Purpose: Much of the contemporary methodological literature tends to be self-referential and frequently ignorant of the breadth and depth of philosophical assumptions underpinning various methodological positions. Without a clear understanding of the philosophical underpinnings, logically deriving applicable validity criteria becomes very difficult (if not impossible). As a result, the purpose of this paper is to present a critical review of historical and more recent philosophical arguments for qualitative, quantitative, and mixed methods research in social science. Design/methodology/approach: A targeted review of seminal philosophy of science papers dealing with ontological and epistemological assumptions of, and relation between, natural and social science. Findings: The paper highlights the link between ontological/epistemological assumptions and methodological choices in social science. Key differences between the natural and social science are discussed and situated within the main paradigms. Originality/value: The paper draws attention to a range of difficulties associated with the adoption of the natural sciences and the related positivist approaches as a role model for work in the social sciences. Unique contributions of interpretive and critical approaches are highlighted. The paper may be of value to scholars who are interested in the historical context of the still-ongoing qualitative-quantitative debate.