LOGICAL PATTERNS

Perhaps the most familiar example of “following logically” is a pattern of words like the following:

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.