Paradox
From Wikipedia, the free encyclopedia
For other uses, see Paradox (disambiguation).
Robert Boyle
's self-flowing flask fills itself in this diagram, but perpetual motion machines cannot exist.A paradox is an apparently true statement or group of statements that seems to involve an unexpected outcome. The stated 'factually true' outcome defies intuition, just because intuition is unable to form correct expectation as it ingores pertinent causal factors. Philosophical and mathematical paradoxes may seem to involve contradiction.
Typically, either the statements in question do not really imply the contradiction, the puzzling result is not really a contradiction, or the premises themselves are not all really true or cannot all be true together. The recognition of ambiguities, equivocations, and unstated assumptions underlying known paradoxes has led to significant advances in science, philosophy and mathematics.
The word paradox is often used interchangeably and wrongly with contradiction; but where a contradiction by definition cannot be true, many paradoxes do allow for resolution, though many remain unresolved or only contentiously resolved, such as Curry's paradox. Still more casually, the term is sometimes used for situations that are merely surprising, albeit in a distinctly "logical" manner, such as the Birthday Paradox. This is also the usage in economics, where a paradox is an unintuitive outcome of economic theory.
Social sciences are particularly victims of unthinking intuition giving rise to paradoxes. They can achieve great advances by resolving the paradoxes through careful causal analysis. It is very important to bust the paradoxes and the falsehoods based on unthinking intuition, because great many crimes against humanity are committed according to false theories created by thoughtless intuition. This includes crimes against humanity based on the Paradox of Fertility to impose forcible sterilization or coercive birth control, the Paradox of Slum Preference to deny desperate rural paupers a chance to survive in the cities, and the Paradox of Poverty which prevents the reform of monetary systems to permanently solve needless poverty by enabling employment of productive people who are unemployed because of perversions in monetary systems.
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Paradox versus Illusion
A paradox in social science is akin to illusion in natural science. An illusion occurs as a result of faults of observation owing to faulty sensory organs. In an illusion, reality appears to be other than what it is. For example, when an airplane flies away, the observer sees that it is becoming smaller and smaller and ultimately it vanishes from view. But the observer also knows that the plane is actually not becoming smaller at all. There are great many examples of optical illusion where things seem to be other than what they really are.
Every sensory organ is liable to misperception or illusion. Just as our eyes fail to see extremely distant or extremely tiny objects, our ears fail to hear sounds that are above or below a certain range of audibility. In short, we hear only a fraction of the sound around us, and do not hear the other sounds. Our senses of smell and touch are also limited, meaning that we fail to detect many smells or feel many kinds of touches. Our tongues are also unable to taste things unerringly, as they tend to get confused by mixtures of substances.
Natural sciences have devised various instruments of observation to overcome the failure of sensory organs. Thus telescopes can see distant objects that our naked eyes fail to see; and microscopes can see tiny objects that our naked eyes cannot see. Likewise, there are instruments of observation to overcome the failure of other sense organs.
Paradox is a different kind of illusion in that it does not relate directly to observation, but to the causal meaning of observation. Just as a naked eye is not equipped to correctly detect the presence of microorganisms, the untrained mind or naked mind (usually called intuition) is not equipped to assign a correct causal meaning to events. In other words, an intuition is the illusion of the unthinking mind, and it creates a paradox.
For example,the diamond-water paradox arises before the unthinking mind as it creates a causally wrong prediction or expectation about relative price: it wrongly expects prices to be proportional to usefulness. In reality, price depends on both demand factors (such as relative usefulness or marginal utility) and supply factors (such as relative scarcity or marginal opportunity cost). The high price of diamond relative to water should not have been unexpected in the first place so that the sense of paradox would not arise at all.
If we stubbornly insist on using our naked eyes, we are bound to get wrong ideas about microorganisms, namely the wrong idea that they do not exist at all. Likewise, if we insist on intuition, we are bound to reach wrong conclusions about causal relations in social spheres. Intuition prevents us from understanding the complex social events, because it ignores pertinent factors and thereby promotes ignorance.
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Intuition is the Biggest Enemy of Social Science
Intuition is indeed the biggest enemy of scientific understanding of social realities. We understand social realities in terms of human motives. Intuition supplies an uncritical motivational link to an event in which human action has some relevance. In the diamond-water paradox, the intuition is uncritical, and assigns the human motive to paying price such that the price is proportional to the relative usefulness of the object. This motivational premise is false, and it is the result of lazy minds refusing to consider relevant factors.
The uncritical mind thinks that reasonable humans would not pay a high price for something of low usefulness. This intuition is of course false, because people do pay high prices for things presumed to be of little usefulness. But the explanation requires a more thorough analysis of many pertinent factors, such as the marginal utility and the marginal cost of production.
The treachery of intuition has very adversely harmed humanity, especially with respect to economic matters. Almost all economic events are paradoxical: they are beyond the grasp of unthinking intuition. However, great many authors and speakers promote what is called an intuitive approach, which is like the promoting superstition and quackery. We are indeed deluged with cheap shots of unthinking charlatans. They appeal to us because we refuse to think and readily swallow false statements just because the sound credible or plausible.
