What does a paradox mean?
Paradox (literature)
Paradox, however, is essential to the structure and being of the poem. In "The Well Wrought Urn" Brooks shows that paradox was so essential to poetic meaning that paradox was almost identical to poetry. According to literary theorist Leroy Searle, Brooks' use of paradox emphasized the indeterminate lines between form and content. "The form of the poem uniquely embodies its meaning," and the language of the poem "affects the reconciliation of opposites or contraries." While irony functions within the poem, paradox often refers to the meaning and structure of the poem and is thus inclusive of irony. This existence of opposites or contraries and the reconciliation thereof is poetry and the meaning of the poem.
Paradox of voting
Some argue that the paradox appears to ignore the collateral benefits associated with voting, besides affecting the outcome of the vote. For instance, magnitudes of electoral wins and losses are very closely watched by politicians, their aides, pundits and voters, because they indicate the strength of support for candidates, and tend to be viewed as an inherently more accurate measure of such than mere opinion polls (which have to rely on imperfect sampling). However, these arguments themselves ignore that adherents to the paradox believe their individual vote makes a negligible difference; not only to the electoral outcome but also, by extension, to these supposed "collateral benefits". Another argument that has been raised, is that researching who or what to vote for may increase the voter's political knowledge and community awareness, both of which may contribute to a general sense of civic duty, although in such a case the act of voting itself contributes nothing to this.
Proebsting's paradox
because if he wins he will have 1.5 (the 0.5 from winning the 25% bet at 2 to 1 odds) plus 5"f"*; and if he loses he must pay 0.25 from the first bet, and "f"* from the second. Taking the derivative with respect to "f"* and setting it to zero gives:
Paradox
The apparent paradox is caused by a hasty generalization, for if the surgeon is the boy's father, the statement cannot be true. The paradox is resolved if it is revealed that the surgeon is a woman—the boy's mother.
Automation
The paradox of automation says that the more efficient the automated system, the more crucial the human contribution of the operators. Humans are less involved, but their involvement becomes more critical.
Paradox of voting
The paradox of voting, also called Downs paradox, is that for a rational, self-interested voter, the costs of voting will normally exceed the expected benefits. Because the chance of exercising the pivotal vote (i.e., in an otherwise tied election) is minuscule compared to any realistic estimate of the private individual benefits of the different possible outcomes, the expected benefits of voting are less than the costs.
Code-talker paradox
A code-talker paradox is a situation in which a language prevents communication. As an issue in linguistics, the paradox raises questions about the fundamental nature of languages. As such, the paradox is a problem in philosophy of language.
John Frazee
The paradox arises when one considers what would happen if one attached a piece of buttered toast (butter side up) to the back of a cat, then dropped the cat from a large height.
Paul Grice
Grice's paradox shows that the exact meaning of statements involving conditionals and probabilities is more complicated than may be obvious on casual examination.
Guarded logic
A real-world example is the idea of paradox: something cannot be both true and false. A guarded logical choice is one where any change in true affects all decisions made down the line.
Paradox
A paradox is a statement that, despite apparently valid reasoning from true premises, leads to an apparently-self-contradictory or logically unacceptable conclusion. A paradox involves contradictory-yet-interrelated elements that exist simultaneously and persist over time.
Paradox of thrift
In this form it represents a prisoner's dilemma as saving is beneficial to each individual but deleterious to the general population. This is a "paradox" because it runs contrary to intuition. Someone unaware of the paradox of thrift would fall into a fallacy of composition and assume that what seems to be good for an individual within the economy will be good for the entire population. However, exercising thrift may be good for an individual by enabling that individual to save for a "rainy day", and yet not be good for the economy as a whole.
Gray's paradox
in which,
Paradox
A paradoxical reaction to a drug is the opposite of what one would expect, such as becoming agitated by a sedative or sedated by a stimulant. 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.
Paradox of hedonism
The paradox of hedonism, also called the pleasure paradox, refers to the practical difficulties encountered in the pursuit of pleasure. Unfortunately for the hedonist, constant pleasure-seeking may not yield the most actual pleasure or happiness in the long run—or even in the short run, when consciously pursuing pleasure interferes with experiencing it.
Siegel's paradox
Siegel's Paradox is the phenomenon that uncertainty about future prices can theoretically push rational consumers to temporarily trade away their preferred consumption goods (or currency) for non-preferred goods (or currency), as part of a plan to trade back to the preferred consumption goods after prices become clearer. For example, in some models, Americans can expect to earn more American dollars on average by investing in Euros, while Europeans can expect to earn more Euros on average by investing in American dollars. The paradox was identified by economist Jerry Siegel in 1972.
Mere addition paradox
Thus, there is a paradox. The following intuitively plausible claims are jointly incompatible: (a) that A+ is no worse than A, (b) that B− is better than A+, (c) that B− is equally as good as B, and (d) that B can be worse than A.
