Argument Mapping By James Wallace Gray 2/13/2012 Table of Contents Argument Mapping...1 Introduction...2 Chapter 1: Examples of argument maps...2 Chapter 2: The difference between multiple arguments and multiple premises...6 Chapter 3: The difference between supporting arguments and objections...7 Chapter 4: The difference between objections to conclusions, premises, and arguments...9
Introduction Argument mapping (also known as persuasion mapping or reasoning mapping) is a visual representation of arguments. They can help clarify arguments and help us make important distinctions. I will give examples of argument maps and use them to illustrate the difference between premises and conclusions; multiple arguments and multiple premises; supporting arguments and objections; and objections against conclusions, premises, and arguments. Chapter 1: Examples of argument maps Consider the argument: 1. All men are mortal. 2. Therefore, Socrates is a mortal. An argument map can illustrate this argument in the following way: The map clarifies which statement is a premise and which statement is a conclusion. It illustrates that the premise supports the conclusion by coloring the premise blue and having an arrow point to the conclusion. Although this argument could be persuasive as shown here, it is actually not a complete argument because it's not clear how the fact that all men are mortal relates to the fact that Socrates is mortal. If Socrates is a vampire or god, then the conclusion would seem to be false.
Consider the improved argument: 1. All men are mortal. 2. Socrates is a man. 3. Therefore, Socrates is mortal. This improved argument can be illustrated using the following argument map: This time two premises combine to form a single argument to support the conclusion. There is a line connecting both premises to show that they combine to form a singe argument. This argument is complete because the premises are sufficient to prove the conclusion. If the premises are true, then the conclusion must also be true. Although the two above argument maps make it perfectly clear what the conclusion is, we should keep in mind that premises can be used as conclusions because we often need to justify our premises. Consider that someone might doubt that all men are mortal. In that case we might want to justify the fact that all men are mortal. How can we know such a thing? We could argue the following: 1. If not all men are mortal, then we probably would have found an immortal one by now. 2. We haven't found an immortal one by now. 3. Therefore, all men are probably mortal. Yet, once again we could be asked to justify one of our premises. How do we know that we haven't found an immortal man yet? We could then present the following argument:
1. If we found an immortal man, then it would probably be in the historical record. 2. There are no immortal men in the historical record. 3. Therefore, We probably haven't found an immortal man yet. And again we can provide a justification for one of the premises. How do we know that the historical record would probably mention the existence of an immortal man? We could then present the following argument: 1. People are very interested in immortality. 2. People put things that are very interesting to them in history books. 3. Therefore, if we found an immortal man, then it would probably be in the historical record. All of these arguments can be shown in a single argument map:
This argument map makes it clear what premise is justified by further argumentation. Each of those premises are both premises and conclusions. Keep in mind that (almost all) premises can be further justified and it's not always clear at what point we should stop justifying our premises. At some point we might have to admit that our premises are assumptions that will not be proven by argumentation. That is often satisfactory in a debate when the assumption is shared we need not prove anything in a debate when everyone already agrees with it. Chapter 2: The difference between multiple arguments and multiple premises. Many people give a series of simple arguments rather than a series of premises, and we should keep in mind the difference between the two. Consider the following: 1. Sometimes we find out criminals are innocent after we kill them. 2. Human life has value. 3. Therefore, the United States shouldn't use the death penalty. In this case the two premises are two separate arguments two different and somewhat unrelated reasons used to support the conclusion as is illustrated by this argument map: We should make sure to differentiate two supporting arguments from arguments with multiple premises, such as the following:
1. Sometimes we find out criminals are innocent after killing them. 2. It's better to save a single innocent life from an unjust death penalty than to kill several guilty criminals. 3. Therefore, the United States shouldn't use the death penalty. The argument map for this argument looks like the following: This argument map makes it clear that both premises combine to form a single argument. They are not separate and unrelated reasons to accept the conclusion. They both must be true for us to prove the conclusion is true. Chapter 3: The difference between supporting arguments and objections. Supporting arguments are shown on argument maps in blue and the word support is used to distinguish them from objections. Objections are arguments, just like supporting arguments. Objections are also known as challenges, refutations, or counter arguments. When someone presents us with an assertion, conclusion, or argument; we might disagree with it and provide an argument of our own against it. Objections can be used to show beliefs to be in need of further justification, irrational, counterintuitive, or known to be false. Objections can also be used to show arguments to be logically invalid or unsound.
