Abduction: the missing link between deduction and induction. A comment on Ormerod's 'rational inference: deductive, inductive and probabilistic thinking'

I was interested to read Ormerod’s (2010) paper on Rational Inference: Deductive, Inductive and Probabilistic Thinking for it covers an important, but seldom discussed, topic—the nature of rational, inferential thinking and its relationship to operational research (OR). In the paper, three forms of reasoning are discussed: deduction, in which particular instances are deduced to follow from general laws or assumed premises; induction, in which general laws are induced from particular examples or instances; and a more recent approach, probabilistic and particularly Bayesian reasoning, in which evidence is used to alter the probabilities associated with a particular hypothesis, that is, to confirm or disconfirm it. However, in this viewpoint I wish to draw attention to another form of inferential reasoning that I believe is of great practical relevance, and that can provide a link between deduction and induction, as well as being compatible with Bayesianism. This approach is known as abduction, or retroduction and was originally developed by the American pragmatist philosopher C.S. Peirce (1931– 1958; Psillos, 2009) and has been adopted more recently as the heart of the philosophy of science known as critical realism (CR) (Bhaskar, 1978; Bhaskar, 1979; Mingers, 2000). It is somewhat surprising that Ormerod made no mention of this since he himself wrote a paper on pragmatism and OR (Ormerod, 2006) which included a section on Peirce who was in many ways the founder of pragmatism. On re-reading this paper, it is apparent that Ormerod mis-describes Peirce’s views on inference, a point we shall come back to at the end. As we have said, deduction involves going from a general premise to a particular conclusion. Peirce’s own example is (2.623, all references to Peirce show the volume and section in the collected works):