Breaking out of a paradox—whether it is a logical, philosophical, or psychological one—often requires changing your perspective, questioning underlying assumptions, or embracing the paradox rather than trying to resolve it directly. Paradoxes are often "tenacious because they play with the ambiguity of definition" or force you into a false binary.
By defining the paradox at hand first, you set yourself up better to find a solution to it. In some cases the solution is a trade-off, where you cannot solve the problem “perfectly”. You either choose one opposing force or you go with a compromise. In some cases you will be able to find a win-win solution.
Self-reference, contradiction and infinite regress are core elements of many paradoxes. Other common elements include circular definitions, and confusion or equivocation between different levels of abstraction.
The Failure Paradox You have to fail more to succeed more. Our greatest periods of growth often stem directly from our greatest moments of failure. Don't fear failure. Learn to fail smart and fast—never fail the same way twice.
This idea is explained here: If God is able to do anything, may this mean He is able to make a mountain heavier than He is able to lift? This is a paradox because: If God is able to make a mountain heavier than He is able to lift, then there may be something He is not able to do: He is not able to lift that mountain.
There isn't one single "most famous" paradox, but top contenders include Zeno's Paradoxes (like Achilles and the Tortoise) questioning motion, Russell's Paradox shaking mathematics' foundations, the Liar Paradox ("This statement is false") challenging logic, and the Grandfather Paradox in time travel, with the Fermi Paradox (where are the aliens?) also very well-known in science.
When a worrying thought comes up, try to actively switch your focus to what is around you. Focus on breathing, observe what you can see and hear, and ground yourself in the present moment. By being mindful, we pay attention to our present moment and accept it without judgment.
How is he both strong and gentle, worthy and lowly, infinitely holy yet merciful toward his enemies? This is the wonderful paradox of Jesus. He holds together seemingly opposite excellencies in one God-man.
We as humans have in our nature its own paradoxes. The paradox of doing things that are totally in contradiction with our principles and beliefs is probably the most common paradox. Because it is inherent in our nature, it is almost impossible for us to change.
Classical Logical Paradoxes. The four main paradoxes attributed to Eubulides, who lived in the fourth century BC, were “The Liar,” “The Hooded Man,” “The Heap,” and “The Horned Man” (compare Kneale and Kneale 1962, p114).
The Anxiety Paradox - When Anxiety is a Problem (and when it is not.) Anxiety is a funny thing. Actually it really isn't, but it can be very peculiar and confounding. The more you try to avoid it, the worse it becomes.
Paradoxical intention (PI) is an insomnia treatment developed in the 1970s, which instructs patients to gently attempt to remain awake while in bed at night with the lights off.
“Holding the tension of paradox” is a critical thinking practice where space is created to safely discuss two or more contradicting points of view. This problem-solving practice may lead to more robust, agreeable and sustainable solutions.