Ambiguity arising from Quantification


Consider every woman loves a man. This could mean:

Picture of Brad Pitt

i.e. ∃X: man(X) ∧ ∀Y (woman(Y) ⇒ loves(Y, X))

(in other words, there is a particular man and every woman loves him)  
 

... or else it could mean:

Wall plaque that reads 'I'm as lucky as I can be/because the world's best dad belongs to me'

i.e. ∀Y woman(Y) ∃X: (man(X) ∧ loves(Y, X))

In other words, a possibly different man for every woman (in this case the man is the woman's father).