LESSON #15

Standard Form, Mood and Figure

Click here to skip the following discussion and go straight to the assignments.

Now we will combine categorical propositions to create what are called categorical syllogisms.

To be in standard form a categorical syllogism meets the following strict qualifications:

· It is an argument with two premises and one conclusion.

· All three statements are categorical propositions.

· It contains exactly three different terms.

· Each term is used exactly twice.

The following notes apply to standard form categorical syllogisms:

· Major term (P) = Predicate of conclusion

· Minor term (S) = Subject of conclusion

· Middle term (M) = Term that occurs in both premises

Don't let the fact that in this chapter S and P stand for "minor term" and "major term," and last chapter they stood for "subject term" and "predicate term" confuse you. It would have been good to use different letters, but, sadly, Major, Minor and Middle all start with "M." Just remember that they now mean something somewhat different.

· Major Premise = Premise containing major term

· Minor Premise = Premise containing minor term

List major premise first and minor premise second (conclusion, of course, is last).

HELPFUL NOTE: The second term in your conclusion will always be in the top premise. (This follows from the definition of major premise)

Once a categorical syllogism is in standard form, we can then determine its mood and figure. The form of the syllogism is named by listing the mood first, then the figure.

· Mood depends upon the type of propositions ( A, E, I or O) It is a list of the types beginning with the major premise and ending with the conclusion.

· Figure depends on the arrangement of the middle terms in the proposition. You must memorize the four figures on p. 255

It is quite simple to determine the mood and figure of a standard form categorical syllogism. Don't make it difficult.

Once you have determined the mood and figure you can look at the first chart on p. 256 (unconditionally valid) to determine whether the argument is valid or not. If the argument form is in the chart, the argument is valid.

If it is not in the chart, and if you can certify that the required terms of the syllogism exist, then check the second chart.  If it is on this chart, the argument is valid. If you don't know about the existence of the terms (you were only given the argument form with no particular content) you can call the forms on the second chart conditionally valid.

If the argument form is on the second chart but the terms don't exist the argument is invalid, and if the form is on neither chart it is invalid.

Reconstruction

You will also need to be able to reconstruct a "generic" standard form categorical syllogism, when you are given the mood and figure. This is also quite simple if you take it step by step:

STEP 1. Preceding each line, write the statement type letter. (A-E-I or O)

STEP 2. Create a skeleton for each statement. Write your quantifier (All, Some, No); skip a blank space; write your copula (are, are not); leave a blank space.

STEP 3. Based on the figure, fill in the middle terms (M).

STEP 4. Place your minor terms (S)

A. In the first blank in the conclusion, and

B. In remaining blank in second premise.

STEP 5. Place your major term (P)

A. In last blank in conclusion, and

B. In remaining blank in first premise.

e. g., EAE-2

 Step 1. E A E

 Step 2. E No are A All are E No are

 Step 3. E No are M A All are M E No are

 Step 4. E No are M A All S are M E No S are
 Step 5. E No P are M A All S are M E No S are P

Logic Coach Assignment: 5.1 I all, II all III 1-5

Assignment 1: (Six points each)

Identify the major, minor, middle terms and the mood and figure of each of the following standard form categorical syllogisms. Determine whether the argument is valid or invalid.

1. All cats are felines
No dogs are cats

No dogs are felines

2. No islands are men
Some islands are continents
Some continents are not men

3. Some paintings are works by Renoir
All works by Renoir are masterpieces

Some masterpieces are paintings.

4. All ducks are birds
All griffins are ducks

Some griffins are birds

5. Some P are not M

All S are M

Some S are not P

Assignment 2: (10 points each)

Put the following syllogisms into standard form, name the mood and figure and determine whether the argument is valid or invalid. Use letters to represent the terms (i.e., abstract the form from the content). Be sure to tell what the letters stand for. You may need to refer to section 4.7  (pp. 241-249) for help translating these statements into standard form propositions.

1. Some triple crown winners were sired by Northern Dancer. Secretariat was sired by Northern Dancer. So Secretariat will be a triple crown winner.

2. All unicorns are one-horned animals. No unicorns exist because no one-horned animals exist.

3. Communism is not a viable economic system. All viable economic systems must allow free enterprise and communism does not allow such enterprise.

4. Some homosexuals are AIDS victims. Jim is homosexual so he must have AIDS.

Assignment 3: (five points each)

Reconstruct the following syllogisms:

1. OAO-4

2. AAI-1

3. EEO-2

4. EAO-3

5. III-1

6. AEE-2