Arguments from Analogy

Preface

Introduction

Arguments from analogy are a sort of deductive argument that are weaker than a common argument from entailment. An argument from entailment says that given some premises, a conclusion necessarily follows. An argument from analogy requires the following elements:

1. An analogy to the situation at hand.
2. The situation and the analogy sharing some relevant property.
3. Some reason that gets you to a conclusion.

The reason why the argument from analogy is not as strong as an argument from entailment is that the argument only works if the analogy is accepted by an interlocutor.

Argument From Entailment

In many cases the argument from analogy is reverse engineered from a certain kind of argument from entailment:

Reason Giving Premise: For all X, If X is F, then X is G.

Domain of Discourse: A is an X.

Instance Premise: A is F.

Conclusion: Therefore, A is G.

An argument from analogy teases someone into accepting the first premise of this sort of argument. We call this premise of the argument the reason giving premise, since it states the reason why we think A is F means A is G (it does this by showing that the kind of thing A is, implies that if they have property F, they have property G). Unfortunately, unlike a standard argument from entailment, the interlocutor can always disagree with the reason giving premise. This will be clearer in an example of this form of argument:

Reason Giving Premise: For all People, if a person is a killer, then that person is a lawbreaker.

Domain of Discourse: Ken is a person.

Instance Premise: Ken is a killer.

Conclusion: Therefore, Ken is a lawbreaker.

So, if someone was confused why Ken was a lawbreaker given they were a killer, we could appeal to the reason giving premise since it states that Ken being a lawbreaker due to being a killer is a product of Ken being a person (the stated domain of discourse). 

Analogies

Analogs

In the case of an argument from analogy, it is usually presented the following way:

1. A is F.
2. B is F.
3. If B is F, then B is G.
4. So, A is G.

In the context of the set of statements above, we have an enthymeme (an argument without all the premises explicitly stated). The domain of discourse of the analogs (A and B) are not stated, nor is the reason giving premise stated. Many people who make arguments from analogy may become confused about how to set up an argument because of these unstated premises. It may be useful to show the two methods by which this sort of argument goes wrong, and what conditions you must meet to make a good analogy.

Analogs Must Be in the Domain of Discourse

Take an analogy of this form:

1. An innocent pig got egregiously hurt by someone.
2. An innocent boy got egregiously hurt by someone.
3. If an innocent boy got egregiously hurt by someone, then the innocent boy has the right to prosecute who hurt them.
4. So, an innocent pig has the right to prosecute who hurt them.

This argument looks reasonable at first glance, but if the discourse continues, one may find the reason for why they think the pig and the boy are proper analogs. Assume the person who makes this argument gives you the reason for thinking these two analogs imply the right to prosecution:

I think all persons have the right to prosecute their perpetrators.

We can paraphrase this response into the form of a reason giving premise in the argument from entailment:

For all persons, if you are an innocent person who got egregiously hurt, then the innocent person has the right to prosecute who hurt them.

One objection to this argument is that the pig is not a person. This is obviously a rejection of the idea that the analog is in the proper domain of discourse of 'personhood' in the reason giving premise. This is a proper argument to make, since a legal definition of personhood only includes individuals who have (or should have) the same legal entitlements as most human beings.

So, if an analog is not the same kind of thing as what is being discussed, the analogy can be rejected.

The Reason Giving Premise is False

The reason giving premise follows a specific rule given above. However we can dissect how it works a bit better:

For all things that have some property F, F is sufficient for all of those things to necessarily have the property G.

A good example of this  necessity and sufficiency relation is thinking about squares and rectangles:

1. Necessity: All X things are necessarily Y things. For instance, all squares are necessarily rectangles. All humans are not immortal. In both cases, there can be non-square rectangles, but all squares are rectangles. Necessity points out this second condition of there being no non-rectangle squares.
2. Sufficiency: All X things are sufficient to be Y things. Being a square is sufficient to be a rectangle. Being a human is sufficient to be mortal. In both cases, there can be non-human mortals, but humans are necessarily mortal. Sufficiency points out the first conditions of there being other non-human mortals but only mortal humans.

