A Role for Representation Theorems. Issue 3 (27th April 2018)

• Record Type: Journal Article
• Authors: Ippoliti, Emiliano
• Is Part Of: Philosophia Mathematica. Volume 26:Issue 3(2018)
• Page Start: 396
• Page End: 412
• Publication Date: 2018-04-27
• Subjects: Mathematics -- Philosophy -- Periodicals; Wiskunde; Filosofische aspecten; Mathematics -- Philosophy; Periodicals; 510.105
• DOI: 10.1093/philmat/nky007
• Languages: English
• ISSNs: 0031-8019

Abstract

Abstract: I argue that the construction of representation theorems is a powerful tool for creating novel objects and theories in mathematics, as the construction of a new representation introduces new pieces of information in a very specific way that enables a solution for a problem and a proof of a new theorem. In more detail I show how the work behind the proof of a representation theorem transforms a mathematical problem in a way that makes it tractable and introduces information into it that it did not contain at the beginning of the process.