Types and Properties of Arguments
Suppose someone wants to assert a claim that something is true. Following convention we will call that claim q (recall that our letters stand for propositions, sentences which are either true or false). Now if q is not obviously true, it seems appropriate for the person asserting the claim to support it with some type of evidence, or at the very least provide reasons for claiming q is true. Since evidence comes in the form of propositions which are either true or false, then we can also denote each piece of evidence as p, r, s, etc. When we do this, we are saying that because of p, r, s, etc. it is reasonable to accept the claim q as true.
One of the major goals of philosophical logic is classifying arguments and discovering whether an argument really gives good reasons for accepting its main claim. This process of reflection and analysis is called reasoning, and as a matter of fact, it is of such importance that many textbooks define philosophical logic as the process of distinguishing between good and bad reasoning! Let us now informally define the argument.
It is important to note that an argument consists of two parts, a conclusion and at least one premise given to support the conclusion. Informally, an argument is similar to the following abstract claim: "because p is true, then it is reasonable to conclude q is true". In this case, p is the premise or set of premises, and q is the conclusion.
In real life arguments are far more complex than this simple abstract example, and we will examine many in this section. In particular most arguments have more than one premise and many times more than one conclusion. When this happens, we can try to identify the main conclusion and consider the other conclusions as acting as premises (in context of the entire argument) which are intended to support the main conclusion. Let's illustrate this process with some examples:
Since there was heavy rush-hour traffic, I feel certain that Tom missed his flight.
In this case, our conclusion (claim) is, "Tom missed his flight", and the reason given for this claim is the single premise, "there was heavy rush hour traffic". In this simple case, it is easy to see which part of the argument is the conclusion and which is the premise. The ignored phrase, "I feel certain" is not really part of the argument, but rather acts as an indicator that the person making the arguments feels strongly that the stated conclusion is actually true. The word "since" is an important indicator that what follows immediately after this word is a premise, rather than a conclusion.
If Henry is the person who damaged the rental car, then he must have been in San Diego during Spring Break. If Henry were in San Diego during Spring Break, then he could not have been in Tucson at the same time. But we know Henry was in Tucson during Spring Break, so Henry is not the person who damaged the rental car.
In this example, the conclusion is that Henry is not the person who damaged the rental car. The premise that Henry was in Tucson during Spring Break supports the claim that Henry was not in San Diego, which in turn leads directly to the conclusion that Henry was not responsible for the damaged rental car, since after all, the very first premise asserts that, "If Henry is the person who damaged the rental car, then he must have been in San Diego during Spring Break."
This is an example of a chain of reasoning, where one premise leads to another conclusion which together with another premise leads to the final conclusion. Chains of reasoning are also called hypothetical syllogisms, which we will study more in Part 2.
It is a good idea to make sure you have working fire alarms in your house. Just look at the family whose house burned down on Christmas. They lost everything in their house, and almost lost their daughter who nearly died of smoke inhalation. Their house did not have working fire alarms, and for that reason, the fire itself went unnoticed while the family slept. They were saved only by the chance occurrence of a neighbor's teenage son arriving home late from a Christmas-eve date who noticed the fire and woke the family up.
Example 2.0.3 is a bit more complicated than the previous examples but it is more like arguments we encounter in our daily lives and merits a more detailed analysis.
In order to start our analysis of the argument we break it down into its parts, which means finding its premises and the principle conclusion. To find the main conclusion, consider each sentence in turn, and ask, "Is this the main claim all the other sentences taken together aim to establish?" Another way to detect the main conclusion is to look for key words and phrases which often are stated before the conclusion (or could be stated before the conclusion without change in meaning). A list of such words and phrases would include:
- it follows that
- we can see
- we conclude
While it is not always true, many times the conclusion is the first sentence of an argument or the last sentence of an argument. Sometimes a general conclusion is stated first and a more specific conclusion is stated in the last line of the argument.
Using the criteria above, we see that the main conclusion is stated at the very start of the argument, namely, "Its a good idea to make sure you have working fire alarms in your house." The remainder of the sentences basically give reasons that support this conclusion.
Since premises are reasons given to support the main conclusion, let's turn to those reasons now and examine how they support the conclusion. In doing so, we may have to identify some unwritten assumptions that the author has made, and re-write some sentences so that they take the form of propositions (sentences which are either true or false). To help with this process, let's enumerate each sentence of the argument and consider each in turn:
- It is a good idea to make sure your have working fire alarms in your house.
