Schoolman

Too easy! Relations can be handled by "immediate inference by converse relation", which was recognized by Aristotle. Thus, in every relational expression it's possible to find the converse, e.g.: A is the mother of B => B is the child of A A is larger than B => B is not larger than A A loves B => B is loved by A etc... So the above arguments are easily dealt with. L = lamp post A = animals T = Tiger 1. Some L is left of All A 2. All T is A 3. All A is right of Some L (converse of 1.) 4. All T is right of Some L (2, 3 Dictum de Omni) 5. Some L is left of All T (converse of 4.) The second argument is much the same. The machinery of the predicate calculus is not necessary to handle multiply quantified relational propositions.