Consider the following objection: 1. Kicking people can hurt them. 2. Therefore, we should reject the belief that it's never wrong to kick people. An example of an argument map of an objection is the following: This argument map illustrates an argument against a belief. Someone is said to conclude or believe that it's never wrong to kick people and the objection against that belief is that kicking people can hurt them. The objection is shown in pink and the word opposes is used to distinguish it from supporting arguments. However, we aren't justified to reject the belief based on the single premise shown above, which is an incomplete argument. We can expand the objection as the following: 1. People sometimes kick others to hurt them. 2. Sometimes it's wrong to do something to try to hurt people. 3. Therefore, we should reject to belief that kicking people is never wrong. We can represent this argument using the following argument map:
This time two premises are combined to form a single argument against the belief. Chapter 4: The difference between objections to conclusions, premises, and arguments. I've already given an example of an objection to a belief. Objections to conclusions are the same as objections to beliefs. Those are arguments that give us a reason to reject a certain belief. However, we still need to know what objections are that are given to premises and other arguments. Objections to beliefs and conclusions Another example of an objection to a belief is the following: 1. Someone argues that kicking people can hurt them. 2. However, kicking people while sparring in kung fu class is not wrong. 3. Therefore, we should reject the belief that it's always wrong to kick people. This argument can be illustrated by the following argument map:
In this case there is both an argument for and against a conclusion. Objections are generally only considered to be objections when someone actually believes and argues for the belief we object to. Objections to premises One potential shortcoming with objections to beliefs is that other people might have arguments for those beliefs. If we are stuck with an argument for and an argument against a belief, then we still need to know which argument is better. Otherwise it won't be clear if we should accept the belief or not. In that case it is necessary to provide an argument against a relevant premise or argument. If we want to prove a belief to be unjustified, then we not only need an argument against the belief; but we also need to show why the arguments in support of the belief are unjustified. For example, consider someone who argues that Socrates is a mortal because he is a dog. This argument should be rejected, but that does not give us a good reason to reject the conclusion. We need an additional reason to reject the conclusion. Even so, arguments against premises are essentially the same as arguments against conclusions and beliefs. The main difference is simply that a premise of an argument is opposed by an objection. An example of an objection to a premise is the following: 1. Someone argues that it's always wrong to kick people because it's always wrong to hurt people and kicking people hurts them. 2. However, it's not wrong to hurt people when you need to do so to protect yourself. 3. Therefore, we should reject the premise that states that it's always wrong to hurt people.
This objection can be illustrated with the following argument map: Objections to arguments There are two main ways to object to arguments without objecting to a premise. One, we can argue that the opposing argument is logically invalid. Two, we can argue that the premises are not appropriate sufficient to support the conclusion for some other reason. An example of an invalid argument is the following: 1. If Socrates is a man, then he is mortal. 2. Socrates is mortal. 3. Therefore, Socrates is a man.
Am example of an argument map of an objection to this argument is the following:
I will not explain this argument map in detail because I will discuss logical validity in detail later on. However, it should be noted that the objection is further supported by another argument, which is in blue rather than pink. Arguments that support objections are in blue instead of pink, even though they could be considered to be part of the relevant objection. Another example of an objection to an argument without objecting to a specific premise in particular is the following: 1. Someone argues that there is life on another planet in the galaxy; there is no life on another planet in the galaxy; therefore there are other stars in the galaxy. 2. However, it's impossible for contradictions to exist. 3. Moreover, the two premises form a contradiction. 4. Therefore, at least one of the premises must be false. The argument map for this objection looks like the following:
The conclusion of the first argument is true, but that's not good enough. The problem is the argument itself is flawed. We don't know which premise is false, but we don't have to. We know that at least one of the premises has to be false.