The aim of the paper is to expose the main characteristics of the philosophy of science as developed in classical pragmatism. The author differentiates between philosophy of science in narrow (internalist, epistemological) and broader (externalist, sociocultural) senses. Classical pragmatist philosophy of science embodies the integration of social, historical, anthropological, axiological, ethical and other aspects of science as substantial for its philosophical understanding. The relation between pragmatist philosophy and science is complex, both respectful and critical. It is neither anti-scientistic nor scientistic philosophy. To understand it, the author provides the reconstruction of the key historical stages of the relations between classical pragmatism and logical positivism/empiricism. Further, the overall outline of the main features of the conceptions of science in Ch. S. Peirce, W. James and J. Dewey with the focus on the concept of inquiry and its sociocultural context is provided. This all adds up to the conclusion that the core of the classical pragmatist philosophy of science is the Deweyan “cultural naturalism”.