More complex arguments

Extended arguments

The arguments we have looked at so far have been short and simple. It is very common, however, for arguments to have several steps. Here’s an example:

If the minimum wage is raised, then shops will need to put their prices up in order to pay their workers. If shops put their prices up, then we will all pay more for goods, and the general cost of living will rise. So, if the minimum wage goes up, the general cost of living will rise. We should not increase the cost of living for those who can least afford it. Therefore the minimum wage should not be raised.

The final conclusion of this argument is “The minimum wage should not be raised”. There is another conclusion in the argument, however. In the third sentence a conclusion is drawn. That conclusion is then used as a reason for the final conclusion. So it is operating as both a conclusion, and as a premise. We can call such conclusions, which are also premises, “intermediate conclusions”. To see how that works, here’s the argument in standard form:

P1. If the minimum wage is raised, then shops will need to put their prices up in order to pay their workers.
P2. If shops put their prices up, then we will all pay more for goods, and the general cost of living will rise (for everyone).
                                                      
C1/P3. If the minimum wage goes up, the general cost of living will rise (for everyone).
P4. We should not increase the cost of living for those who can least afford it.
                                                      
C. The minimum wage should not be raised.

An argument can have any number of intermediate conclusions. An argument has only one final conclusion: that is the ultimate thing the arguer wishes to persuade you of. We still number premises sequentially, but in an extended argument the intermediate conclusions are also numbered.

When assessing the validity of an extended argument each inference is assessed. (An inference occurs whenever the arguer proposes that a conclusion follows from premises. In standard form, an inference occurs every time an inference bar is used.) If even one inference is invalid, the argument as a whole is invalid.

Consider this argument:

If a foetus is a person then abortion is murder. To be a person, something must be self-aware. But a foetus isn’t self-aware. It follows that a foetus is not a person. And so abortion is not murder.

In standard form we get an extended argument as follows:

P1. To be a person, something must be self-aware.
P2. A foetus is not self-aware.

C1/P3. A foetus is not a person.
P4. If a foetus is a person then abortion is murder.
                                             
C. Abortion is not murder.

The first inference, from P1 and P2 to C1, is a valid inference. But the second inference, from C1 and P4 to C2, commits the fallacy of denying the antecedent. It is not a valid inference. So this argument as a whole is invalid.

To identify an intermediate conclusion it is best to start at the end of the argument and work backwards. So, begin by asking what the arguer is (ultimately) trying to persuade you of. This is the final conclusion. Then, ask what reasons are given for that. Once you have those reasons, ask yourself if those reasons are supported by any further reasons. If a reason is supported by a further reason, it is operating as an intermediate conclusion. It can often help to sketch out the structure of the argument. For examples of how to do this, see the section on argument trees below.

Dealing with longer texts

Even relatively short arguments can have intermediate conclusions. Most of the arguments you will encounter in everyday life are not this short. Most arguments occur within longer texts which include background information, irrelevant material, pieces of rhetoric, anecdotes and stories, repetition, and (sometimes) rambling. If you try to go through a long piece of text sentence by sentence, it is easy to end up overwhelmed, and to get bogged down. Instead, try the following:

• Read the text all the way through, and then put it out of sight.
• Ask yourself “what was the main point the person was trying to persuade me of?”. That is the final conclusion.
• Ask yourself “what were the main reasons the person gave for the conclusion?”. These are the main premises.
• Ask yourself whether anything was said to support those main reasons.

You’re now putting together the main line of argument. It is likely that none of what you have noted down follows the wording of the original. That is fine. It is not the precise words the arguer uses that matter, but the ideas which they communicate.

Once you have have noted down the main line of argument in this way, you can return to look at the original argument to see if you missed anything important. But it is still important not to get bogged down by particular phrasing, or by the detail of the argument. It is more important to present the basic point to others in your reconstruction. You can’t easily do this if you have 37 premises. Instead, make a fair and charitable reconstruction of the main points, and then assess those.