Question

A long time ago, I read something about three stages in the development of a scientific or mathematical theory, namely the naive, the formal, and the critical phase. This appeared very natural to me, e.g. with respect to mathematical theories like set theory or category theory where people explicitly use the word naive.

Later I tried to find out two who this goes back, and for a while I thought it must be an idea from Kuhn's Structure of Scientific Revolutions, but he is not explicitly using these words I think?

Is there a well known work that makes this naive/formal/critical distinction explicit?

Answer 1

The concept of three stages in theory development, namely the naive, formal, and critical phase, is not explicitly discussed in Kuhn's Structure of Scientific Revolutions. However, this distinction is made explicit in works like How to Do Theory by Wolfgang Iser and can also be observed in the history of philosophy.

Step-by-step explanation:

The idea of three stages in the development of a scientific or mathematical theory, namely the naive, the formal, and the critical phase, is not explicitly discussed in Kuhn's Structure of Scientific Revolutions. However, there is a well-known work that makes this distinction explicit: How to Do Theory by literary critic Wolfgang Iser. In this work, Iser suggests that the natural sciences operate under hard-core theories, which are problem-solving and governed by general laws, while the humanities use soft-core theories, which are more descriptive and rely on metaphors and images.

The concept of three stages in theory development can also be seen in the history of philosophy, such as in the progression from mythopoetic thought to primitive scientific thinking and then to philosophy as rational inquiry. During this progression, thinkers moved from relying on belief to basing their thinking on reason and critically examining cosmogony.

Overall, while the concept of three stages in theory development is not explicitly discussed in Kuhn's work, it can be found in other works like How to Do Theory and in the history of philosophy.