The last relation on the square runs down the sides: from A to I and from E to O. Each universal is the superaltern, and the particular below it with the same quality is its subaltern.
Key idea
On the traditional square, truth flows down (if A is true, I is true; if E is true, O is true) and falsity flows up (if I is false, A is false; if O is false, E is false). Everything else is undetermined.
Why it works
If every one of the students is a swimmer, and there is at least one student (the traditional assumption), then at least one student is a swimmer: truth flows down. If not even one student is a swimmer, then certainly not all of them are: falsity flows up. But "some are" does not make "all are" true, and "not all are" does not make "some are" false, so truth does not flow up and falsity does not flow down.
Worked examples
Worked example: Truth down
"No birdwatchers are early risers" is true. What follows about "Some birdwatchers are not early risers"?
- E and O are subalterns, with E on top.
- Truth flows down: if none are, then (assuming there are birdwatchers) some are not.
Answer: true
Worked example: Truth does not flow up
"Some musicians are painters" is true. What follows about "All musicians are painters"?
- I is the subaltern of A.
- Truth flows down, not up. Some being painters fits both "all are" and "only some are".
Answer: undetermined
Common mistake
Sending truth up the square: "Some S are P" being true does not make "All S are P" true. Check with a case where only some S are P: the I is true and the A false, so the I alone could not decide the A.
Subalternation depends on the subject class having members. On the modern reading it fails, as a later lesson shows.