# On the Ability to Reason Backwards

“In solving a problem of this sort, the grand thing is to be able to reason backwards. That is a very useful accomplishment, and a very easy one, but people do not practice it much. In the everyday affairs of life, it is more useful to reason forwards, and so the other comes to be neglected. There are fifty who can reason synthetically for one who can reason analytically. Most people, if you describe a train of events to them, will tell you what the result would be. They can put those events together in their minds, and argue from them that something will come to pass. There are few people, however, who, if you told them a result, would be able to evolve from their own inner consciousness what the steps were which led up to that result. This power is what I mean when I talk of reasoning backwards, or analytically.”

— Thus spoke the famous detective Sherlock Holmes to his companion Dr. John H. Watson, in describing the analytical device of reasoning backwards.

This method of retrogate analysis is a reasoning technique that starts with empirically-derived data and then reconstructs plausible conditions in order to deduce what had happened. An inferred explanation is attempted by interpreting observed phenomena and organizing them under a predicate. It may therefore be described as inference to the best/possible explanation. Observed data is used to infer the hypotheses that make the best explanatory description. If C is a collection of data/facts and A is a hypothesis that explains those facts, then there is plausible reason to accept A as true, given that no other hypothesis can explain the observed facts as well as A does.

The U.S. philosopher and logician Charles Peirce defined this process of “forming an explanatory hypothesis” as abduction. “The first starting of a hypothesis and the entertaining of it, whether as a simple interrogation or with any degree of confidence is an inferential step which I propose to call abduction. This will include a preference for any one hypothesis over others which would equally explain the facts”, writes Peirce. He expresses the emphasis of abduction as the only logical operation to introduce new hypotheses or new ideas. It is a form of presumptive thinking “in which the observed facts show that the truth is similar to the fact asserted in the conclusion”. If, for instance, the logician comes across a room and finds a number of bags that all contain different kinds of beans. If the table has a handful of white beans on it and one of the bags contains only white beans, then employing the presumptive inference of the process of abduction, there is reason for the logician to construct a plausible hypothesis that the handful of beans was taken from that bag.

According to Peirce, abductive reasoning is just one step in the process of inference. In order to validate the plausible hypothesis generated, the abductive process must be preceded by induction and followed by deduction. In order to validate abduction, the process of induction compares predicted and actual results. In this manner, abduction connects deduction and induction such that its “deductive consequences can be tested by induction”. Since abductions are largely conjectural, the statistical analysis of the inductive step provides an objective probability. Induction is therefore “this kind of reasoning which from what is true of a part, concludes what is true from a whole.” It is a self-correcting method that allows us to extract what we know and generalise it to determine what we do not know. Deduction explicates the predictive consequences of the resulting hypotheses. “From its abductive suggestion, deduction can draw a prediction which can be tested by induction”, writes Pierce. Abduction is complemented by the predictive power of deduction and by the corrective power of induction.

Peirce says, “The deductions which we base upon the hypothesis which has resulted from Abduction produce conditional predictions concerning our future experience. That is to say, we infer by Deduction that if the hypothesis is true, any future phenomena of certain descriptions must present such and such characters. We now institute a course of quasi-experimentation in order to bring these predictions to the test, and thus to form our final estimate of the value of the hypothesis, and this whole proceeding I term induction”.

Peirce recognized the abductive method of inference as the only logical operation to come up with new ideas. In examining the works of Johannes Kepler, he writes: “he [Kepler] found that the observed longitudes of Mars, which he had long tried in vain to get fitted with an orbit, were (within the possible limits of error of the observations) such as they would be if Mars moved in an ellipse. The facts were thus, in so far, a likeness of those of motion in an elliptic orbit. Kepler did not conclude from this that the orbit really was an ellipse; but it did incline him to that idea so much as to decide him to undertake to ascertain whether virtual predictions about the latitudes and parallaxes based on this hypothesis would be verified or not. This probational adoption of the hypothesis was an Abduction. An Abduction is Originary in respect to being the only kind of argument which starts a new idea.”.

Because it is a form of presumptive thinking that is largely conjectural, abductive reasoning is a weak form of inference in itself in that it is not certain. However, it is the only step that can lead to innovative creativity, the ideas of which are consequently subjected to the filtering funnel of experimentation, made possible by the process of induction.

Featured image: Sherlock Holmes and John Watson – Sidney Paget Illustrations