Transcending Communal Boundaries: Brouwer’s Intuitionism in Philosophical Discourse
摘要
This chapter explores the divergent receptions of Brouwer’s intuitionism within the fields of mathematics and philosophy. While Brouwer’s ideas largely faded from mainstream mathematical practice by the mid-twentieth century, they continue to hold a significant place in philosophical discussions on the foundations of mathematics. Through an analysis of influential works in the philosophy of mathematics, the chapter reveals how philosophers have upheld intuitionism as a profound perspective on mathematical truth and existence, even as mathematicians moved on to frameworks that better served practical needs. This chapter considers the historical and conceptual reasons behind this disparity, suggesting that intuitionism’s philosophical depth and challenge to conventional ideas about knowledge and reality have preserved its relevance for philosophers. By examining how intuitionism traversed disciplinary boundaries, this chapter highlights philosophy’s unique role in preserving and advancing ideas that may be sidelined within their original scientific domains, ultimately underscoring the distinct standards, norms, and purposes that shape how each community engages with new theories.