Paradox
[5][6][7] They result in "persistent contradiction between interdependent elements" leading to a lasting "unity of opposites".
[8] In logic, many paradoxes exist that are known to be invalid arguments, yet are nevertheless valuable in promoting critical thinking,[9] while other paradoxes have revealed errors in definitions that were assumed to be rigorous, and have caused axioms of mathematics and logic to be re-examined.
[10][11] Others, such as Curry's paradox, cannot be easily resolved by making foundational changes in a logical system.
Escher featured perspective-based paradoxes in many of his drawings, with walls that are regarded as floors from other points of view, and staircases that appear to climb endlessly.
[15] Other common elements include circular definitions, and confusion or equivocation between different levels of abstraction.
[15] Another core aspect of paradoxes is non-terminating recursion, in the form of circular reasoning or infinite regress.
Often a seemingly paradoxical conclusion arises from an inconsistent or inherently contradictory definition of the initial premise.
For example, the Grelling–Nelson paradox points out genuine problems in our understanding of the ideas of truth and description.
Hence these contradictions are due to faulty ideas about thought or language, and they properly belong to epistemology.
[23] A taste for paradox is central to the philosophies of Laozi, Zeno of Elea, Zhuangzi, Heraclitus, Bhartrhari, Meister Eckhart, Hegel, Kierkegaard, Nietzsche, and G.K. Chesterton, among many others.
Some are common and are used regularly in medicine, such as the use of stimulants such as Adderall and Ritalin in the treatment of attention deficit hyperactivity disorder (also known as ADHD), while others are rare and can be dangerous as they are not expected, such as severe agitation from a benzodiazepine.
In the smoker's paradox, cigarette smoking, despite its proven harms, has a surprising inverse correlation with the epidemiological incidence of certain diseases.
