Chapter 7 Arguments from Definition and Enthymemes

7.1 Reasoning with Definitions

As we have just seen, when we provide a good definition, we will state essential features that things must have for the term to apply to them. These features will usually be facts about the world that are independent of language, and this means that the meanings of words have knowledge about things embedded in them, knowledge that we can use when we make inferences and give arguments.

When we reason and when we formulate arguments, we always rely to a certain extent on information that is implicitly available in the form of knowledge carried simply by the meaning of words. This might be somewhat “free-floating” knowledge, which anyone who is proficient in a language would know. But the vast majority of what “everyone knows”—that water is wet, that dogs are animals, that you can buy food to eat at a restaurant, and so on—is just knowledge that everyone has by virtue of being part of a culture and knowing a language. However, a lot of “free-floating” knowledge that “everyone knows” can just be simple prejudice or overgeneralization. Reasoning is damaged by unchecked assumptions, and we will look into this further in part 3 when we examine fallacies and biases.

So what makes a good argument from definition—an argument where we make deductions based on the definitions of words? Here we talk about how a good argument from definition can contain implicit information that if made explicit shows that the argument is valid.

Consider “Bruce is a parent, so Bruce has a child”; here the conclusion “Bruce has a child” is presented as following from the meaning of “parent” and from the fact that a good definition of “parent” will include the requirement that if someone is a parent, then that person has a child.

Since a statement that is necessarily true is true in every possible circumstance, adding a necessary truth to an argument cannot make a valid argument invalid. A good argument from definition is therefore implicitly valid and can be shown to be valid by making the definitional connection explicit.

7.2 Validity and Definitional Arguments

The definition of “bungalow” is “a single-story house.” Let’s look at the argument from “X is a bungalow” to “X is a house.” How do we prove that an argument from a good definition is valid? This means that the concept of being a “bungalow” includes the concept of being “single-story” and being “a house.” This means that the assertion that “X is a bungalow” implicitly includes the assertion that it is a house and that it is single-story.

How do we construct this information into a valid argument?

1. 1. X is a bungalow (the premise).

However, since “bungalow” means “single-story house,” and “X is a bungalow” says the same thing as “X is a single-story house,” we can substitute one for the other, and so by substituting one for the other, we can rewrite 1 as

1. 2. X is a single-story house.

Again, since “X is a single-story house” says both that X is a house and that X is a bungalow, we replace it by these two claims, and so by substitution again, we can rewrite 2 as

1. 3. X is single-story, and X is a house.

But if X is both single-story and a house, then X is a house, so we can conclude from 3 that

1. 4. X is a house (the conclusion).

What does this mean for validity? Validity is the formal property of arguments where if the premises are true, then the conclusion must also be true. To put this again, validity is the formal property of arguments where there’s no situation in which the premises are true and the conclusion is false. Consider the argument again:

Or

But premises 2 and 3 are contained within premise 1, so what we are really doing is saying, “X is a bungalow, therefore X is single story,” or “X is a bungalow, therefore X is a house.” This demonstrates a derivation by way of a definition, since the conclusion is information from the premises.

Now we ask the validity question: Is it possible for all the premises 1–3 to be true and the conclusion false? This is the work validity does—it explains how the premises can force a conclusion to be true. Here, if the premises 1–3 were true (which is basically a way of saying that the definition of a bungalow is what we think it is) and the conclusion were false, it would mean that X is both single-story and not single-story. This would be a contradiction, which rules it out.

These logical moves depend on making explicit what is included in the definition of a bungalow. We might just say that the conclusion was “included” in the premise, and it follows from it by the definition of the term “bungalow.” Once again, the argument is valid because the conclusion must be true if the premises are true.

Some caution is warranted in extracting information from definitions. Definitions are after all human creations, and just to the extent that the terms are not fully defined, we need to be cautious about argument from definition. This just underscores the importance of defining your terms. The practice of defining your terms carefully imposes the clarity your arguments need. When arguing, if we can appeal to common terms and definitions, then it is easier to make reasonable inferences that we will find more rationally persuasive and secure.

