The syllogism

The typical reasoning of a proof is the syllogism: from two premises a necessary conclusion is drawn.

Example — Syllogism

1. “Every man is mortal” (hypothesis — relation)
2. “Gianni is a man” (hypothesis — property)
3. Therefore: “Gianni is mortal” (thesis)

In set-theoretic terms: $\{\text{uomini}\}\subset\{\text{mortali}\}$, and Gianni $\in\{\text{uomini}\}$.

Be careful, however, not to reverse the direction of the inclusion: it is a very frequent logical error.

Caution — Faulty syllogism

“All men have a nose” and “Iacopo has a nose” does not imply “Iacopo is a man”. The set of men is contained in the set of those who have a nose, but not vice versa.

Links

Topics: Euclidean geometry
Concepts: Proof · Syllogism
Skills: Proving