What Is an Analogy? Reasoning by Resemblance and Where It Breaks

An analogical argument identifies a source, a target and a set of shared features, and concludes that a further feature of the source is probably present in the target. Its strength depends on several things that can be assessed. The number of relevant similarities matters, and relevance matters far more than number, since a hundred trivial resemblances are worth less than one that bears on the feature being inferred. The number and relevance of known differences matters equally, since a disanalogy in exactly the respect that produces the feature in the source destroys the argument. The diversity of the cases supporting the analogy matters, since a pattern holding across varied instances is stronger. And the modesty of the conclusion matters, since a weaker claim is easier to support. Analogical arguments are never deductively valid, which is not a defect since they are not meant to be, and they range from worthless to compelling depending on those factors.

The history of science includes analogies that were substantially productive:

• •Harvey reasoning from pumps and valves to the circulation of blood, which is a mechanical analogy that turned out to be nearly literal
• •Darwin arguing from artificial selection by breeders to natural selection, which is the central argumentative move of the theory and is explicitly analogical
• •The analogy between light and sound as waves, which was productive while being wrong in important respects and which led to the search for a medium that did not exist
• •Rutherford's solar system model of the atom, which was useful, gave the right general picture and is wrong in detail
• •The comparison between electrical current and fluid flow, which underlies most introductory teaching and most engineering intuition
• •Biological analogies in economics and social theory, which have been productive and have repeatedly been pushed further than the resemblance supports

The failure modes are identifiable and most bad analogies fit one. Selecting resemblances after choosing the conclusion means the argument establishes nothing, since almost any two things resemble each other in some respect. Ignoring a relevant disanalogy is the commonest substantive error, particularly when the difference concerns exactly the mechanism producing the feature in the source. Treating the analogy as an explanation rather than a suggestion confuses a heuristic with an account, which is what happens when a model is mistaken for the thing modelled. Extending an analogy beyond the range where it was tested is the standard scientific failure and is why the wave model of light produced an unnecessary ether. In argument, false analogies function rhetorically by importing the emotional weight of the source, which is why comparisons to historical atrocities are so common and so rarely informative. And an analogy can be technically apt and still unhelpful if the target is better understood directly.

Despite the failure modes, reasoning by resemblance is not optional. Genuinely novel situations offer nothing else, since a case with no precedent cannot be reasoned about from precedent and must be approached through whatever resembles it. Legal reasoning in common law systems is explicitly analogical, deciding a new case by reference to the cases it most resembles and distinguishing those it does not, and the craft of the discipline consists largely in arguing about which resemblances matter. Medical diagnosis reasons from the presentation to comparable cases. Engineering reasons from designs that worked. Teaching depends on it entirely, since a new concept is introduced through something familiar and there is no other route. Cognitive research indicates that analogical mapping is a basic operation in human thinking rather than a technique layered on top of it. The practical conclusion is not to avoid analogies but to state them explicitly, since an analogy made visible can be examined and one left implicit cannot.

Strength depends on the relevance of the similarities rather than their number, on known differences in exactly the respect that matters, and on how modest the conclusion is. Darwin's argument from breeders to natural selection is explicitly analogical. The standard failure is extending an analogy beyond where it was tested, which is what produced the search for an ether. Stating an analogy explicitly is what allows it to be checked.