This purpose of this paper is to indicate how one should understand John Dewey's attention to and appreciation for the methods and views of modern science. Against the idea that Dewey is a believer in the methods and views of modern science--which would make his philosophy into a form of positivism or scientism--the author argues that Dewey's ambition has been to show the limits of science, both in terms of scientific knowledge and in terms of scientific rationality. Although Dewey has nothing against science as such, his work is motivated by a concern about the impact of a particular version or interpretation of modern science, namely, the one which says that modern science is the only way towards true knowledge about the world. Dewey shows that there is no philosophical justification for the hegemony of modern science. In this regard Dewey's philosophy can be seen as a radical critique of the hegemony of modern science. (Contains 35 notes.)