Abductive Inference and C. S. Peirce: 150 Years Later

An iconoclastic philosopher and polymath, Charles Sanders Peirce (1837-1914) is among the greatest of American minds. In 1872, Peirce conducted a series of experiments to determine the distribution of response times to an auditory stimulus, which is widely regarded as one of the most significant statistical investigations in the history of nineteenth-century American mathematical research (Stigler, 1978). On the 150th anniversary of this historic experiment, we look back at Peirce's view on empirical modeling (especially his views on abductive inference) through a modern statistical lens. `AIM' of the present study and its utility for economists: Abductive inference plays a fundamental role in empirical scientific research as a tool for discovery and data analysis. Heckman and Singer (2017) strongly advocated `Economists should abduct.' Arnold Zellner (2007) stressed that `much greater emphasis on reductive [abductive] inference in teaching econometrics, statistics, and economics would be desirable.' But, currently, there are no established theory or practical tools that can allow an empirical analyst to abduct. My goal in this paper is to introduce some new principles and concrete procedures to the Economics and Statistics community. Using Peirce's data, it is shown how empirical analysts can abduct in a systematic and automated manner. I termed the proposed approach as Abductive Inference Machine (AIM).