Two premises, one conclusion

In the picture

1. 1Major premise: the red loop (humans) lies wholly inside the blue loop (mortals) — all humans are mortal.
2. 2Minor premise: the figurine (Socrates) stands inside the red loop — Socrates is human.
3. 3Middle term: the red loop appears in both premises and links them.
4. 4Conclusion: the figurine stands inside the blue loop — Socrates is mortal, and the middle term drops out.

Examples

• All buses on this route stop at the station; the 42 is on this route; so the 42 stops at the station.
• Every ticket bought today is valid for a week; you bought yours today; so it is valid for a week.

Quiz: Two premises, one conclusion (Age 17)

1. 1

   From “All birds have feathers” and “A penguin is a bird”, which conclusion must be true?

   • All animals with feathers are birds
   • A penguin has feathers
   • A penguin can fly
2. 2

   In “All mammals breathe air; all whales are mammals; so all whales breathe air”, which is the middle term?

   • breathe air
   • whales
   • mammals
3. 3

   In a valid syllogism, if both premises are true, what can you say about the conclusion?

   • It must be true
   • It is probably true but could still be false
   • It is true only if you can also check it by observation

The answers, each with its explanation, are in the app. This lesson has left the free week, so its quiz is part of the subscription.