Obversion uses complements to say the same thing in the opposite quality. It works for every form.
Key idea
To obvert: (1) change the quality (affirmative ↔ negative: A ↔ E, I ↔ O) and (2) replace the predicate with its complement. The obverse always means the same as the original.
| Original | Obverse |
|---|---|
| All S are P | No S are non-P |
| No S are P | All S are non-P |
| Some S are P | Some S are not non-P |
| Some S are not P | Some S are non-P |
Why it works
The two changes cancel each other, like two negations. "All S are P" says no S lies outside P. "Outside P" is exactly "in non-P", so it says no S are non-P. Saying an S is not in non-P is the same as saying it is in P, because P and non-P split everything with no gap and no overlap.
Worked examples
Worked example: Obverting an E
Obvert "No coders are musicians".
- Change the quality: E becomes A ("All … are").
- Complement the predicate: musicians → non-musicians.
Answer: All coders are non-musicians
Worked example: Removing a "non-"
Obvert "No cyclists are non-debaters".
- Change the quality: E becomes A.
- Complement the predicate: the complement of non-debaters is debaters.
Answer: All cyclists are debaters
Obversion is the main tool for removing a "non-" from an argument. When a syllogism seems to have four terms because one of them is a complement, obverting a premise often brings it back to three (you will use this in Unit 6).
Common mistake
Doing only half the job: changing the quality but forgetting to complement the predicate ("No S are P" from "All S are P" means something very different), or complementing the subject instead of the predicate. Check: the subject term must come through untouched, and exactly one "not" or "no" is added or removed.