Another way to think about these conditions is in form of a Venn Diagram:

As you can see, squares are a subset of rectangles, so a shape being a square is a sufficient condition for it to being a rectangle, while a shape being a rectangle is a necessary condition for it being a square.

We can now think about arguments from analogy which are rejected in virtue of the reason giving premise in them being false:

1. My dad is smart.
2. John Clauser is smart.
3. John Clauser won the Nobel Prize.
4. So, My dad will win the Nobel Prize.

You can then ask the person the reason why they think this analogy makes sense:

Smart people win Nobels.

You can then paraphrase this reason in the form of the reason giving premise. 

For all people, if a person is smart, then the person can win a Nobel Prize.

 Unfortunately, this reason is faulty. Being smart may be a necessary condition to win a Nobel prize, but it is certainly not sufficient. You have to do a lot of work to win a Nobel, and you have to be doing work on the cutting edge of research. Being smart does not guarantee you will win a Nobel Prize, the person who made the analogy confused necessary and sufficient conditions.

In a Venn Diagram, the true relation between being smart and winning a Nobel looks like this:

In this case, winning a Nobel is a subset of being smart. All Nobel winners are smart, but not all smart people are Nobel winners. For the analogy maker to be correct, Nobel Winners would have to encompass all smart people who exist or smart people would have to be a subset of all Nobel winners.

There is another kind of error someone can make when they give their reason:

1. Roger killed someone in a war.
2. Tim is a serial killer.
3. Tim should have and did go to jail.
4. So, Roger should go to jail.

In this case, the implied reason behind this argument follows something along the lines of:

For all people, if a person kills someone, then said person should go to jail.

This reason fails, because there is no reason to think all killers should go to jail, some killers should not go to jail. This means that being a killer is not sufficient to prescribe said killer to go to jail, nor are the killers necessarily people who should go to jail. Killing someone in war should be permitted if said killing is done in an ethical way (with respect to war time rules of conduct).

The Venn Diagrams of killers and people who should go to jail looks something like this:

Probabilistic Reasons

Sometimes, people don't say all things with some property have another property, but that most things with a property have another property. These arguments can be dissected in a similar way. Take the following argument:

1. Most Game of Thrones watchers are nerds.
2. Most Dungeons and Dragons players are nerds.
3. Most Dungeons and Dragons players have no sex lives.
4. So, most Game of Thrones watchers have no sex lives.

In this case we have an extra means of defeating the analogy. Can we really demonstrate that most Game of Thrones watchers are nerds? The truth condition for that claim is proving that more than 50% of the people who watch game of thrones are nerds? This sort of reason applies to the rest of the premises too.

The reader of this piece may also wonder how necessary and sufficient conditions work in this case. Doesn't this argument assume that there are no such things? This is not true. Since the truth conditions in this case are just that more than 50% of people who who do X are nerds implies that more than 50% of people who do X have no sex life, we have a black and white truth condition, so the reason just needs to follow this truth table:

More than 50% of X people are nerds	More than 50% of X people have no sex life	If more than 50% of X people are nerds, then more than 50% of X people have no sex life
T	T	T
T	F	F
F	T	T
F	F	T

This form of the argument is much more complex than what is presented above, but a full treatment of this kind of argument relies on mountains of explanation and nuance.

Closing Remarks

When you run an argument from analogy make sure that you keep the following in mind:

1. Analogs are in the Domain of Discourse: The analogs are the same kind of thing and are the relevant kind of thing picked out in the reason behind thinking having some property implies having another property.
2. Not Confusing Necessary and Sufficient Conditions in the Reason Giving Premise: Make sure you don't flip the two parts of the conditional in your reason giving premise. Just because you are smart, being smart is not sufficient to win a Nobel prize.
3. The Reason Giving Premise has Necessary and Sufficient Conditions: Make sure all of some kind of thing with one property is a subset of the same kind of thing with another property. If not all killers need to go to jail, you have no reason that gets you your conclusion in the argument from analogy.
4. For Probabilistic Forms of the Argument, Make Sure the Truth Conditions are met: If the analogy only quantifies most or a minority or more than 30% etc, make sure the data corresponds to the claim.