Lesson · 4 min Gentle

All and Some

In one line “All A are B” places any A among the B; it cannot be turned around, and one exception breaks it.

“All swans are white” makes a big promise. It lets you say of any swan that it is white. It does not let you say that anything white is a swan, and it says nothing about what is not a swan. Turning an “all” sentence around is one of the commonest slips in everyday reasoning.

A big promise is easy to break. One black swan sinks “all swans are white,” however many white swans came before. “Some” works the other way. One white swan proves “some swans are white,” and no number of black ones can unprove it.

Watch for the quiet slide from “some” to “all.” A story about a few becomes a claim about everyone, and then a rule. When a claim says “all,” ask what one case would break it, and whether anyone has looked for that case.

Go deeper

Aristotle sorted simple claims into four forms. All A are B; no A are B; some A are B; some A are not B. Two of them turn around safely. “No A are B” gives “no B are A,” and “some A are B” gives “some B are A.” The other two do not. “All A are B” does not give “all B are A.” And “some A are not B” does not give “some B are not A.” Medieval teachers drew the four on a square and marked which pairs could both be true and which could not. The habit worth keeping is simpler than the square: before you turn a sentence around, ask which of the four it is.

The hiring rule

Kofi’s manager says, “All our best salespeople came through the trainee program,” and wants to hire only trainees from now on. Kofi draws it out. Even if every top seller was a trainee, the turned-around sentence, “all trainees become top sellers,” is a different claim. The records show plenty of trainees who left within a year.

Then he finds Amira, a top seller hired from a rival. One case, and the “all” is gone. The program may still help; the rule needs a smaller word.

Try this today Catch yourself saying “all” or “everyone” once today, and ask whether you mean all, most, or the ones you happen to have met.

Cite or share this lesson

A plain reference you can paste into notes or an essay:

Quest2Reason. “All and Some.” https://quest2reason.com/learn/lesson/all-and-some. Accessed 14 November 2026.

Sources

Stanford Encyclopedia of Philosophy, “The Traditional Square of Opposition” — The four classic sentence forms, all, none, some and some not, and which of them can be turned around.
Aristotle, Prior Analytics — The first systematic treatment of arguments built from “all” and “some” sentences, in Jenkinson’s translation.
John Stuart Mill, A System of Logic — Book II on the syllogism and Book III on induction: how a claim about all rests on cases, and what one contrary case does to it.