Module 5: Analogical Reasoning
5.1 The Form of Analogical Arguments
Perhaps the most common use of analogical reasoning is to predict how the future will unfold based on similarities to past experiences. Consider this simple example. When Matthew first learned that the movie The Wolf of Wall Street was coming out, he predicted that he would like it. His reasoning went something like this:
Notice, first, that this is an inductive argument. The conclusion, that he will like The Wolf of Wall Street is not guaranteed by the premises; as a matter of fact, his prediction was wrong and he really didn’t care for the film. But our real focus here is on the fact that the prediction was made on the basis of an analogy. Actually, several analogies, between The Wolf of Wall Street, on the one hand, and all the other Scorsese/DiCaprio collaborations on the other. The new film is similar in important respects to the older ones; he liked all of those; so, he’ll probably like the new one.
We can use this pattern of reasoning for more overtly persuasive purposes. Consider the following:
That passage is trying to convince people not to eat pork, and it does so on the basis of analogy: pigs are just like other animals we would never eat—dogs and dolphins.
Analogical arguments all share the same very basic structure. We can lay out this form schematically as follows:
a1, a2, …, an, and c all have P1, P2, …, Pk
a1, a2, …, an all have Q
/∴ c has Q
This is an abstract schema, and it’s going to take some getting used to, but it represents the form of analogical reasoning succinctly and clearly. Arguments from analogy have two premises and a conclusion. The first premise establishes an analogy. The analogy is between something, marked ‘c’ in the schema, and some number of other things, marked ‘a1’, ‘a2’, and so on in the schema. We can refer to these as analogues
. They’re the things that are similar, analogous to ‘c’. This schema is meant to cover every possible argument from analogy, so we do not specify a particular number of analogues; the last one on the list is marked ‘an’, where ‘n’ is a variable standing for any number whatsoever. There may be only one analogue; there may be a hundred. What’s important is that the analogues are similar to the thing designated by ‘c’. What makes different things similar? They have stuff in common; they share properties. Those properties—the similarities between the analogues and c—are marked ‘P1’, ‘P2’, and so on in the diagram. Again, we don’t specify a particular number of properties shared: the last is marked ‘Pk’, where ‘k’ is just another variable (we don’t use ‘n’ again, because the number of analogues and the number of properties can, of course, be different). This is because our schema is generic: every argument from analogy fits into the framework; there may be any number of properties involved in any particular argument. Anyway, the first premise establishes the analogy: c and the analogues are similar because they have various things in common—P1, P2, P3, …, Pk.
Notice that ‘c’ is missing from the second premise. The second premise only concerns the analogues: it says that they have some property in common, designated ‘Q’ to highlight the fact that it’s not among the properties listed in the first premise. It’s a separate property. It’s the very property we’re trying to establish, in the conclusion, that ‘c’ has (‘c’ is for conclusion). The thinking is something like this: c and the analogues are similar in so many ways (first premise); the analogues have this additional thing in common (Q in the second premise); so, c is probably like that, too (conclusion: c has Q).
Check Your Understanding
It will be helpful to apply these abstract considerations to concrete examples. We have two in hand. The first argument, predicting that Matthew would like The Wolf of Wall Street, fits the pattern. Here’s the argument again, for reference:
The conclusion is something like ‘he will like The Wolf of Wall Street’. Putting it that way, and looking at the general form of the conclusion of analogical arguments (c has Q), it’s tempting to say that ‘c’ designates Matthew, while the property Q is something like ‘liking The Wolf of Wall Street. But that’s not right. The thing that ‘c’ designates has to be involved in the analogy in the first premise; it has to be the thing that’s similar to the analogues. The analogy that this argument hinges on is between the various movies. It’s not Matthew that ‘c’ corresponds to; it’s the movie we’re making the prediction about. The Wolf of Wall Street is what ‘c’ picks out. What property are we predicting it will have? Something like ‘liked by Matthew’. The analogues, the a’s in the schema, are the other movies: Gangs of New York, The Aviator, The Departed, and Shutter Island. (In this example, n is 4; the movies are a1, a2, a3, and a4.) These we know have the property Q (liked by Matthew); he had already seen and liked these movies. That’s the second premise: that the analogues have Q. And as for the first premise, which establishes the analogy among all the movies, what do they have in common? They were all directed by Martin Scorsese, and they all starred Leonardo DiCaprio. Those are the P’s—the properties they all share. P1 is ‘directed by Scorsese’; P2 is ‘stars DiCaprio’.
The second argument we considered, about eating pork, also fits the pattern. Here it is again, for reference:
Again, looking at the conclusion—‘Eating pork is immoral’—and looking at the general form of conclusions for analogical arguments—‘c has Q’—it’s tempting to just read off from the syntax of the sentence that ‘c’ stands for ‘eating pork’ and Q for ‘is immoral’. But that’s not right. Focus on the analogy: what things are being compared to one another? It’s the animals: pigs, dogs, and dolphins; those are our a’s and c. To determine which one is picked out by ‘c’, we ask which animal is involved in the conclusion. It’s pigs; they are picked out by ‘c’. So we have to paraphrase our conclusion so that it fits the form ‘c has Q’, where ‘c’ stands for pigs. Something like ‘Pigs shouldn’t be eaten’ would work. So Q is the property “shouldn’t be eaten”. The analogues are dogs and dolphins. They clearly have the property: as the argument notes, (most) everybody agrees they shouldn’t be eaten. This is the second premise. And the first establishes the analogy. What do pigs have in common with dogs and dolphins? They’re smart, cute, and playful. P1 = ‘is smart’; P2 = ‘is cute’; and P3 = ‘is playful’.
