Kitcher's philosophical approach has moved from the reflection on the nature of mathematical knowledge to an explicit social concern about science, because he considers seriously the relevance of democratic values to scientific activity. Focal issues in this trajectory – from
the internal perspective to the external – have been naturalism and scientific progress, which includes studies of the uses of scientific findings in the social milieu. Within this intellectual context, the chapter pays particular attention to his epistemological and methodological evolution.
The analysis of Philip Kitcher's contents on progress begins with mathematics, a conception that follows a naturalist perspective. Thereafter, the growth of science comes to the front line, an advancement that he views according to realism and cognitive naturalism. Later, the social concern
about science receives a visible consideration, when his vision of scientific undertaking is characterized following modest realism and social naturalism. After these four steps (philosophical context, progress in mathematics, the growth in science, and the social concern about science), there
is an analysis of his philosophical-methodological framework in retrospective. This is continued by the presentation of the origins of this book and the bibliography related to this thinker.