LESSON #11

Components of Categorical Propositions, Quantity, and Quality

Reading Assignment: 4.1 & 4.2 (pp. 199-207) Also, for your information 4.7 (241-249)

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

Categorical propositions are propositions ("proposition" is a synonym for "statement") that assert something about classes of things in a particular way. We dealt with what are called categorical propositions in an informal way in Lesson #5. Now we are going to get serious about them. In Chapter 4, we will be analyzing and learning many things about single propositions, and then in Chapter 5 we will be combining the propositions into arguments called syllogisms.

This exercise consists of a lot of memorization of names and conventions. SORRY!.

Categorical propositions have a standard form. There are only four types of standard form categorical propositions. We represent each of the four types of standard form categorical propositions as a capital letter (A, E, I and O). :

The first term is called the subject term and the second or last term is called the predicate term. These terms must be classes, not merely adjectives, adverbs, etc.

The words all, some and no are called quantifiers because they determine the quantity (how much) of the subject class is or is not in the predicate class. No other words can be used as quantifiers in standard form propositions.

Finally, the words are and are not are called copulas because they connect the subject and predicate (same root as copulate). No other words can be used as copulas.

Most statements, obviously, are not in this form, but can be translated into it, with a certain amount of tinkering and common sense. Though you will not be asked merely to translate English statements into categorical propositions, you should look over the suggestions for doing this in section 4.7. It will help you learn the form and in a couple of exercises later in the course it will be assumed that you can do this.

Each of the these four types of statement has a quality (affirmative or negative) and quantity (universal or particular). You will need to memorize the following chart.

NOTE: "All S are not P" is NOT a standard form proposition. It is ambiguous. (and oooh philosophers HATE ambiguity!) This formulation, when you hear it in common language, sometimes means "some S are not P" (O statement) and sometimes means "No S are P" (E statement)  For example, the first version may be uttered in protest when someone has claimed that all of the S's are P's, and the speaker wants to point out that only most, but not really "all" are. The second version may occur as a protest against someone who claims that only some S's are not P's, when really none of them are. 

(ALSO NOTE: The concept of distribution, which is also mentioned in this chapter, will become useful in Lesson #16--you can memorize it then or now, whichever you prefer.)

Logic Coach Assignment: 4.1 I 1-3; 4.2  II, III, IV

Assignment 1: (five points each)

For the following standard form categorical propositions:

A. Identify the quantifier, subject and predicate terms, and the copula, and then the letter name (type), quantity and quality.

1. Some pigs are wild animals.

2. All elderly members of the Dragon club are inveterate prattlers.

3. No canaries are melancholy creatures.

4. Some holidays spent in the mountains are not stimulating and refreshing vacations.

5. Some professors are terrible bores.

Assignment 2: For the following exercise be sure to keep your answers in standard form. (i.e., A, E, I or O--'All S are not D' is not in standard form.) Go slowly. It is easy to make mistakes on these.

B. Change the quality but not the quantity.

1. No coins are square objects.

2. Some professors are terrible bores.

3. All hogs are porcine creatures.

4. Some women are beautiful people.

5. No catfish are feline creatures.

 

C. Change the quantity but not the quality.

1. Some people are ugly people.

2. Some right triangles are not Pythagorean figures.

3. All politicians are trustworthy persons.

4. Some spiders are web spinners.

5. No elderly ladies are talkative people.

 

D. Change both the quantity and the quality.

1. All rabbits are furry animals.

2. Some concerts are enjoyable affairs.

3. No teachers are students.

4. Some teachers are not competent teachers.

5. All wallabies are marsupials.

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