Some words in everyday statements change the order of the terms. The most important is only.
Key idea
"Only S are P" and "None but S are P" become All P are S (swap the terms). "The only S are P" becomes All S are P (keep the order). "All except S are P" makes two claims: All non-S are P, and No S are P.
Why it works
"Only members may vote" sets a requirement on voters: to vote, you must be a member. That is a claim about every voter: all voters are members. It says nothing about every member; some members may stay home. So the class after "only" is the one the other class must fit inside, and it becomes the predicate. "The only" works the other way: "The only animals in the canyon are skunks" says every animal in the canyon is a skunk.
| Everyday wording | Standard form |
|---|---|
| Only ticket holders are allowed backstage. | All people allowed backstage are ticket holders. |
| None but seniors may park on campus. | All students who may park on campus are seniors. |
| The only dogs here are puppies. | All dogs here are puppies. |
| All except seniors are campers. | All non-seniors are campers, and no seniors are campers. |
Worked examples
Worked example: Only
Put "Only adults may use the hot tub" in standard form.
- The class after "only" is the requirement: adults.
- Every person who may use the hot tub must be an adult.
Answer: All people who may use the hot tub are adults.
Worked example: All except
Put "All except the drummers are singers" in standard form.
- An exceptive makes two claims: one about everyone else, one about the exceptions.
- Everyone who is not a drummer is a singer: All non-drummers are singers.
- The drummers are the exception: No drummers are singers.
Answer: All non-drummers are singers, and no drummers are singers.
Common mistake
Keeping the order of the words. "Only members may vote" does not say that all members vote; it says that all voters are members. Check with a case: picture a member who stays home. Is the rule broken? No, so the rule is not about every member.