What is mathematics? A classification based on universals by Eduardo Bellani
I find that it is hard for me to motivate myself to learn a subject that one cannot define. So I made an effort to define mathematics, and the best source I have ever found was (Franklin 2014).
To sum up my views on the topic: at the core of philosophical inquiry, one finds a deep division into 2 opposites as their regard to the universals, realism and nominalism(and its kantian variant, conceptualism)(De Wulf 1911). Taking that into consideration and (Franklin 2014), Here is a taxonomy of definitions for what is mathematics:
Realism
- Platonism
- Knowledge of another dimension
- Aristotelianism
- Knowledge of instantiation of universals and structure (parts to whole)
Nominalism
- Language
- A Language of science
- Logicism
- A process to guide inferences
- Formalism
- The manipulation of uninterpreted symbols
References
De Wulf, Maurice. 1911. “Nominalism, Realism, Conceptualism.” The Catholic Encyclopedia, Vol 11. https://www.newadvent.org/cathen/11090c.htm.
Figure 1: Venerabilis nominalium incaeptor (the venerable fouder of nominalism)