From the early nineteenth century, the successful use of fossils in stratigraphy oriented paleontology (and particularly the study of fossil invertebrates) towards geology. The consequent marginalising of biological objectives was countered in the twentieth century by the rise of 'Paläobiologie', first in the German cultural area and only later, as 'paleobiology', in the anglophone world. Several kinds of paleobiological research flourished internationally after the Second World War, among them the novel field of 'paleoecology'. Within this field there were attempts to apply functional morphology to the problematical cases of fossil organisms, for which functions cannot be observed directly. This article describes the origins of the kind of functional inference for fossils that I proposed in 1961 as the method of 'paradigms' (a year before Thomas Kuhn made that word more widely familiar with a quite different meaning). Here I summarize some of my 'worked exemplars', which were intended to show the paradigm method in action. These case-studies were all taken from the paleontologically important phylum of the Brachiopoda, but the method was claimed to have much wider implications for the interpretation of the fossil record in terms of adaptive evolution. This article takes the history of the paradigm method as far as the late 1960s. I hope to trace, in a sequel, its ambivalent fate during the 1970s and beyond, when for example Gould's critique of 'the adaptationist programme' and the rise of computer-based quantitative methods for the evolutionary interpretation of the fossil record led to the relative eclipse of functional morphology in paleontology.