7.3 Enthymemes

Arguments from definition are not the only kinds of arguments relying on implicitly available information. We often rely on our audience to share common knowledge with us, which we therefore do not need to state. Arguments that rely on this sort of shared knowledge are called “enthymemes.”

Why do enthymemes matter? If we want to be convincing, we have to pay very close attention to what we are assuming and background information. Arguments necessarily require a lot of background knowledge, and making as much of that as explicit as possible helps guard against any logical errors.

Consider the argument “Dogs are animals, so they are not machines.” This seems right to us, of course, but we are relying on our audience to agree on something that is not explicit. This is a deductive argument, and when making a deductive argument, the premises and conclusion need an explicit connection. Here’s what this enthymeme looks like with the implicit premise explicitly stated:

Before the implicit premise was made explicit, someone without our particular background knowledge would be left to wonder how “animals” and “machines” are related to each other. The enthymeme was appealing to “what everyone knows.” “Dogs” were in premise 1 and the conclusion, so that made some sense, but we needed a way to tie together “animals” and “machines.” We tie them together by explicitly stating that “animals are not machines.” Even though this is negative, it demonstrates what their relationship is.

Let’s try another one: Seattle is south of Vancouver, so Vancouver is north of Seattle. Notice that “Vancouver” and “Seattle” both appear in the premise and the conclusion. So what do we need to make explicit about their relationship to make the conclusion work?

Here, the speaker is assuming you know how south and north operate. You might say this is a type of argument from definition, but that doesn’t mean we can’t make this information explicit so that someone who doesn’t understand or doesn’t use the concepts “south” and “north” can understand that the argument is valid (recall: there’s no way for premises 1 and 2 to both be true and the conclusion false).

Do we always have to make everything explicit in an argument? Won’t we always be relying on background information and implicit premises to some extent? Insofar as we are sharing a language, we are going to have to take some things for granted, but when we can make something explicit so that our reasoning is more solid and clear, we should do so.

Example 1 has as an implicit premise that living beings require water. This is how you can infer that the lack of water on Venus means there isn’t any life. Notice that Venus is in the premise and the conclusion, but the argument lacks an explicit connection between life and water. We make this explicit by adding that life requires water.

Example 2 takes a general rule and applies it to an individual. But it doesn’t give us enough information about that individual to know if the conclusion follows. Do you know anything about Mary? Maybe Mary’s friends and relatives don’t need this to be explicit, but to make the argument public so that anyone reading it can follow the logic, we need to know that Mary loves children. This is how we make the argument explicit and demonstrate its validity. If we stated clearly that “people who love kids make great teachers; Mary loves kids, therefore Mary would make a great teacher,” can you imagine a case in which the premises are true and the conclusion false? Can it be the case that people who love kids make great teachers and Mary loves kids are true, but at the same time, Mary would not make a great teacher? That would be impossible, therefore the argument is valid.

Although the enthymemes we have gone over have implicit premises of different kinds, what they all have in common is that in a particular context, leaving the implicit assumption unstated can be reasonable. The trouble with enthymemes is that they assume that you will notice the implicit assumption or premise and fill it in and, so, get the point. But this doesn’t always happen, even when the thing that you fail to notice is something you know well and that might be obvious at times. Context functions to highlight certain relevant considerations, but it can also make us inattentive to other considerations that are obvious but that the context does not highlight. This adds a dimension of unreliability that we want to avoid. Thus in order to evaluate arguments with implicit parts, we need to be able to reconstruct them to make what is implicit explicit.

Hopefully you can see that an important part of critical thinking is simply being careful, and making implicit assumptions explicitly available is one way of being careful. Often there will be a fallacious inference that has been made without being noticed, and reconstructing the argument will reveal the error.