Paradox exists at the boundary of knowledge  where truth collides with truth.

I became fascinated by the nature of paradox when writing a short story about Fermi’s Paradox, which received an Honorable Mention in the 2012 L. Ron Hubbard Writers of the Future contest and has since been published under the title By the Numbers.

Strictly speaking, a paradox is an apparent contradiction between two things which are reasonably true. A paradox is resolved if one of the apparent truths is in fact false, or if the apparent contradiction is not really a contradiction. Let’s take a look at how this applies to the major types of paradox:

Esoteric Paradox

These are the paradoxes that play games with your mind. Some trick of language or of a mathematical model leads to a real or apparent contradiction. Often these involve self-referential statements or statements involving mathematical oddities such as infinity. The usual resolution is to determine that the apparent contradiction is not really a contradiction. For example, Zeno’s Paradox:

In the paradox of Achilles and the Tortoise,  Achilles is in a footrace with the tortoise. Achilles allows the tortoise a head start of 100 meters, for example. If we suppose that each racer starts running at some constant speed (one very fast and one very slow), then after some finite time, Achilles will have run 100 meters, bringing him to the tortoise’s starting point. During this time, the tortoise has run a much shorter distance, say, 10 meters. It will then take Achilles some further time to run that distance, by which time the tortoise will have advanced farther; and then more time still to reach this third point, while the tortoise moves ahead. Thus, whenever Achilles reaches somewhere the tortoise has been, he still has farther to go. Therefore, because there are an infinite number of points Achilles must reach where the tortoise has already been, he can never overtake the tortoise.  [Wikipedia]

Scientific Paradox:

We may call a conflict between accepted scientific theory and fact a paradox. Usually the theory is wrong, or the observation is in error. This type of paradox is the engine that moves science forward, since it keeps challenging us to reexamine our accepted theories.

For example:

Paradox Defines Our Knowledge of the Universe by Orion Jones

The Paradoxes that Threaten to Tear Modern Physics Apart

Mundane Paradox:

We sometimes describe a conflict in personal or social characteristics as a paradox. It is the nature of people to have multiple values and emotional responses at the same time, hence this type of paradox is very common. However, the interplay of conflicting responses to a situation is often interesting and instructive about human nature.

For example:

“He wanted to be near her, but paradoxically kept pushing her away.” Presumably, he had a conflicting desire, such as wanting to avoid commitments.