Reading

• Jim Pryor’s ‘What Is an Argument?'
• Jim Pryor’s ‘Vocabulary Describing Arguments’
• Ted Sider’s notes on argument extraction
  • This is a paper assignment from one of his intro courses, but it includes an excellent explanation of argument extraction. Ignore the assignment itself. Start reading at the bold “Extracting” on page 1.

Numbered-premise arguments

Here’s an argument presented in numbered-premise form:

1. If you legally voted in the previous U.S. presidential election, then you are a U.S. citizen.
2. My cat is not a U.S. citizen.
3. Therefore, my cat did not legally vote in the previous U.S. presidential election.

(1) and (2) are the premises. (3) is the conclusion. Listing out the premises and conclusion of an argument makes the argument easier to think and talk about.

Argument extraction

Usually the arguments that we study in this course are not presented in numbered-premise from by their authors. To extract the argument from a prose text is to turn it into numbered-premise form.

For example, here’s an argument from the Gorgias that we’ll consider in a later class:

I believe that nature itself reveals that it’s a just thing for the better man and the more capable man to have a greater share than the worse man and the less capable man. Nature shows that this is so in many places; both among the other animals and in whole cities and races of men, it shows that this is what justice has been decided to be: that the superior rule the inferior and have a greater share than they…I believe that these men do these things in accordance with the nature of what’s just—yes, by Zeus, in accordance with the law of nature, and presumably not with the one we institute. (483c-e)

Here’s one way to extract the argument from this passage:

1. It is natural for the strong to get a greater share than the weak.
2. Everything natural is just.
3. Therefore, it is just for the strong to get a greater share than the weak.

See how much easier this is to think about than the original wall of text?

Note that (2) isn’t explicitly stated in the passage, but I’ve included it because it’s being tacitly assumed and is needed to support the conclusion.

Argument evaluation

When evaluating an argument, ask yourself:

• Do the argument’s premises support its conclusion?
• Are the argument’s premises true?

One way for an argument’s premises to support its conclusion is for them to entail its conclusion. This means that it’s impossible for the conclusion to be false if all the premises are true. In this case, we say that the argument is valid:

• Validity: An argument is valid if and only if its premises entail its conclusion.¹

Whether an argument is valid depends only on its logical structure. Valid arguments can have false premises, and false conclusions. But if all of a valid argument’s premises are true, then we say that the argument is sound:

• Soundness: An argument is sound if and only if: (1) it is valid and (2) all of its premises are true.

It follows from these definitions that if an argument is sound, then its conclusion must be true. So if you deny an argument’s conclusion, then you must deny that it is sound. In other words, you must either claim that its premises don’t entail its conclusion or that not all of its premises are true.

Argument repair

Even if an argument is unsound, there might be a way to revise it to make it sound. For example, consider this argument:

1. There is a law against cheating on your taxes.
2. It is always wrong to break the law.
3. Therefore, cheating on your taxes wrong.

(2) is false because it’s not wrong to break unjust laws. Nonetheless, there’s a straightforward way to repair the argument:

1. There is a just law against cheating on your taxes.
2. It is always wrong to break just laws.
3. Therefore, cheating on your taxes is wrong.

(The tradeoff to this revision is that it makes (1) more controversial.)

Your evaluation of an argument should include an attempt to repair it if you think it is unsound.

Deductive vs. inductive arguments

Although one way for the premises of an argument to support its conclusion is for them to entail it, that’s not the only way. For example, consider this argument:

1. It has not snowed in Toronto in July in the past 50 years.
2. Therefore, it will not snow in Toronto next July.

(1) doesn’t entail (2), because it’s possible for it to snow in Toronto next July, no matter what the weather in the past has been. Nonetheless, (1) still gives you good reason to accept (2).

An argument like this one, whose premises are supposed to support but not entail its conclusion, is inductive.² An argument whose premises are supposed to entail its conclusion is deductive. Most of the arguments that we’ll consider in this course are deductive.

Exercises

1. Classify each of the following arguments as valid or invalid:
   • Argument 1:
     1. Grass is green.
     2. Therefore, grass is green.
   • Argument 2:
     1. All men are mortal.
     2. Socrates is a man.
     3. Grass is green.
     4. Therefore, Socrates is mortal.
   • Argument 3:
     1. If you jump out of a two story building, then you will break your legs.
     2. Therefore, if you jump out of a two story building, then you will feel pain.
2. Come up with a valid argument for the conclusion that Toronto is the capital of Monaco.
3. Extract the argument from the following passage:

   Some people fail to vote because they think one vote won’t make a difference. But what if everyone thought that way? It’d be terrible, since our democracy would collapse.

Solutions

1. 1. Valid. Necessarily, if grass is green (and the premise is true), then grass is green (and the conclusion is true). But this is still a bad argument, since it is question-begging. Note that this argument is also sound, since grass is green.
   2. Valid. (3) does no work and should be omitted. Nonetheless, it’s true that, necessarily, if all the premises are true, then the conclusion is true.
   3. Invalid. It is possible for the conclusion to be false even if the premise is true. For example, you might be on heavy painkillers when you jump out of the building. However, we can make the argument valid if we add a premise to it:
      1. If you jump out of a two story building, then you will break your legs.
      2. If you break your legs, then you will feel pain.
      3. Therefore, if you jump out of a two story building, then you will feel pain.

2. There are infinitely many correct responses. Following argument 1 from the previous exercise, you could just say:

   1. Toronto is the capital of Monaco.
   2. Therefore, Toronto is the capital of Monaco.

   If you want a more interesting valid argument, you could say:

   1. Toronto is identical to Beijing.
   2. Beijing is the capital of Monaco.
   3. Therefore, Toronto is the capital of Monaco.

   This highlights that the mere existence of a valid argument for a given claim does nothing whatsoever to support the claim. There is a valid argument for every claim.

3. The tacit conclusion of the argument in the passage is that no one should fail to vote. Here’s a first try to extract the argument for this conclusion:

   1. Terrible consequences would follow from everyone failing to vote.
   2. Therefore, no one should fail to vote.

   The problem is that this argument is invalid: by itself, (1) doesn’t entail (2). But the proponent of the argument probably has an tacit premise in mind which would make the argument valid. Here’s one way to supply the tacit premise:

   1. Terrible consequences would follow from everyone failing to vote.
   2. If terrible consequences would follow from everyone doing something, then no one should do it.
   3. Therefore, no one should fail to vote.

   This extraction is better than the first one because it makes explicit an important premise that the argument tacitly relies on.³