Paradox (literature)
Literary or rhetorical paradoxes abound in the works of Oscar Wilde and G. K. Chesterton. Most literature deals with paradox of situation; Rabelais, Cervantes, Sterne, Borges, and Chesterton are recognized as masters of situation as well as verbal paradox. Statements such as Wilde's "I can resist anything except temptation" and Chesterton's "spies do not look like spies" are examples of rhetorical paradox. Further back, Polonius' observation that "though this be madness, yet there is method in't" is a memorable third. Also, statements that are illogical and metaphoric may be called paradoxes, for example: "The pike flew to the tree to sing." The literal meaning is illogical, but there are many interpretations for this metaphor.
Epimenides paradox
If we assume the statement is false and that Epimenides is lying about all Cretans being liars, then there must exist at least one Cretan who is honest. This does not lead to contradiction since it is not required that this Cretan be Epimenides. This means that Epimenides can say the false statement that all Cretans are liars while knowing at least one honest Cretan and lying about this particular Cretan. Hence, from the assumption that the statement is false, it does not follow that the statement is true. So we can avoid a paradox as seeing the statement "all Cretans are liars" as a false statement, which is made by a lying Cretan, Epimenides. The mistake made by Thomas Fowler (and many other people) above is to think that the negation of "all Cretans are liars" is "all Cretans are honest" (a paradox) when in fact the negation is "there exists a Cretan who is honest", or "not all Cretans are liars". The Epimenides paradox can be slightly modified as to not allow the kind of solution described above, as it was in the first paradox of Eubulides but instead leading to a non-avoidable self-contradiction. Paradoxical versions of the Epimenides problem are closely related to a class of more difficult logical problems, including the liar paradox, Socratic paradox, and the Burali-Forti paradox, all of which have self-reference in common with Epimenides. Indeed, the Epimenides paradox is usually classified as a variation on the liar paradox, and sometimes the two are not distinguished. The study of self-reference led to important developments in logic and mathematics in the twentieth century.
Russell's paradox
While appealing, these layman's versions of the paradox share a drawback: an easy refutation of the barber paradox seems to be that such a barber does not exist, or that the barber is a woman and therefore doesn't shave. The whole point of Russell's paradox is that the answer "such a set does not exist" means the definition of the notion of set within a given theory is unsatisfactory. Note the difference between the statements "such a set does not exist" and "it is an empty set". It is like the difference between saying "There is no bucket" and saying "The bucket is empty".
Barber paradox
The barber paradox is a puzzle derived from Russell's paradox. It was used by Bertrand Russell himself as an illustration of the paradox, though he attributes it to an unnamed person who suggested it to him. It shows that an apparently plausible scenario is logically impossible. Specifically, it describes a barber who is defined such that he both shaves himself and does not shave himself.
Discursive dilemma
Discursive dilemma or doctrinal paradox is a paradox in social choice theory. The paradox is that aggregating judgments with majority voting can result in self-contradictory judgments.
Grossman-Stiglitz Paradox
A paradox introduced by Sanford J. Grossman and Joseph Stiglitz in a joint publication in American Economic Review in 1980 that introduces that idea that because information is costly, prices cannot perfectly reflect the information which is available, since if it did, those who spent resources to obtain it would receive no compensation, leading to the conclusion that an informationally efficient market is impossible.
Philosophical Fragments
But God can't make himself understood because he's completely unlike every other human being. God has not sinned, whereas every human being has. This is a paradox but the ultimate paradox is that a single individual who looks just like everyone else is God. "The thesis that God has existed in human form, was born, grew up; is certainly the paradox in the strictest sense, the absolute paradox." Christianity is also a paradox as well as the forgiveness of sins. Kierkegaard is saying that the "Moment" the individual comes in contact with the Paradox is of utmost importance because this is where the decision is made. This is his Either/Or. Either believe or be offended. Reason is attempting to understand the Paradox but comes to its own limit and can't understand what it knows nothing about.
Gibbs paradox
In statistical mechanics, a semi-classical derivation of the entropy that does not take into account the indistinguishability of particles, yields an expression for the entropy which is not extensive (is not proportional to the amount of substance in question). This leads to a paradox known as the Gibbs paradox, after Josiah Willard Gibbs who proposed this thought experiment in 1874‒1875. The paradox allows for the entropy of closed systems to decrease, violating the second law of thermodynamics. A related paradox is the "mixing paradox". If one takes the perspective that the definition of entropy must be changed so as to ignore particle permutation, the paradox is averted.
Paradox
For example, consider a situation in which a father and his son are driving down the road. The car crashes into a tree and the father is killed. The boy is rushed to the nearest hospital where he is prepared for emergency surgery. Upon entering the surgery-suite, the surgeon says, "I can't operate on this boy. He's my son."
