This simply means that the story you're writing doesn't abide by classical logic. By the virtue of the square-circle simply existing (being a thing) we can conclude that it is logical under whatever system of logical laws your story adheres to, e.g. a paracosnsitent logic?

That's not necessarily true, there's a whole trope in fiction for events or objects that deviate from the rules of logic that the world follows making it strange.

http://tvtropes.org/pmwiki/pmwiki.php/Main/HowIsThatEvenPossible

Also it's a stretch to think that every author who creates a character capable of doing illogical actions, intent was to show that the world operates on different rules of logic instead of trying to just show that the rules of logic don't apply to the character.