Back during the ideological battle over masks in the last pandemic, I used arguments by analogy to defend governmental mask requirements. My silly comparison was to laws against public nudity. My serious comparisons were to such things as automobile safety laws and regulations for food handling. During discussions, I often encountered the fallacy of perfect analogy, which is the subject of this essay.
Informally speaking, an argument by analogy is an argument in which it is concluded that because two things are alike in certain ways, they are alike in some other way. More formally, the argument looks like this:
Premise 1: X and Y have properties P, Q, R.
Premise 2: X has property Z.
Conclusion: Y has property Z.
X and Y are variables that stand for whatever is being compared, such as mask ordinances and automobile safety regulations. P, Q, R, and are also variables, but they stand for properties or features that X and Y are known to possess, such as protecting people from danger. Z is also a variable, and it stands for the property or feature that X is known to possess, such as being an acceptable imposition by the government. The use of P, Q, and R is just for the sake of the illustration—the things being compared might have many more properties in common.
An argument by analogy is an inductive argument. This means that it is supposed to be such that if all the premises are true, then the conclusion is probably true. Like other inductive arguments, the argument by analogy is assessed by applying standards to determine the quality of the logic. Like all arguments, there is also the question of whether the premises are true.
The strength of an analogical argument’s logic depends on three factors. To the degree an analogical argument meets these standards it is a strong argument. To the degree that it fails, it is weak. If the argument is weak enough it can be considered a fallacy (an error in logic). In this case, it would be a false or weak analogy.
The first standard is that the more properties X and Y have in common, the better the argument. This standard is based on the commonsense notion that the more two things are alike in other ways, the more likely it is that they will be alike in some other way. It should be noted that even if the two things are very much alike in many respects, there is still the possibility that they are not alike regarding Z. This is one reason why analogical arguments are inductive.
The second is the more relevant the shared properties are to property Z, the stronger the argument. A specific property, for example P, is relevant to property Z if the presence or absence of P affects the likelihood that Z will be present. It should be kept in mind that it is possible for X and Y to share relevant properties while Y does not actually have property Z. Again, this is part of the reason why analogical arguments are inductive.
The third is that it must be determined whether X and Y have relevant dissimilarities as well as similarities. The more dissimilarities and the more relevant they are, the weaker the argument.
These can be simplified to a basic standard: the more like the two things are in relevant ways, the stronger the argument. And the more the two things are different in relevant ways, the weaker the argument. To focus the discussion, I will make use of two analogies to mask regulations. I do not want to get bogged down in the distinctions between ordinances, laws, and such, so I am using the vague term “regulations.” Any substantial battles over the exact terminology can be addressed in the context of law.
When arguing about masks, my concern was with the ethics of such regulations, and I left the legal wrangling to the legal experts. There are two main strategies when using an argument by analogy to argue that something is morally acceptable (or unacceptable). The first is to find something the target audience believes is morally acceptable (or unacceptable) and argue that it is like what you are trying to prove to be morally acceptable (or unacceptable). For example, most people think that laws against public nudity are morally acceptable and hence drawing an analogy between them and mask regulations would be a plausible approach. This differs from an appeal to belief fallacy in that the point is not that something is good (or bad) because people believe it. Rather, it is an appeal to consistency: if a someone accepts public nudity laws as ethical and mask regulations are like these nudity laws, then they should accept the mask regulations are ethical as well.
The second is to find something for which there are already strong arguments for being morally acceptable (or unacceptable) and show how the thing in question is like that thing. This is analogous to how lawyers make use of precedent: if a type of case is already well argued, then a successful analogy to that case allows one to apply the same arguments. As an example, the regulations governing automobile safety (like requiring working brakes) have good arguments supporting them. If it can be shown that mask regulations are like these regulations, then these arguments would also apply to mask regulations, thus providing support for them. While these uses of the argument are reasonable, they can also be reasonably challenged. But the challenges can also be fallacious. It is to the challenges that I now turn.
As noted above, the premises of any argument can be challenged. In the case of an argument by analogy, once counter involves arguing that either (or both) X or Y lack the attributed properties. Another counter is to argue that X lacks Z—this approach can be used against both approaches.
If the argument is a targeted analogy, a person who does not accept that X has Z can reject the analogy. For example, a person who is morally fine with public nudity can reject the analogical argument which assumes laws against public nudity are morally acceptable. If the argument is aimed at making an analogy with something that has established moral arguments, then arguing against these arguments would undercut the analogy. For example, an anarchist could make use of the usual arguments against all the laws of the state to undercut my analogy between masks and automobile safety laws. The arguments that refute the claim that requiring brakes by law is morally acceptable would, by analogy, also refute the claim that mandating mask usage is morally acceptable. This, of course, cannot merely be asserted, it still needs to be argued.
