Syllogisms
📋 What it is
A syllogism draws a conclusion from two premises that share a middle term (“All A are B; all B are C; so all A are C”).
🗣️ Coach says
A syllogism is a two-step chain. The premises share a “middle” idea that links them. “All dogs are mammals; all mammals breathe air; so all dogs breathe air.” The middle term (mammals) is the bridge — and it appears in both premises but NOT the conclusion.
🧠 Memory hook
Two premises, one shared bridge word, one conclusion. The bridge drops out at the end.
😂 Giggle
What did the conclusion say to the premises?
"I couldn't exist without you — you're my logical support!"
😲 Whoa!
Aristotle catalogued every valid syllogism form — medieval students memorised them with nonsense words like “Barbara” and “Celarent” to remember which patterns work.
✅ Quick check: “All squares are rectangles; all rectangles have four sides; so ___?” Finish it validly.
Say your answer out loud first — then reveal.
“…so all squares have four sides.” The bridge (rectangles) links squares to four-sidedness.
A valid syllogism chains the two premises through the shared middle term.
🪄 Trick question: “All cats are animals; some animals are dogs; so some cats are dogs.” Valid?
Careful — think it through, then reveal.
Invalid — “some animals are dogs” doesn’t connect to cats; the pieces don’t chain, even though each premise is true.
A syllogism is valid only if the terms genuinely link; here the middle term isn’t used correctly.
🧪 Try it! (2 minutes)
Build your own: pick A→B and B→C facts, then state A→C. Check the middle word appears in both premises only.