Natural sciences are about material phenomena, and those sciences fight against illusion by using instruments of observation. Social sciences must also fight against intuition by pursuing causal analysis. The problem is not the facts as such (unlike in natural science), but what the facts mean. Economists rarely disagree over the facts, but they vociferously debate what the facts mean. In this battle, the usual winner is the enemy of science: the ever beguiling intuition, the favorite of the lazy thinkers who refuse to think but lazily rely on unthinking minds.
Intuition is the mother of all superstitions. It is also the only reason people fall prey to cheats. The fraud presents arguments that seem credible only because the victim does not bother to check the purported fact or in most cases the presumed logic. If something sounds credible, it is not necessarily so until a serious scrutiny establishes that it is so. The first part of the scrutiny is to falsify it, or try to say that the purported fact is not true or the logic is not valid. The second part is to confirm the facts by careful observation.
Humanity at large is being cheated on grand scale by purveyors of all kinds of superstitious and fraudulent claims. The only recourse is to wake up the minds, equip them with critical ability and defeat intuition (and the products of intuition, which are superstition, fraud, and falsehood).
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How to Defeat Intuition and Resolve Paradoxes?
To defeat intuition, one must begin with the dogmatic stance that ‘if it is intuitive, it is false’. This is not meant to be a statement about truth, but the statement of an attitude of skepticism. It is a call to deploy analysis. The skeptic should try to contradict and refute any statement that relies on intuition. To contradict is to try to present an opposite meaning. To refute is to present contrary factual evidence and/or logical argument. But to contradict and refute is to think, and that is indeed the medicine for the unthinking mind: force it to think.
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Examples
Sometimes supernatural or science fiction themes are held to be impossible on the grounds that they result in paradoxes. The theme of time travel has generated a whole family of popular paradoxes, supposed to arise from a person's interference with the past. Suppose Jones, who was born in 1950, travels back in time to 1900 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 Jones himself would have lived; etc. This is known as the Grandfather 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. 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.
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Etymology
The etymology of paradox can be traced back the use of the word paradoxo, used in Plato's Parmenides by the Greek philosopher Zeno of Elea, who lived at 490-430 BC. The word was used to describe seminal philosophic ideas posited by Zeno, known as Zeno's paradoxes, which exerted a poignant effect on Greek thinkers that has survived to modern day. 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 revealed some problems in space and time that cannot be resolved without the mathematical methods discovered in the 19th century and perhaps beyond. Although it is unknown if Zeno coined the word, he can certainly be attributed as popularizing it. 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 pa??d???? paradoxos meaning 'contrary to expectation', 'incredible'. The word is composed of the preposition para which means "against" conjoined to the noun stem doxa, meaning "belief". Compare orthodox (literally, "straight teaching") and heterodox (literally, "different teaching"). The liar paradox and other paradoxes were studied in medieval times under the heading insolubilia.
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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.
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Types of paradoxes
W. V. Quine (1962) distinguished between three classes of paradoxes.
- A veridical paradox produces a result that appears absurd but is demonstrated to be true nevertheless. Thus, the paradox of Frederic's birthday in The Pirates of Penzance establishes the surprising fact that a person may be more than Nine years old on his Ninth birthday. Likewise, Arrow's impossibility theorem involves behaviour of voting systems that is surprising but all too true.
- A falsidical paradox establishes a result that not only appears false but actually is false; there is a fallacy in the supposed demonstration. The various invalid proofs (e.g. that 1 = 2) are classic examples, generally relying on a hidden division by zero. Another example would be the Horse paradox.
- A paradox which is in neither class may be an antinomy, which reaches a self-contradictory result by properly applying accepted ways of reasoning. For example, the Grelling-Nelson paradox points out genuine problems in our understanding of the ideas of truth and description.
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See also
http://en.wikipedia.org/wiki/Edgeworth_paradox http://en.wikipedia.org/wiki/Bertrand_paradox_%28economics%29 Arrow’s Paradox http://en.wikipedia.org/wiki/Arrow%27s_Impossibility_Theorem
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References
- R. M. Sainsbury (1988). Paradoxes. Cambridge.
- W. V. Quine (1962). "Paradox". Scientific American, April 1962, pp. 84–96.
- Michael Clarke (2002). Paradoxes from A to Z. London: Routledge.
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External links
- Open Directory Project: Paradoxes
- Definability paradoxes
- Insolubles (at the Stanford Encyclopedia of Philosophy)
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External Links
http://ideas.repec.org/p/wpa/wuwpmi/0405008.html http://www.ritsumei.ac.jp/~akitaoka/index-e.html www.torinfo.com/illusion/directory.html http://www.iep.utm.edu/p/par-russ.htm http://www.mathpages.com/rr/s3-07/3-07.htm