Even if a critic accepts the truth of the premises, they can still reject the argument in a principled manner by arguing that the analogy is weak: that it fails to meet the three standards adequately. If the analogy is bad enough, it could even be the fallacy of false or weak analogy. But the critic must also be on guard against committing fallacies.
One error a critic can make is simply asserting that the three standards are not met and therefore the conclusion of the argument is false. The most common version of this is to assert, without adequate support, that a difference is both relevant and significant enough to refute the analogy. This can be pushed to the point where it becomes the perfect analogy fallacy. It is often combined with the fallacy fallacy: concluding that an argument must have a false conclusion because the reasoning is (or is alleged to be) fallacious.
The perfect analogy fallacy has this form:
Argument 1
Premise 1: An argument by analogy concludes that Y has Z (because X has Z and X and Y are similar).
Premise 2: D is a difference between X and Y.
Conclusion: The argument by analogy is a false or weak analogy.
One could also combine the perfect analogy fallacy with the fallacy fallacy in an extended argument:
Argument 2
Premise 1: An argument by analogy A concludes that Y has Z (because X has Z and X and Y are similar).
Premise 2: Argument by analogy A is a false or weak analogy, as per Argument 1.
Conclusion: Y does not have Z.
Or just smash them together:
Argument 3
Premise 1: An argument by analogy A concludes that Y has Z (because X has Z and X and Y are similar).
Premise 2: D is a difference between X and Y.
Conclusion: Y does not have Z.
Argument 2 and 3 would always be fallacies because inferring that the conclusion of a fallacy must be false because it is a fallacy is always a mistake. After all, even an invalid deductive argument can have a true conclusion. For example, consider this invalid argument with all true premises and a true conclusion:
Premise 1: If Tallahassee is the capital of Florida, then it is in Florida.
Premise 2: Tallahassee is in Florida.
Conclusion: Tallahassee is the capital of Florida.
Argument 1 could, however, be modified to make a good argument. What is wanting is a premise that establishes D as a relevant difference between X and Y that would suffice to show that the argument by analogy is weak. This cannot simply be asserted and it would need to be shown to be plausible using an argument.
The reason I call this fallacy the perfect analogy fallacy is that the use of argument 1 would be part of a strategy to reject an argument by analogy in an unprincipled manner. This would involve either refusing to accept the similarities as adequate or simply asserting that almost any difference is relevant and sufficient to undercut the analogy. That is, the critic is requiring a perfect analogy, which is an impossible standard to meet.
For example, a critic might respond to my nudity law analogy by asserting that the mask covers the mouth while other clothes do not. While this is true, they would need to do more than just point to this difference and they would need to show how this undercuts the analogy. One way to do this is to note that while clothing does not impede breathing, a mask over the mouth can, which could be developed into a relevant difference that undercuts my analogy.
As another example, a critic might respond to my brake analogy by asserting that brakes are not worn but masks are. While this is true, it would need to be shown that this is a relevant and significant difference that breaks the analogy. The main challenge would be showing that while the state can compel people to have safe vehicles, they cannot compel people to wear safety devices, such as seat belts and masks. This could be done but requires more than asserting that people do not wear brakes.
Before accusing a critic of committing this fallacy it is important to determine if this charge has a foundation. After all, good faith criticisms of an argument by analogy involve questioning the similarity between the two things and raising questions about relevant differences. If the critic brings up a difference without support for their claim that it is relevant and significant enough to undercut the analogy, then this would be grounds for suspicion. If they keep repeating the difference without supporting their claim or keep shifting to new, unsupported differences to reject the argument, then it would be reasonable to suspect they are engaged in this fallacy. Their strategy would seem to be to require that X and Y be identical before they accept that X having Z supports Y having Z, which is an impossible standard.
When trying to sort out good faith criticism from bad faith perfect analogy attacks there are two main things to look for. The first is, obviously enough, at least an attempt to argue that the claimed difference is relevant and significant. The second is to look for a willingness on the part of the critic to identify what similarities they would accept as relevant. If they refuse or it plausibly seems that they require an unreasonable (or even impossible) level of similarity, then they are likely to be using the perfect analogy fallacy. It should also be noted that people can fall into this fallacy unwittingly. They are not consciously using a bad faith strategy; they simply believe that asserting a difference exists suffices to undercut the analogy. They would be reasoning in error, but not in bad faith. Such an error can often be corrected, since a person arguing in good faith seeks the truth. I am expecting similar perfect analogy fallacies in the next pandemic, assuming that the government even attempts to take action to protect the people.