Weak analogy

The password and the lock

“A password is like the lock on your front door. A basic lock keeps out the casual passerby, and nobody needs a vault door on a house. So a short, simple password is fine.”

Passwords and locks really are alike in some ways: both keep people out, and both can be stronger or weaker. But the conclusion depends on who is trying to get in, and how, and there the cases differ completely. A burglar has to stand at one door and try it by hand. Someone guessing passwords can often use software to try huge numbers of guesses without ever being seen. The similarity is real but beside the point, and the relevant difference goes unmentioned. This is the clear-cut case.

A precedent that doesn’t carry over

A product manager says: “When we redesigned the app two years ago, people complained for about a month and then got used to it. This redesign is getting complaints too, so we can expect them to fade the same way.”

This sounds like sound reasoning from experience, and it compares two very similar cases: the same app, the same users, another redesign. But the earlier complaints faded because nothing people needed had gone away; the buttons had simply moved. Suppose this redesign removed the export feature many users rely on. Then the feature that explained the earlier outcome is missing from the new case, and all the other similarities don’t make up for it. Juthe’s account puts it this way: in the source case, some feature has to be what determines the outcome, and the new case needs a counterpart to that feature, not just a general resemblance.

Ignoring an equally good analogy

“Tipping the person who delivers your takeout is just like tipping a server in a restaurant: someone brings you food. So you should tip the same percentage.”

The analogy isn’t foolish: in both cases a person brings food someone else cooked. But another case is about as close: paying a delivery fee for a package, where nobody expects a tip. Both comparisons share “someone brings you something you ordered”. An argument that offers one analogy and ignores an equally similar one pointing the other way hasn’t yet shown which case this is more like in the respect that decides the question, such as how the person is paid, or what the fee covers. That might well favor tipping, but the argument has to say so.

Douglas Walton’s basic scheme for argument from analogy, which he takes from Walton, Reed and Macagno (2008), sets out the form and three critical questions that test it:

On this view the argument is defeasible: it’s a reasonable argument that shifts some weight toward the conclusion, and it can be defeated if a critical question can’t be answered. A weak analogy is one that doesn’t survive the questions.

André Juthe makes a point that applies to any premise of bare similarity: “Everything is similar to everything in some respect and dissimilar in some other respect, therefore you cannot infer anything from mere similarity as such.” On his account, a good analogy needs two things. Some element of the first case must determine the property being concluded (causally, functionally, or in some other way), and the second case must have a corresponding element. The password example fails the second condition, and so does the redesign.

• Superficial similarity: the two things look or sound alike, but the resemblance has no connection to the conclusion. “Wasps are striped, flying, stinging insects, just like bees, so they must make honey too.”
• A relevant difference left out: the cases really are alike in many ways, but differ in the one that explains the outcome (CQ1).
• A counter-analogy ignored: another case is just as similar and points the other way (CQ3).
• Stretching a good analogy: an analogy that holds for one purpose is pushed into respects it was never meant to cover.

Some logicians classify Two wrongs make a right as a misuse of argument from analogy (see that entry): someone else’s wrong is offered as a case like yours, so yours should be treated the same way. The precedent form of the Slippery slope also relies on an analogy between this case and the next.

What it’s called. Logic references use several names for the same error. The Stanford Encyclopedia of Philosophy calls it the fallacy of faulty analogy; Bradley Dowden’s list in the Internet Encyclopedia of Philosophy uses false analogy, with weak, questionable and improper analogy as other names. This site uses “weak analogy” because it names the point: analogies come in degrees of strength, and David Hume described the failing end of that range as “a very weak analogy, which is confessedly liable to error and uncertainty”.

Not the same error: hasty generalization. A Hasty generalization goes from some members of a group to the rest of it. An analogy goes from one case to another particular case, without necessarily passing through any generalization. Aristotle already distinguished the two: his “argument from likeness” “resembles induction, but is not the same thing”. Juthe (2005) similarly argues that arguments by analogy are different from ordinary inductive or deductive arguments, with distinct features of their own.

Most of what we know about unfamiliar situations comes from comparing them with familiar ones. The Stanford Encyclopedia of Philosophy‘s entry on analogical reasoning collects the standard textbook guidelines, and the one it calls all-important is relevance: whether the similarities and differences bear on the conclusion, not just how many there are. An analogy holds up when:

• The shared features are the ones that produce the outcome. Similarities in cause or structure count for more than surface resemblances.
• No known difference undoes them. Differences in features that have nothing to do with the conclusion don’t weaken it.
• The conclusion is modest. “This will probably behave similarly” or “this is worth checking” asks less of an analogy than “this will certainly happen”.
• Other comparisons point the same way. Several independent analogies supporting the same conclusion strengthen it.
• It’s offered as an explanation, not an argument. An analogy used to make something easier to picture isn’t claiming the two things are alike in every respect.

The test: is the feature the two cases share the reason the conclusion holds in the first case?

Two pans

“My cast-iron pan rusted when I left it soaking overnight. This carbon-steel pan is also mostly iron, and it isn’t seasoned yet. I shouldn’t leave it soaking either.”

The two pans differ in shape, weight, brand and price. None of that matters, because what made the first pan rust (bare iron left in water) is present in the second one too. The conclusion is also modest: it’s about what to avoid, not a prediction about exactly what will happen. That’s the shared features produce the outcome condition, together with the conclusion is modest.

“Think of voltage like water pressure”

A physics teacher says: “Think of voltage like water pressure in a pipe. More pressure pushes more water through; more voltage pushes more current through.” A student objects: “That’s a false analogy. Electricity isn’t wet, and wires aren’t hollow.”

The teacher isn’t arguing that electricity is a liquid, or that anything true of water is true of current. The analogy is there to make one relationship easy to picture. Walton and Hyra, drawing on Lilian Bermejo-Luque, distinguish analogies used to justify a claim from those used to explain or make something vivid, and they are evaluated differently. That’s the explanation, not an argument condition. It would become a weak analogy if someone reasoned from it to a conclusion about electricity the comparison doesn’t support, such as that current leaks out of a cut wire the way water leaks out of a cut pipe.

Analogies are vivid, and they borrow understanding from something familiar, so a comparison can feel like an explanation before anyone has checked whether it fits. It’s also natural to judge an analogy by how many similarities come to mind. Bartha notes that the standard textbook guidelines, such as “the more similarities, the stronger the analogy”, are frequently too vague to provide much insight, and that the hard question they leave open is which similarities and differences are relevant to the conclusion.

Walton and Hyra also point out that a good analogy and an effective one aren’t the same thing: an analogy can be logically weak and still persuade, if the audience accepts the claim on the strength of the comparison.

• Name the respect. Ask exactly which way the two things are supposed to be alike, for this conclusion. Many weak analogies fall apart once that’s said out loud.
• Ask why it’s true of the first case. Then check whether the thing that makes it true is present in the second.
• Look for the difference that matters, not just any difference. Every pair of cases differs somehow; the question is whether the difference touches the conclusion.
• Try a counter-analogy. If an equally similar case points the other way, the argument needs a reason to prefer its own.
• Offer a better comparison when you can. Often the fix isn’t to drop the analogy but to find one that shares the relevant feature.