Conversion is the simplest immediate inference: swap the subject and predicate terms. Whether it is valid depends on the form, and distribution explains which.
| Original | Converse | Valid? |
|---|---|---|
| No S are P | No P are S | yes |
| Some S are P | Some P are S | yes |
| All S are P | All P are S | no |
| Some S are not P | Some P are not S | no |
Key idea
Conversion is valid for E and I, which treat both terms alike. It is not valid for A or O. On the traditional reading, A converts by limitation: from "All S are P" to "Some P are S".
Why it works
In a Venn diagram, E shades the overlap and I puts an X in the overlap. The overlap belongs to both circles equally, so swapping the circles leaves the same picture: same picture, same meaning. A shades the part of S outside P, but its converse shades the part of P outside S, a different region. Distribution says the same: A distributes S but not P, so after the swap P would be distributed without the original statement giving us anything about all P.
Worked examples
Worked example: A valid conversion
Convert "Some bakers are anglers". Is the converse equivalent?
- Swap the terms: "Some anglers are bakers".
- It is an I statement, and I converts validly: both say something is both a baker and an angler.
Answer: Some anglers are bakers: equivalent
Worked example: Conversion by limitation
On the traditional reading, what follows from "All early risers are drummers" by conversion by limitation?
- Plain conversion ("All drummers are early risers") does not follow.
- Swap the terms and weaken "all" to "some": I.
- It needs the traditional assumption that there are early risers.
Answer: Some drummers are early risers
Common mistake
Converting an A proposition: "All cats are animals" does not give "All animals are cats". This illicit conversion is one of the most common mistakes in reasoning. Check: does the converse claim something about every member of a class the original only partly covered? Then it says more than the original.