Implicit Premises

Suppose someone argued that "Alcohol should be illegal because it is a drug and all drugs should be illegal." Doesn't that read a bit unnaturally? It is unlikely that anyone making this argument would state it so longwindedly. More likely he’d simply say: “Alcohol should be illegal because it’s a drug” or perhaps “Alcohol should be illegal because all drugs should be.” Both of these ways of stating the argument omit one of the premises. People often do this when they think it is obvious what premise would be needed to complete their argument and when they think the person they’re speaking with will agree to that premise. If one maps these arguments as written, here’s what one would get:

Map 9:

This map shows three arguments: Argument A is the complete argument with both premises. And arguments B and C each use only one premise. Inference A is a deduction (as strong as an inference can be), where as Inferences B and C are non-sequiturs (as week as an inference can be). But it's obvious what one would need to a to Argument B or C to make a very strong argument—namely, Argument A.

Here is another example of this phenomenon:

Map 8:
	Some of ways this argument might be expressed: I should respect her, because she’s my mother. She’s my mother, so I should respect her. I should respect her, for she’s my mother. She’s my mother. Therefore, I should respect her. I should respect her; she is my mother after all.

This map is a map of the argument expressed in different ways by each of the sentences on the right. But the argument is clearly incomplete as written. Inference A is a non-sequitur, which makes Argument A worthless. But if someone said any of the sentences on the right, you would recognize that he was giving you some reason to believe Proposition 1. This is because there’s another premise, which is plausible that when combined with Proposition 2 would make for a stronger argument as follows.

Map 8a:

In this map, Proposition 3 is enclosed in brackets to indicate that it isn’t stated in the passage we are analyzing and that we have added it ourselves, because we think that the author of the passage intended us to assume it as a premise of the argument. Such unstated premises are called implicit.

When analyzing an argument, it is important to make any implicit premises explicit—that is, to state them. This is necessary because, when you go on to assess the argument, you will need to assess all of the premises in order to determine how strong the argument is. Some arguments appear to be stronger than they are, because their weakest premises are left implicit.

Not every unstated belief held by a person making an argument is an implicit premise of that argument, nor even is every unstated belief that is relevant to the subject of the argument. We can probably imagine all sorts of reasons that the person making this argument has for believing that people should respect their mothers, but none of these reasons count as implicit premises of the argument mapped above. Something is an implicit premise only if it needs to be added to an argument to prevent one of its inferences from being a non-sequitur, and if is likely that the person making the argument intended you to assume it.

Thus, the process of finding implicit premises is closely related to the process of assessing the inference. Once you have identified the stated premises and the conclusion, you may notice that the conclusion does not follow from the premises. At this point, there are two possibilities: either the inference is a non-sequitur; or there is an implicit premise, which does make the conclusion follow from the premises. You need to use your judgment as to which is the case. Is it more likely that the author of the argument made non-sequitur or that he left one of his premises unstated? People rarely make arguments that include obvious non-sequiturs, so in such cases, it is likely that there is an implicit premise that the author intended you to assume. There are some subtle situations where it is difficult to determine whether an argument is bad or whether there is some implicit premise, and there are cases where it is hard to tell which of several different premises might be implicit; but more often than not it is very clear when someone is relying on an implicit premise and what that premise is.