more from Euclid

Single Idea 13907

[catalogued under 4. Formal Logic / C. Predicate Calculus PC / 2. Tools of Predicate Calculus / c. Derivations rules of PC]

Full Idea

Euclid begins proofs about all triangles with 'let ABC be a triangle', but ABC is not a proper name. It names an arbitrarily selected triangle, and if that has a property, then we can conclude that all triangles have the property.

Gist of Idea

If you pick an arbitrary triangle, things proved of it are true of all triangles


report of Euclid (Elements of Geometry [c.290 BCE]) by E.J. Lemmon - Beginning Logic 3.2

Book Reference

Lemmon,E.J.: 'Beginning Logic' [Nelson 1979], p.106

A Reaction

Lemmon adds the proviso that there must be no hidden assumptions about the triangle we have selected. You must generalise the properties too. Pick a triangle, any triangle, say one with three angles of 60 degrees; now generalise from it.