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Cambridge Lectures on Reasoning and the Logic of Things: Types of Reasoning

For the sake of brevity I have abstained from speaking of the argument from analogy, which Aristotle terms [paradeigma]. I need hardly say that the word analogy is of mathematical provenance This argument is of a mixed character being related to the others somewhat as the Fourth Figure of syllogism is related to the other three.

…a leading principle of maximum abstractness may be termed a logical principle.

We see three types of reasoning. The first figure empraces all Deduction whether necessary of probable. [—] The third figure is Induction by means of which we ascertain how often in the ordinary course of experience one phenomenon will be accompanied by another. No definite probability attaches to the Inductive conclusion, such as belongs to the Deductive conclusion; but we can calculate how often inductions of given structure will attain a given degree of precision. The second figure of reasoning is Retroduction. Here, not only is there no definite probability to the conclusion, but no definite probability attaches even to the mode of inference. We can only say that the Economy of Research prescribes that we should at a given stage of our inquiry try a given hypothesis, and we are to hold to it provisionally as long as the facts will permit. There is no probability about it. It is a mere suggestion which we tentatively adopt.

This probable reasoning in the second figure is, I apprehend, what Aristotle meant by {apagögé}. There are strong reasons for believing that in the chapter on the subject in the Prior Analytics, there occurred one of those many obliterations in Aristotle’s MS. due to its century long exposure to damp in a cellar, which the blundering Apellicon, the first editor, filled up with the wrong word. Let me change but one word of the text, and the meaning of the whole chapter is metamorphosed in such a way that it no longer breaks the continuity of the train of Aristotle’s thought [—] Supposing this view to be correct, {apagögé} should be translated not by the word abduction, as the custom of the translators is, but rather by reduction or retroduction. In these lectures I shall generally call this type of reasoning retroduction.

I first gave this theory in 1867, improving it slightly in 1868. In 1878 I gave a popular account of it in which I rightly insisted upon the radical distinction between Induction and Retroduction. In 1883, I made a careful restatement with considerable improvement. But I was led away by trusting to the perfect balance of logical breadth and depth into the mistake of treating Retroduction as a kind of Induction. [—] In 1892 I gave a good statement of the rationale of Retroduction but still failed to perceive the radical difference between this and Induction, although earlier it had been clear enough to my mind.

… the second figure reads:

Anything of the nature of M would have the character {p}, taken haphazard,
S has the character {p};
.·. Provisionally, we may suppose S to be of the nature of M.

Still more convenient is the following conditional form of statement:

If {m} were true, {p}, {p}’, {p}” would follow as miscellaneous consequences -
But {p}, {p}’, {p}” are in fact true;
.·. Provisionally, we may suppose that {m} is true.

This kind of reasoning is very often called adopting a hypothesis for the sake of its explanation of known facts.