We have previously proposed that trials of social interventions can be done within a "realist" research paradigm. Critics have countered that such trials are irredeemably positivist and asked us to explain our philosophical position.We set out to explore what is meant by positivism and whether trials adhere to its tenets (of necessity or in practice) via a narrative literature review of social science and philosophical discussions of positivism, and of the trials literature and three case studies of trials.The philosophical literature described positivism as asserting: (1) the epistemic primacy of sensory information; (2) the requirement that theoretical terms equate with empirical terms; (3) the aim of developing universal laws; and (4) the unity of method between natural and social sciences. Regarding (1), it seems that rather than embodying the epistemic primacy of sensory data, randomised controlled trials (RCTs) of social interventions in health embrace an anti-positivist approach aiming to test hypotheses derived deductively from prior theory. Considering (2), while some RCTs of social interventions appear to limit theorisation to concepts with empirical analogues, others examine interventions underpinned by theories engaging with mechanisms and contextual contingencies not all of which can be measured. Regarding (3), while some trialists and reviewers in the health field do limit their role to estimating statistical trends as a mechanistic form of generalisation, this is not an inevitable feature of RCT-based research. Trials of social interventions can instead aim to generalise at the level of theory which specifies how mechanisms are contingent on context. In terms of (4), while RCTs are used to examine biomedical as well as social interventions in health, RCTs of social interventions are often distinctive in using qualitative analyses of data on participant accounts to examine questions of meaning and agency not pursued in the natural sciences.We conclude that the most appropriate paradigm for RCTs of social interventions is realism not positivism.