Logic and

Logic and
Critical Thinking

Philosophy 4

Gale Justin

The objective of today’s class is to learn how:

uTo extract an argument from a passage that contains more information than just the argument.

uTo fill in missing premisses or a missing conclusion and rephrasing some of the statements of the argument.

uTo diagram arguments

We will consider each topic in turn.

uWe begin with extracting an argument from its context.

uWith respect to this topic, you should notice that passages containing arguments often also contain additional material that neither serves as the conclusion or a premiss of the argument.

This extraneous material can be:

uBackground information

uDispensable detail

uRestatement or repetition

uFrills

As an example, consider:

“I cannot believe that my daughter would throw a rock through a school window. Her friends claim that she was with them and that they were no where near the school when it happened. So she could not have done it.”

The first sentence can be classified as “dispensable detail” or perhaps as background information.

The fact a person cannot believe that an event has taken place is not evidence that the event has not occurred. Only the fact that friends claim that the girl was with them and that they were no where near the school when it happened gives us a reason to believe that she could not have done thrown the rcok through the window.

To extract the reasoning (that is, the argument) from the passage, you need to:

uRecognize that some reasoning is going on in the passage.

uSee what supports what.

uSometimes there are argument indicators (p. 12). But sometimes there are not.

Now here’s some groupwork on extracting the argument from a passage.

We must now decide how to write out the argument that is left. You need to put yourself in the author’s shores and ask yourself what he/she wants you to believe.

Consider the French Lunch and the Central Valley Levees passages. These would be put into standard form like this:

The author of the French Lunch wants you to believe that:

Premiss: The number of expensive meals has declined from 48 million in 1990 to 19 million in 2000.

Premiss: Lunch previously took an hour and a quarter but now only takes half an hour.

Premiss: French are avoiding rich sauces,liquors and desserts.

______________________________

Conclusion: There are clear signs that the French lunch is no longer an extravagant affair.

The author of the Central Valley levees wants you to believe that:

Premiss: The levees that gave way had been given high marks by state inspectors.

Premiss: These levees were well-maintained.

______________________________

Conclusion: Nearly all of the Central Valley levees that collapsed in the recent floods should not have given way.

Topic 2: Filling in what is missing:

Sometimes not all the premisses of an argument or the conclusion are stated. When the topic of the argument is familiar, it is not too difficult to fill in what is missing.

For example:

Jean studied at least ten hours for the exam, and she got an A. Sue studied at least ten hours for the exam, and she got an A. Jim probably also got an A.

What premiss is implied and is missing?

Here is another example:

If you think that Proposition 14 on the June ballot is the answer to school overcrowding, you should think again. Prop. 14 contains no guarantee whaever that the funds it generates will be used to reduce class size; the money will just go into a general fund and disappear without a trace, like so many of our tax dollars.

What is implied and is missing?

Sometimes you need to change change the structure of a sentence or change some of the wording. For example,
“Instead of raising the price of a stamp, why not reduce or eliminate the bulk-rate discount for catalogues? Don’t catalogues just cram our mailboxes and add to pollution? People who pay bills should not be penalized yet again.”

In this argument,
you need to change questions into statements and rephrase the last premiss. You could say “Rather than raising the price of a stamp, it would be a good idea to reduce or eliminate the bulk-rate discount for catalogues. This is because catalogues cram our mailboxes and add to pollution. Also, eliminating the bulk rate would not penalize people who pay bills.

In giving an argument, an author wants you to agree to (and sometimes to act on) some claim that he/she is making. In order to understand the author’s argument, you need to be able to “see” the relationship between the reasons being given for the claim and the claim (conclusion) itself. To do this, it can be helpful to know how to diagram an argument.

This brings us to our third topic of diagramming an argument.

Two kinds of support:

uIn some arguments, the reasons/premisses independently support the conclusion.

uIn some arguments, the reasons/premisses jointly support the conclusion.

uIn some arguments, some of the premisses independently support the conclusion and some jointly support it.

Examples of arguments in which the reasons independently support the conclusion.

“(1) Soda has no nutritional value as is evident from the fact that (2) athletes don’t use it before or after exercise. Moreover, (3) doctors don’t advise drinking as a nutritional supplement.”

Examples of arguments in which the reasons must be taken together (linked) to support the conclusion.

“(1) As soon as you hear a delay, you should hang up. Because (2) if it’s an automated calling system, it won’t call you back and (3) if it’s a friend, he will.”

Now consider this argument:

“(1) Professsors who do consulting work are not shortchanging their students. (2) Information gained through the consultations enhance the class lectures. (3) Consulting work often involves having money to pay research assistants. (4) The research assistants can be chosen from among the professor’s students.”

In the latter argument, the first reason independently supports the conclusion. The second and third reason must be linked, if they are to support the conclusion.

Once you find that a passage contains an argument, you want to show its structure.

uPeople can disagree about how to structure any one argument.

uBut some ways of structuring the argument are simply incorrect.

To show the structure of an argument, we adopt the following conventions:

uNumber the statements of the passage in the order in which they occur.

uPlace the number of the conclusion of the argument below its premisses.

uUse an arrow as a conclusion indicator.

This argument has the following structure:

“(1) Soda has no nutritional value as is evident from the fact that (2) athletes don’t use it before or after exercise. Moreover, (3) doctors don’t advise drinking as a nutritional supplement.”

This argument has the following structure:

“(1) As soon as you hear a delay, you should hang up. Because (2) if it’s an automated calling system, it won’t call you back and (3) if it’s a friend, he will.”

Now consider the structure of this argument: