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Examples Sometimes supernatural or science fiction themes are held to be impossible due to resultant paradoxical conditions. The theme of time travel has staged many popular paradoxes arising from the traveler interfering with the past. Suppose Rowan, who was born in 1950, travels back in time to 1901 and kills his own grandfather. It follows that neither his father nor he himself will be born; but then he would not have existed to travel back in time and kill his own grandfather; but then his grandfather would not have died and Rowan himself would have lived; etc. This is known as the grandfather paradox or as simply the time paradox. Paradoxes that arise from apparently intelligible uses of language are often of interest to logicians and philosophers. This sentence is false is an example of the famous liar paradox: it is a sentence which cannot be consistently interpreted as true or false, because if it is false it must be true, and if it is true it must be false. Therefore, it can be concluded the sentence is both true and false. Russell's paradox, which shows that the notion of the set of all those sets that do not contain themselves leads to a contradiction, was instrumental in the development of modern logic and set theory. For more examples, see List of paradoxes. Etymology The etymology of paradox can be traced back to at least Plato's Parmenides, where Zeno of Elea, who lived from 490-430 BCE, used the word "paradoxon" to describe some of his seminal philosophic ideas. Zeno sought to illustrate that equal absurdities followed logically from the denial of Parmenides' views. There were apparently 40 'paradoxes of plurality' and other paradoxes that Zeno used to attack the Greek understanding of the physical world. In fact, Zeno's paradoxes of multiplicity and motion, which revealed problems in the Greek idea of space and time, were resolvable only using mathematics discovered in the 19th century. It is unknown if incarnations of paradox were used before Zeno of Elea. Later and more frequent usage of the word has been traced to the early Renaissance. Early forms of the word appeared in the late Latin paradoxum and the related Greek παράδοξος paradoxos, which means "contrary to expectation", or "incredible". The word is a fusion of the preposition para, meaning "against" or "beyond", and the noun stem doxa, meaning "belief" or "opinion". Common themes Common themes in paradoxes include direct and indirect self-reference, infinity, circular definitions, and confusion of levels of reasoning. Paradoxes which are not based on a hidden error generally happen at the fringes of context or language, and require extending the context or language to lose their paradox quality. In moral philosophy, paradox plays a central role in ethics debates. For instance, it may be considered that an ethical admonition to "love thy neighbour" is not just in contrast with, but in contradiction to an armed neighbour actively trying to kill you: if he or she succeeds, you will not be able to love him or her. But to preemptively attack them or restrain them is not usually understood as loving. This might be termed an ethical dilemma. Another example is the conflict between an injunction not to steal and one to care for a family that you cannot afford to feed without stolen money. Types of paradoxes W. V. Quine (1962) distinguished between three classes of paradoxes. A fourth kind has sometimes been asserted since Quine's work. See also | ||||||||||
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