Implicit premises

When people give arguments in ordinary language, they often leave parts of their arguments out. Often this is because something is so obvious it can be safely assumed that others will accept it, and so it doesn’t need to be explicitly stated. Consider the following argument.

My pet Squeaky is a mouse, and all rodents have teeth that never stop growing. So, Squeaky’s teeth will never stop growing.

There is an unstated assumption here. That is that mice are rodents. Without assuming this, the conclusion of the argument would not validly follow from the premises.

The difficulty with leaving premises unstated is that sometimes the unstated premise is not obvious or easily accepted, but is in fact a highly controversial claim. For this reason, we make any implicit premises explicit when reconstructing arguments. This means that when we assess the argument we can properly assess each premise as true or false.

With the above example, we begin by putting the argument into standard form.

P1) My pet Squeaky is a mouse.
P2) All rodents have teeth that never stop growing.
                                                
C) Squeaky’s teeth will never stop growing.

We then note that the argument is invalid. We could make it valid, however, by adding a premise, like so:

​P1) My pet Squeaky is a mouse.
P2) All rodents have teeth that never stop growing.
P3) All mice are rodents.
                                        
C) Squeaky’s teeth will never stop growing.

The argument is now valid. And, this is a sensible addition to the argument: it’s clearly something that the arguer intended, even though it wasn’t explicitly said.

Sometimes an implicit premise is left out by the arguer because it is so obvious it is hardly worth saying. However, sometimes an unstated premise is doing a lot of work in the argument, and that isn’t evident because it hasn’t been explicitly stated. Sometimes the unstated premise is obviously false, or highly controversial. By exposing implicit premises, and making them explicit, we’re better positioned to assess the argument.

Consider this argument:

Co-sleeping is risky for the baby. So no one should do it.

An initial reconstruction might look like this:

P1) Co-sleeping with a baby carries a risk of harm to the baby.
                                             
C) No one should co-sleep with a baby.

What is the missing premise here? What is needed to make the argument valid? To make the argument valid, a connection needs to be made between the risk of harming the baby, and what shouldn’t be done. So to make the argument valid, we could add an implicit premise such as this:

P1) Co-sleeping with a baby carries a risk of harm to the baby.
P2) No one should do anything with a baby that carries a risk to the baby.
                                             
C) No one should co-sleep with a baby.

This is the minimum that is required to make the argument valid. The arguer must have something like this in mind, otherwise the conclusion of the argument wouldn’t follow. Here, the connecting premise is doing a lot of work in the argument, and it is false. It cannot be true that no one should do anything that would put a baby at risk. If that was true, people would never to be able to take a baby in a car, or an aeroplane, or do very much at all with them. Living a life free of risk would be paralysing, for a baby or for anyone else.

It’s likely that the arguer really meant that the risk of co-sleeping is an unacceptable risk. However, given that their argument doesn’t make an attempt to evaluate risk, or to explain what degree of risk would be acceptable, to adjust their argument in this way would be to do too much work for them. In the absence of any attempt to explicitly link the premise to the conclusion, there is not much we can do but provide the minimally necessary connection, and assess it.

Working out what premise needs to be added to an argument to make it valid is tricky. You need to think about how validity works, and how to connect together what has been provided to ensure that the conclusion follows. The following video gives you some hints to get you started. It’s a good idea to watch it before attempting the questions.

Normative conclusions

Arguments with normative conclusions deserve special mention. They are very common, and they frequently have implicit premises which need to be made explicit.

A normative claim is a statement says what should or ought to happen. In contrast, a descriptive claim is a statement which says how things are. So, the statement “Mount Everest is the highest mountain in the world” is a descriptive statement. It describes a current feature of the world. “Climbers should seek permission before climbing Mount Everest” is a normative statement, as is “Fewer people should climb Mount Everest”.

Conclusions are often normative, because arguments are often trying to persuade people about how things ought to be, or about what ought to happen.

In order to be valid, an argument with a normative conclusion must have at least one normative premise. No valid argument can have only premises which describe the way the world is, and conclude something about how things should be.

Consider this argument:

P1) Some people are finishing their schooling unable to read.
                                                   
C) We should implement a more comprehensive literacy programme in our schools.

The conclusion is a normative one. The factual claim that some people are unable to read can never be enough to support the normative claim. No amount of information about how things are can ever, on its own, support the claim that things should be different. So we can see, merely by noting that the conclusion is normative, that a normative premise is needed for validity.

