Formal Methods for Philosophy
These advances in logic, though stimulated by the need to improve the rigour of mathematics, were seen to have fundamental philosophical consequences. They played a central role in the development of analytic philosophy during the twentieth century. While in the second half of this century the view that philosophy is intimately related to logic was supplanted by methods based on the analysis of ordinary language, and doctrines which rejected any other role for philosophy, we are now seeing a revival of interested in the kind of analytic philosophy which grew from the advances in formal techniques.
Two books of relevance here are:
Philosophy for Formal Methods
Formal methods are generally thought of as essentially mathematical in nature. Mathematicians this century have, by and large, found it possible to do their work in the context of classical set theory without much concern for the fine details of how this system is formalised, or for whether this foundation can or should be improved.
In computer science, set theory has not achieved this kind of status. Where mathematical methods have been adopted without concern for foundations or for formality they are often conducted in a manner consistent with the classical set theoretic context. However, where theoreticians have taken an interest in foundations, they have often adopted and/or advocated radical alternatives to classical set theory. Constructive systems have often been adopted, and there is considerable interest in the use of category theory in a variety of ways, including as a basis for new foundations for computer science and for mathematics.
The stimulus provided by these tendencies in theoretical computing lends interest to philosophical studies which might contribute to objective evaluation of the technical alternatives available.