The paper discusses Toulmin's substantial (jurisprudential) model of argument, as set out in The Uses of Argument (1958), in juxtaposition with his considerations concerning scientific discovery and scientific arguments, as presented in The Philosophy of Science (1953). The author finds Toulmin's search for understanding the nature of science to be a forerunner of his later concep- tion of argument. In addition, he claims that the latter displays much more accurately the 'logic' of both scientific discovery and the arguments in science than the patterns of formal (both inductive and deductive) logic. For actually, in Toulmin's view, no logic in the traditional, formal sense can be ascribed to discovery and scientific arguments - despite all the mathematical techniques they employ. Thus neither the neo-positivistic account nor even the Popperian one can do justice to their specific character. Although the Toulminian model of argument cannot be treated, in a strict sense, as a methodological instruction, it plays an explicatory role, throwing some light on our understanding of scientific enterprises and their rationality. In fact, the author finds Toulmin's concept of argument to be the core of his overall conception of rationality, and the considerations about science to be one aspect of this conception.