Here is a fun way of evaluating logical relations between propositions.
We were driving in the car the other day and my son Collin asks the following “I’m crazy aren’t I dad?” Wanting to be a game player I went along with it “Yes Collin you are crazy.” Collin then gloats and said to his older brother “See Harrison I told you I was crazy” (I don’t know when he began to view crazy as a virtue). To which Harrison replied “Thats only because you asked dad, he will go along with anything you ask him.” Without skipping a beat Collin immediately says “Dad give me a hundred dollars.”
In the square of opposition you have four propositions:
A = Universal Affirmative
E = Universal Negative
I = Particular Affirmative
O = Particular Negative
Chalk one up for the little guy! He realized in order to win the debate he didn’t necessarily have to refute his big brothers argument (that Dad will go along with anything he asks). Collin knew that he just needed to come up with one example where dad wouldn’t go along with anything by taking the argument from an A proposition to an O. And that is how the square of opposition is used.