- 1. All igs are ows.
- 2. All ows are umphs.
- 3. Therefore, all igs are umphs.
If statements 1 and 2 are supposed, then statement 3 is logically true. In other words, statement 3 logically follows from statements 1 and 2. This word pattern is logically true, no matter what substitutions we make for igs, ows, and umphs. For example, we can replace igs by men, ows by animals, and umphs by mortals, and obtain:
- 4. All men are animals.
- 5. All animals are mortals.
- 6. Therefore, all men are mortals.
The invented words “igs,” “ows,” “umphs” mark places in the logical pattern where we can insert any names we are interested in. The words “all,” “are,” “therefore” and the ending s mark the logical pattern. Of course, instead of using invented words like “igs,” “ows,” “umphs” we would usually put A’s, B’s, C’s. This logical pattern is called a syllogism and is one of the most familiar. But there are even simpler logical patterns that are also familiar.
THE SIMPLEST LOGICAL PATTERNS
Many simple logical patterns are so familiar that we often use them without being conscious of doing so. The simple logical patterns are marked by words like “and,” “or,” “else,” “not,” “if,” “then,” “only.” In the same way, simple arithmetical patterns are marked by words like “plus,” “minus,” “times,” “divided by.”
Let us see what some of these simple logical patterns are. Suppose that we take two statements about which we have no factual information that might interfere with logical supposing:
- 1. John Doe is eligible for insurance.
- 2. John Doe requires a medical examination.
In practice, we might be concerned with such statements when writing the rules governing a plan of insurance for a group of employees. Here, we shall play a game:
(1) We shall make up some new statements from statements 1 and 2, using the words “and,” “or,” “else,” “not,” “if,” “then,” “only.”