Abstract
Representations, in particular diagrammatic representations, allegedly contribute to new insights in mathematics. Here I explore the phenomenon of a “free ride” and to what extent it occurs in mathematics. A free ride, according to Shimojima (Artif Intell Rev 15: 5–27, 2001), is the property of some representations that whenever certain pieces of information have been represented then a new piece of consequential information can be read off for free. I will take Shimojima’s (informal) framework as a tool to analyse the occurrence and properties of them. I consider a number of different examples from mathematical practice that illustrate a variety of uses of free rides in mathematics. Analysing these examples I find that mathematical free rides are sometimes based on syntactic and semantic properties of diagrams.
| Original language | English |
|---|---|
| Journal | Synthese |
| Volume | 199 |
| Issue | 3-4 |
| Pages (from-to) | 10475-10498 |
| Number of pages | 24 |
| ISSN | 0039-7857 |
| DOIs | |
| Publication status | Published - Dec 2021 |
Keywords
- Diagrams
- Free rides in mathematics