- Just look at the family whose house burned down on Christmas.
- They lost everything in their house, and almost lost their daughter who nearly died of smoke inhalation.
- Their house did not have working fire alarms, and for that reason, the fire itself went unnoticed while the family slept.
- They were saved only by the chance occurrence of a neighbor's teenage soon arriving home late from a Christmas-eve date who noticed the fire and woke the family up.
Considering each sentence we discover that 2 - 5 support 1, which is just saying that 1 is the main conclusion and 2 - 5 are premises that support that conclusion.
However, a really attentive reader might point out that according to our definition of an argument sentence number 2 does not seem to be part of the argument! Why?
According to the definition of an argument, premises are propositions, and propositions are statements which are either true or false. In this case, sentence number 2 is a command, not a proposition. Commands are neither true or false (whether or not you obey the command is a proposition, but the command itself is not). According to our definition, 2 can not form part of our argument. But that sentence is connected in some way to the to the argument as a whole and should not be ignored. How do we resolve the problem? Of course, we could just simply re-define the term "argument" to include cases like these, or just throw out sentence 2, but there is a less drastic option which logicians employ constantly; we simply re-state the essence of the sentence in such a form as to keep its connection to the main conclusion, while turning it into a proposition. Such a restatement of 2 may be: "A family's house burned down on Christmas." Now clearly, this statement is either true or false, and is important to the conclusion and the remaining sentences, and this re-writing of 2 fully preserves the original's connection to the whole, hence logicians consider this an acceptable change. After we have made this change, we see the remaining sentences are indeed propositions and support the main conclusion.
But what is the nature of their support for the main conclusion? To answer this question the concept of unstated assumptions, or unstated premises, made by the argument is helpful. What are some of these assumptions which make the premises relevant to the conclusion?
Let's start with our modified premise 2, "A family's house burned down on Christmas". What is it about this premise that makes it relevant to the claim that, "It is a good idea to make sure your have working fire alarms in your house"? There are several possibilities, but let's explore the obvious by first asking, Would it matter if the premise stated that the house burned down on another day rather than Christmas? If not, then the fact that it burned down on Christmas is not as important as another fact, that being that it burned down (to see this, just change 2 to state, "A family's house did not burn down . . .", and ask if that changes its connection to the conclusion). So the fact that a house has burned down is at least relevant to having working fire alarms, but we need to pursue the issue more. Suppose the family did have working fire alarms, would that fact result in the house not burning down? This one is harder to answer, as it requires more information than we know or can reasonably guess. Whether or not having a working fire alarm would prevent the house from burning down, the argument gives us another line of reasoning - premise 3 suggests that losing everything, including the life of a loved one is undesirable, and premise 4 argues that without working fire alarms, one might sleep through a fire, and as a result lose one's life. Finally premise 5 suggests that unless one wants to leave one's alert system to chance, then one should have a working fire alarm. What has been assumed in all of this? At least the following (and probably more):
- It is possible that houses burn down.
- It is better that family members live than die in house fires.
- One can die from house fires which go unnoticed.
- Many things go unnoticed while sleeping.
- A working fire detector can sound the alarm, which, at the very least will alert even sleeping people to a fire which might otherwise go unnoticed.
- A fire detector can monitor one's house at all times, especially late at night when people are asleep.
- It is better not to leave the fire alarm alert to chance.
- Fire alarms are easy to buy and do not cost much, especially when compared to the possible cost of not having a fire alarm.
With these assumptions in mind, we can re-read Example 2.0.3 and see that each sentence is connected to each of the above assumptions, and the natural conclusion is that it is better to have a working fire alarm than none at all. It is, of course, a legitimate question as to whether the person making the above argument should include the above assumptions as additional premises, but the point of example 2.0.3 was to examine an argument that is more like one encountered in our daily lives. Notice that we have not stated anything about the strength of the above argument, or just how relevant the premises are to the conclusion, whether any single premise or conjunction of premises implies the conclusion nor have we said anything about the likelihood of the conclusion being true, or in general, whether a given argument presents a good case for its specific conclusion(s). These concepts will be the detailed subject of later investigations.
To get us started down that road, we now first consider how to combine propositions, and then turn to the very important concept of inference where we will use that concept to classify arguments in terms of what can be said about the likelihood of a conclusion given the assumption that all of the premises are true.