Here the argument can be rendered valid by adding a conditional:

​P1) Some people are finishing their schooling unable to read.
P2) If some people are finishing their schooling unable to read, then we should implement a more comprehensive literacy programme in our schools.
                                          
C) We should implement a more comprehensive literacy programme in our schools.

Inferring a normative conclusion from descriptive premises is such a common type of argument failure that it has its own name: it is called “the fallacy of deriving ought from is”. However, it is generally easily avoided by adding the necessary normative premise.

Using conditionals and generalisations as connecting premises

Any argument, no matter how far the premises appear to be removed from the conclusion, can be made valid. Sometimes, when there is no obvious link between the premises and the conclusion, the easiest way to make the argument valid is by adding a conditional claim. The definition of a valid argument is “if the premises are true, then the conclusion must be true also”. So, by constructing a conditional that says “if [other premises], then [conclusion]”, and adding that conditional as a further premise, any argument can be rendered valid. We can call such a conditional a “corresponding conditional” (because it is the conditional that corresponds to the argument).

Here’s how it works.

Suppose someone gives an argument that says

Fish can’t ride bicycles. Therefore the moon isn’t made of green cheese.

In standard form:

P1) Fish can’t ride bicycles.
                                        
C) The moon is not made of green cheese.

It might look, at first glance, as if there is no way to connect these two ideas. They are completely unrelated. But, we assume that the arguer intended there to be a connection, because we assume the arguer meant to give a good argument. To connect them, we form a corresponding conditional: we say “if the premise, then the conclusion”. Here, that gives us

P1) Fish can’t ride bicycles.
P2) If fish can’t ride bicycles, then the moon is not made of green cheese.
                                             
C) The moon is not made of green cheese.

This is a valid argument.

Whether the argument is a good argument or not depends on whether or not P2 is true. Using a corresponding conditional to make an argument valid shifts the burden of assessing the argument to a particular premise.

A corresponding conditional will make any argument valid, but it is not always the best way of making an argument valid. You will still (ultimately) need to assess the truth of the conditional, and that is not always very easy to do. Sometimes a good technique is to start with a corresponding conditional, and then to think about whether there is some generalisation which makes that conditional true. So, take the argument

P1) Squeaky is a mouse.
                                      
C) Squeaky is a mammal.

The corresponding conditional which makes this argument valid is “If Squeaky is a mouse, then Squeaky is a mammal”. But what makes that claim true is the generalisation “All mice are mammals”. So, we can use the generalisation to connect P1 to the conclusion:

​P1) Squeaky is a mouse.
P2) All mice are mammals.
                                       
C) Squeaky is a mammal.

Whether it is better to use a generalisation or a conditional will depend partly on how specific the connection needs to be. Consider this argument:

P1) It is Friday night.
                                     
C) Jerry will end up drunk tonight.

What sort of connection could be used here? The corresponding conditional is “If it is Friday night, then Jerry will end up drunk”. There are a wide range of generalisations that cover this conditional. Here are some options:

1. Everyone gets drunk every night.
2. Everyone gets drunk on Friday nights.
3. Jerry gets drunk every night.
4. Jerry gets drunk every Friday night.

The first and second of these would make the argument valid. However, they’re not charitable connections to choose, because they are clearly false. We don’t want to make the argument worse than it needs to be. While the third option is possible, the fourth seems a better option. Given that we know nothing but what is claimed in the premise, and we need to connect it to the conclusion, it seems likely that the arguer wants to appeal to something such as this. It is more general than the corresponding conditional. But there would be no reason for the arguer to present P1 as a reason for the conclusion unless a generalisation such as the fourth option were true. So this generates a good reconstruction of the argument as valid:

​P1) It is Friday night.
P2) Jerry gets drunk every Friday night.
                                              
C) Jerry will end up drunk tonight.

If you’re unsure how to make an argument valid, it can help to begin with a corresponding conditional, and then to make that claim more general. The limit on how general you should make it is the limit of what is reasonable or believable. If there is no reasonable generalisation available, it may be better to leave it as a corresponding conditional.

Although a corresponding conditional can be used to make any argument valid, it should not always be used. Sometimes there is a more obvious option for a connecting premise.  For example, consider this argument:

P1. All mice have tails.
                               
C. Minnie has a tail.

The corresponding conditional is “If all mice have tails, then Minnie has a tail.” But a simpler premise to add as P2, which like the corresponding conditional would do the job of making the argument valid, would be “Minnie is a mouse.”