In the philosophical part of nnLab we discuss higher category theory and its repercussions in philosophy. More widely, the entries on philosophy in nLab should also contain philosophy of mathematics in general, and of logic and foundations in particular. As it is usual for philosophy and the study of thought, it is usefully carried on via study of historical thinkers and their ideas, hence some idea-related aspects of the history of mathematics are welcome.


There are many articles which are not directly philosophical, but rather essays on general mathematics, often opinion pieces on what is important and so on. Although mathematicians will often speak of their ‘philosophy’, this is not philosophy per se, but it may be relevant to an understanding of the nature of mathematics through its practice, see, for instance, development and current state of mathematics.

Idea of relevance of higher categories

Philosophical interest in n-categories may be characterised as belonging to one of two kinds.

  • Metaphysical: The formation of a new language which may prove to be as important for philosophy as predicate logic was for Bertrand Russell and the analytic philosophers he inspired (see, e.g., Corfield 20).

  • Illustrative of mathematics as intellectual enquiry: Such a reconstitution of the fundamental language of mathematics reveals much about the discipline as a tradition of enquiry stretching back several millennia, for instance, the continued willingness to reconsider basic concepts (see, e.g., Corfield 12, Corfield 19).




“Mathematical wisdom, if not forgotten, lives as an invariant of all its (re)presentations in a permanently self–renewing discourse.” (Yuri Manin)

To categorify mathematical constructions properly, one must have understood their essential features. This leads us to consider what it is to get concepts ‘right’. Which kind of ‘realism’ is suitable for mathematics? Which virtues should a mathematical community possess to further its ends: a knowledge of its history, close attention to instruction and the sharing of knowledge, a willingness to admit to what is currently lacking in its programmes?

Philosophical positions




Some philosophical aspects of the role of category theory are touched upon in some parts of the introductory paper


category: philosophy

Last revised on October 9, 2021 at 02:47:26. See the history of this page for a list of all contributions to it.