By Stephanie Gibbons and Justine Kingsbury, adapted by Marc Chao and Muhamad Alif Bin Ibrahim

Implicit Premises

When people present arguments in everyday language, they often leave out parts of their arguments. This is usually because some points are so obvious that they can be safely assumed and do not need to be explicitly stated.

Consider the following argument:

There is an unstated assumption here: that mice are rodents. Without this assumption, the conclusion does not logically follow from the premises.

The problem with leaving premises unstated is that sometimes the unstated premise is not obvious or easily accepted and may even be highly controversial. Therefore, when reconstructing arguments, we make any implicit premises explicit. This allows us to properly assess each premise as true or false.

Using the example above, we can put the argument into standard form:

We then note that the argument is invalid. We can make it valid by adding a premise:

The argument is now valid. This addition is sensible because it is clearly something the arguer intended, even though it was not explicitly stated.

Sometimes an implicit premise is left out because it is so obvious it hardly needs stating. However, sometimes an unstated premise is doing a lot of work in the argument, and this is not evident because it has not been explicitly stated. Sometimes the unstated premise is obviously false or highly controversial. By exposing implicit premises and making them explicit, we are better positioned to assess the argument.

Consider this argument:

An initial reconstruction might look like this:

What is the missing premise here? To make the argument valid, a connection needs to be made between the risk of harming one’s health and what should not be done. We could add an implicit premise like this:

This is the minimum required to make the argument valid. The arguer must have something like this in mind; otherwise, the conclusion would not follow. Here, the connecting premise (Premise 2) 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 one’s health at risk. If that were true, people would never eat fried food, drink coffee, or participate in sports. Living a life free of risk would be paralysing for anyone.

It is likely that the arguer meant that the risk of eating dessert every day is an unacceptable risk. However, since their argument does not evaluate risk or explain what degree of risk is acceptable, adjusting their argument in this way would be doing too much work for them. In the absence of any attempt to explicitly link the premise to the conclusion, we can only provide the minimally necessary connection and assess it.

Determining what premise needs to be added to an argument to make it valid is tricky. You need to understand how validity works and how to connect the provided information to ensure that the conclusion follows. The following video by Stephanie Gibbons offers some hints to get you started [6:40]. It is a good idea to watch it before attempting the questions.

Normative Conclusions

Arguments with normative conclusions require special attention. They are quite common and often contain implicit premises that need to be made explicit.

A normative claim (or conclusion) is a statement about what should or ought to happen, whereas a descriptive claim (or conclusion) is a statement about how things are. For example, “Mount Everest is the highest mountain in the world” is a descriptive statement, as it describes a current feature of the world. In contrast, “Climbers should seek permission before climbing Mount Everest” and “Fewer people should climb Mount Everest” are normative statements: it goes beyond merely describing how things are and instead prescribes how things should be.

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

For an argument with a normative conclusion to be valid, it must include at least one normative premise. No valid argument can consist solely of premises that describe the way the world is and then conclude something about how things should be.

Consider this argument:

The conclusion here is normative. The factual claim that some people are unable to read is not sufficient to support the normative claim. No amount of information about how things are can, on its own, support the claim that things should be different. Therefore, we can see that a normative premise is needed for validity.

The argument can be made valid by adding a conditional premise:

Inferring a normative conclusion from descriptive premises is a common type of argument failure known as “the fallacy of deriving ought from is”. However, this can generally be avoided by adding the necessary normative premise.