam made it more rigorous in 1975, the question of why fields such as physics and mathematics should agree so well has been debated. Proposed solutions point out that the fundamental constituents of mathematical thought, space, form-structure, and number-proportion are also the fundamental constituents of physics. It is also worthwhile to note that physics is nothing but a modeling of reality, and seeing causal relationships governing repeatable observed phenomena, and much of mathematics, especially in relation to the growth of the calculus, has been developed precisely for the goal of developing these models in a rigorous fashion. Another approach is to suggest that there is no deep problem, that the division of human scientific thinking through using words such as 'mathematics' and 'physics' is only useful in their practical everyday function to categorize and distinguish.
Fundamental contributions to the sociology of mathematical knowledge have been made by Sal Restivo and David Bloor. Restivo draws upon the work of scholars such as Oswald Spengler (The Decline of the West, 1926), Raymond L. Wilder and Lesley A. White, as well as contemporary sociologists of knowledge and science studies scholars. David Bloor draws upon Ludwig Wittgenstein and other contemporary thinkers. They both claim that mathematical knowledge is socially constructed and has irreducible contingent and historical factors woven into it. More recently Paul Ernest has proposed a social constructivist account of mathematical knowledge, drawing on the works of both of these sociologists.
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