Paradox in the context of "Quantum entanglement"

A tragedy is a genre of drama based on human suffering and, mainly, the terrible or sorrowful events that befall a main character or cast of characters. Traditionally, the intention of tragedy is to invoke an accompanying catharsis, or a "pain [that] awakens pleasure," for the audience. While many cultures have developed forms that provoke this paradoxical response, the term tragedy often refers to a specific tradition of drama that has played a unique and important role historically in the self-definition of Western civilization. That tradition has been multiple and discontinuous, yet the term has often been used to invoke a powerful effect of cultural identity and historical continuity—"the Greeks and the Elizabethans, in one cultural form; Hellenes and Christians, in a common activity," as Raymond Williams puts it.

Originating in the theatre of ancient Greece 2500 years ago, where only a fraction of the works of Aeschylus, Sophocles and Euripides survive, as well as many fragments from other poets, and the later Roman tragedies of Seneca; through its singular articulations in the works of Shakespeare, Lope de Vega, Jean Racine, and Friedrich Schiller to the more recent naturalistic tragedy of Henrik Ibsen and August Strindberg; Nurul Momen's Nemesis' tragic vengeance & Samuel Beckett's modernist meditations on death, loss and suffering; Heiner Müller postmodernist reworkings of the tragic canon, tragedy has remained an important site of cultural experimentation, negotiation, struggle, and change. A long line of philosophers—which includes Plato, Aristotle, Saint Augustine, Voltaire, Hume, Diderot, Hegel, Schopenhauer, Kierkegaard, Nietzsche, Freud, Benjamin, Camus, Lacan, and Deleuze—have analysed, speculated upon, and criticised the genre.

Heraclitus (/ˌhɛrəˈklaɪtəs/; Ancient Greek: Ἡράκλειτος Hērákleitos; fl. c. 500 BC) was an ancient Greek pre-Socratic philosopher from the city of Ephesus, which was then part of the Persian Empire. He exerts a wide influence on Western philosophy, both ancient and modern, through the works of such authors as Plato, Aristotle, Georg Wilhelm Friedrich Hegel, Friedrich Nietzsche, and Martin Heidegger.

Little is known of Heraclitus's life. He wrote a single work, of which only fragments survive. Even in ancient times, his paradoxical philosophy, appreciation for wordplay, and cryptic, oracular epigrams earned him the epithets "the dark" and "the obscure". He was considered arrogant and depressed, a misanthrope who was subject to melancholia. Consequently, he became known as "the weeping philosopher" in contrast to the ancient atomist philosopher Democritus, who was known as "the laughing philosopher".

In aesthetics, the concept of taste has been the interest of philosophers such as Plato, Hume, and Kant. It is defined by the ability to make valid judgments about an object's aesthetic value. However, these judgments are deficient in objectivity, creating the 'paradox of taste'. The term 'taste' is used because these judgments are similarly made when one physically tastes food.

Curry's paradox is a paradox in which an arbitrary claim F is proved from the mere existence of a sentence C that says of itself "If C, then F". The paradox requires only a few apparently-innocuous logical deduction rules. Since F is arbitrary, any logic having these rules allows one to prove everything. The paradox may be expressed in natural language and in various logics, including certain forms of set theory, lambda calculus, and combinatory logic.

The paradox is named after the logician Haskell Curry, who wrote about it in 1942. It has also been called Löb's paradox after Martin Hugo Löb, due to its relationship to Löb's theorem.

In mathematics, a series is, roughly speaking, an addition of infinitely many terms, one after the other. The study of series is a major part of calculus and its generalization, mathematical analysis. Series are used in most areas of mathematics, even for studying finite structures in combinatorics through generating functions. The mathematical properties of infinite series make them widely applicable in other quantitative disciplines such as physics, computer science, statistics and finance.

Among the Ancient Greeks, the idea that a potentially infinite summation could produce a finite result was considered paradoxical, most famously in Zeno's paradoxes. Nonetheless, infinite series were applied practically by Ancient Greek mathematicians including Archimedes, for instance in the quadrature of the parabola. The mathematical side of Zeno's paradoxes was resolved using the concept of a limit during the 17th century, especially through the early calculus of Isaac Newton. The resolution was made more rigorous and further improved in the 19th century through the work of Carl Friedrich Gauss and Augustin-Louis Cauchy, among others, answering questions about which of these sums exist via the completeness of the real numbers and whether series terms can be rearranged or not without changing their sums using absolute convergence and conditional convergence of series.

This article contains a discussion of paradoxes of set theory. As with most mathematical paradoxes, they generally reveal surprising and counter-intuitive mathematical results, rather than actual logical contradictions within modern axiomatic set theory.