[[archetype]]al example of [[form|syllogism]]: all men are mortal. Socrates is a man. Therefore Socrates is mortal. # [[quantifier]] consider [[universal]] "all p q" where p is some [[object identification|nominal]] and q is some [[predicate]]. take [[evaluation context]] $C[q] := \text{``All people q"}$. we have $x \text{ lives} \implies x \text{ was born}$ so $C[\text{live}] \implies C[\text{were born}]$. so "all" is [[monotone increasing|upward entail]]ing in the [[predicate]]. eg $C[p] =\text{``All } p\text{ are mortal"}$ ([[quantifier]]) we have $\text{men} \implies \text{animals}$ but $C[\text{animals}] \implies C[\text{men}]$; so "all" is [[monotone decreasing|downward entail]]ing in the [[object identification|nominal]].