A paradox is defined as a statement that seems to contradict itself and yet still might be true. As one approaches a paradox from the outside and begins to ponder its complexities and subtleties, one can sometimes find a path to reason whether it is true or false, plausible or unlikely. However, typically, the unraveled paradox can still provide insight into something that had not been clear before its consideration.
Poking about online I came across a number of sites that have assembled a collection of paradoxes. Some use words that you might claim to be fictional:
Cole's paradox: Even a tiny fecundity advantage of one additional offspring would favor the evolution of semelparity.
Some will get you to wondering how such a thing is possible:
Potato paradox: If you let potatoes consisting of 99% water dry so that they are 98% water, they lose 50% of their weight.
Some will give you a smile of recognition:
Hedgehog's dilemma: Despite goodwill, human intimacy cannot occur without substantial mutual harm.
Some will make you curious:
Faraday paradox: Diluted nitric acid will corrode steel, while concentrated nitric acid doesn't.
Some will make you think about anthropomorphism:
Crocodile dilemma: If a crocodile steals a child and promises its return if the father can correctly guess exactly what the crocodile will do, how should the crocodile respond in the case that the father correctly guesses that the child will not be returned?
Finally, some will be seen as easily dismissible by most, except those who have been hurt by those closest to them:
Loneliness paradox: A close and loving family is a blessing. But the more people we love and the more deeply we love them, the more vulnerable we are to loss and grief and loneliness.