Formalism

Abstract

The great ideas and tools that intuitionism and logicism discovered in solving the crisis in mathematics were gathered by formalism in the concept of the formal axiomatic system. Later, formal axiomatic systems led to seminal discoveries about axiomatic theories and mathematics in general. Particularly important to us is the fact that formal axiomatic systems also gave rise to the need for a deeper understanding of the concepts of algorithm and computation. To appreciate this need, we devote this chapter to the understanding of formal axiomatic systems in general and describe those particular formal axiomatic systems that played a crucial role in the events to follow.

The form of something is its shape and structure. Something that is done in a formal way has a very ordered, organized method and style. Formalism is a style in which great attention is paid to the form rather than to the contents of things.