An analogy is a claim that two things, \(X\) and \(Y\) are ‘the same’ with respect to some aspect \(P\). As popularly deployed, analogies come in a variety of styles:

• metaphor – “\(X\) is \(Y\) (implicitly: with respect to \(P\))”; commonly idiomatic

  • e.g. “the news is music to my ears”
  • e.g. “time is money”
  • e.g. “my memory is foggy”
  • e.g. “the building is a maze”

• simile – “\(X\) is like \(Y\) (implicitly: with respect to \(P\))” or “\(X\) is as \(P\) as \(Y\)”

  • e.g. “the desert was like an ocean of sand”
  • e.g. “the empty suitcase is as light as a feather”
  • e.g. “the paper is as white as snow”

• allegory – a story about the \(P\) of \(X\) that parallels the \(P\) of \(Y\)

  • e.g. the story “Animal Farm” by George Orwell is about the corruption of a animal-managed farm that parallels the corruption of communism in the Russian Revolution of 1917
  • e.g. Aesop’s fables, such as the fable of “the fox and the grapes” which parallels the propensity to publically deride that which one desires but cannot achieve
  • e.g. the Star Trek episode “A Private Little War” which parallels the US involvement in the Vietnam War

• anecdote – claim about the \(P\) of \(X\) as an example of the \(P\) of \(Y\)

  • “Here is an example of a young mother who is worrying about how to secure her children’s next meal. Poor people in this neighborhood have it hard.”
  • “Here is my experience in the field of underwater basket-weaving. You can expect to have a similar experience to mine.”

Analogy can be a useful way to communicate an intuition about the \(P\) of \(Y\) be appealing to an intuition about the \(P\) of \(X\). As an example of both analogy’s usefulness and of anecdote:

For teaching about electric current in introductory physics courses, an often useful analogy is that between electric current in a circuit and water current in a pipe. A circuit is like a pipe system, voltage is like pressure, and resistance is like pipe diameter. Since the flowing of water in a pipe is immediately intuitive, using this analogy allows some of that intuition for electric circuits. The difficult, complicated, and unfamiliar behavior of electricity in circuits can be roughly reorganized to follow different abstract but intuitive rules.

The analogy between electric circuits and water pipes is appealing, especially before a detailed understanding of the underlying electrodynamics. But an analogy can only go so far if the analogized things are not identical (in which case we would have the identity analogy). Electric circuits are like water pipes in a few high-level respects, but not in the vast majority of other respects. Why doesn’t electricity ‘spill out’ of a circuit with loose ends?

Overall, the water pipes analogy gives you an intuition about electric current, but that intuition didn’t actually teach you anything about electric current (no matter how much it may feel like you’ve learned something). Even the analogical claim that electric circuits are like water pipes in a few particular respects is not really something about electric circuits themselves, but extrinsically about the relationship between water pipes and electric circuits.

I think that this observation is very often covertly sidestepped or just ignored. Analogies so commonly are given as if they were arguments and even explanations – all the time! Generally, there are two main tactics:

• “The \(P\) of \(X\) is that because \(X\) is like \(Y\) (implicitly: with respect to \(P\)) and the \(P\) of \(Y\) is that”
  • The analogy “\(X\) is like \(Y\) with respect to \(P\)” is used as if it were an explanation, but it explains nothing about \(X\) itself and relies purely on the extrinsic comparison between \(X\) and \(Y\)
  • e.g. “The Vietnam War is bad because the conflict in Star Trek’s ‘A Private Little War’, which critiques the Vietnam War, is bad”
• ”\(X\) is like \(Y\) with respect to \(Q\) because \(X\) is like \(Y\) (implicitly: with respect to \(P\)).”
  • The conclusion sneaks in a new aspect \(Q\) that may look superficially similar or related to \(P\), but is not implied by \(P\).
    • e.g. “A country’s citizenry is like a big family, so a country should not let in anyone who is not like family.”
    • e.g. “Computers are just big fancy calculators, so we shouldn’t expect a computer to every be as intelligent as a human.”

TODO: more examples of bad analogical arguments

I’ve argued that these argument tactics are misuses of analogy, but to be clear they are only misuses when they are used in place of good arguments. It is so easy to use analogy in place of arguments because analogies are very persuasive, satisfying, and by nature intuitive. But analogical arguments have these attractive qualities regardless of whether they are being used to support a good or a bad argument.

My warnings given, analogy does have many good uses, including in arguments. I began with the claim that “Analogy can be a useful way to communicate an intuition about the \(P\) of \(Y\) be appealing to an intuition about the \(P\) of \(X\),” which is still true even if the analogy doesn’t at all justify that or explain why the \(P\) of \(X\) and the \(P\) of \(Y\) are the same. My ideal use of analogy is to first demonstrate and explain how the \(P\) of \(X\) is the same as the \(P\) of \(Y\), and then explain how this gives rise to an intuitive analogy between \(X\) and \(Y\) with respect to \(P\).

Many analogies reflect a deeper truth about a shared nature of \(X\) and \(Y\) that accounts for why the \(P\) of \(X\) is the same as the \(P\) of \(Y\). From the observation that electric circuits behave similarly to water pipes in the mentioned respects, to learn what laws of nature are acting similarly on these two very different kinds of systems is really to learn something new about circuits and pipes, as well as learning something more general about all systems that are acted upon by natural laws in the same way.

This process of generalization is very powerful and the center of what most people consider the pursuit of interesting knowledge. What makes information interesting is it’s ability to explain many different aspects of a domain in a concise way. The most interesting mathematical theorems lend insight into a large range of interesting questions. The most interesting algorithms demonstrate strategies that abstract over large classes of tasks. The most interesting literature/film/etc. reflect situations that many people experience in many different ways.

But what is the difference between analogy and generalization? Well, analogy is a rhetorical style of generalization – one that seems particularly intuitive to most people. However, as it is used, analogy is only the claim of generalization, rather than the process of developing and accounting for the generalization.

Consider Aesop’s fable of “the fox and the grapes”. The story is entertaining and makes sense because, as a human audience, we already have an intuitive understanding of the sense of spite the fox ends up feeling because it cannot get the grapes. The story did not instill nor explain that understanding; the story embodies the claim that the phenomenon is common and natural, and little else. Perhaps the story highlights an observation that the claim seems to be true, but even that relies on the fact that the audience can instinctually derive the claim from the story.

Consider George Orwell’s “Animal Farm”. The story is not just the analogical claim that the Russian Revolution’s communist ideals (and, perhaps, optimistic communist ideals in general) were corrupted. The story gives a step-by-step account for how, gradually, the populace of well-meaning and optimistic revolutionaries are taken advantage of leaders who know how to say just what they want to hear in the right style of language in order to get away with injustice. The story itself is an abstract explanation for how the analogy between the animal farm and the revolutionary communists holds – importantly, the story is not just an assertion that the analogy holds. Reading the story can provide some understanding of how optimistic revolutionary movements can be corrupted, which is made intuitive and non-specific by the allegory to a managable set of characters who’s cartoonish actions are abstractions of the complex situations that occur in real-world revolutions.