Hausdorff paradox
The Hausdorff paradox is a paradox in mathematics named after Felix Hausdorff. It involves the sphere "S" (a 2-dimensional sphere in "R"). It states that if a certain countable subset is removed from "S", then the remainder can be divided into three disjoint subsets "A", "B" and "C" such that "A", "B", "C" and "B" ∪ "C" are all congruent. In particular, it follows that on "S" there is no finitely additive measure defined on all subsets such that the measure of congruent sets is equal (because this would imply that the measure of "B" ∪ "C" is simultaneously 1/3 and 2/3 of the non-zero measure of the whole sphere).
Born coordinates
The rotating disk is not a paradox. What ever method the observers use to analyze the situation: at the end they find themselves analyzing a rotating disk and not an inertial frame.
Liar paradox
Arthur Prior asserts that there is nothing paradoxical about the liar paradox. His claim (which he attributes to Charles Sanders Peirce and John Buridan) is that every statement includes an implicit assertion of its own truth. Thus, for example, the statement "It is true that two plus two equals four" contains no more information than the statement "two plus two equals four", because the phrase "it is true that..." is always implicitly there. And in the self-referential spirit of the Liar Paradox, the phrase "it is true that..." is equivalent to "this whole statement is true and ...".
Boy or Girl paradox
The paradox occurs when it is not known how the statement "at least one is a boy" was generated. Either answer could be correct, based on what is assumed.
Two capacitor paradox
The two capacitor paradox or capacitor paradox is a paradox, or counterintuitive thought experiment, in electric circuit theory. The thought experiment is usually described as follows: 
Two identical capacitors are connected in parallel with an open switch between them. One of the capacitors is charged with a voltage of formula_1, the other is uncharged. When the switch is closed, some of the charge formula_2 on the first capacitor flows into the second, reducing the voltage on the first and increasing the voltage on the second. When a steady state is reached and the current goes to zero, the voltage on the two capacitors must be equal since they are connected together. Since they both have the same capacitance formula_3 the charge will be divided equally between the capacitors so each capacitor will have a charge of formula_4 and a voltage of formula_5. At the beginning of the experiment the total initial energy formula_6 in the circuit is the energy stored in the charged capacitor: 
At the end of the experiment the final energy formula_8 is equal to the sum of the energy in the two capacitors 
Thus the final energy formula_8 is equal to half of the initial energy formula_6. Where did the other half of the initial energy go?
Liar paradox
If (B) is neither true nor false, then it must be not true. Since this is what (B) itself states, it means that (B) must be true. Since initially (B) was not true and is now true, another paradox arises.
Does not compute
In the "Doctor Who" story "The Green Death", the Doctor attempts to put the computer BOSS, which claims to be infallible, out of action using the liar paradox. BOSS feigns suffering from confusion as he appears to try to resolve the paradox, but has in fact summoned security.
Mage: The Ascension
In the Mage setting, everyday reality is governed by commonsense rules derived from the collective beliefs of sleepers. This is called the consensus. Most Magi's paradigms differ substantially from the consensus. When a mage performs an act of magic that does not seriously violate this commonsense version of reality, in game terms this is called coincidental magic. Magic that deviates wildly from consensus is called vulgar or dynamic magic. When it is performed ineptly, or is vulgar, and especially if it is vulgar and witnessed by sleepers, magic can cause Paradox, a phenomenon in which reality tries to resolve contradictions between the consensus and the Mage's efforts. Paradox is difficult to predict and almost always bad for the mage. The most common consequences of paradox include physical damage directly to the Mage's body, and paradox flaws, magic-like effects which can for example turn the mage's hair green, make him mute, make him incapable of leaving a certain location, and so on. In more extreme cases paradox can cause Quiet (madness that may leak into reality), Paradox Spirits (nebulous, often powerful beings which purposefully set about resolving the contradiction, usually by directly punishing the mage), or even the removal of the Mage to a paradox realm, a pocket dimension from which it may be difficult to escape.
Inventor's paradox
The inventor's paradox is a phenomenon that occurs in seeking a solution to a given problem. Instead of solving a specific type of problem, which would seem intuitively easier, it can be easier to solve a more general problem, which covers the specifics of the sought-after solution. The "inventor's paradox" has been used to describe phenomena in mathematics, programming, and logic, as well as other areas that involve critical thinking.
Movement paradox
A movement paradox is a phenomenon of grammar that challenges the transformational approach to syntax. The importance of movement paradoxes is emphasized by those theories of syntax (e.g. lexical functional grammar, head-driven phrase structure grammar, construction grammar, most dependency grammars) that reject movement, i.e. the notion that discontinuities in syntax are explained by the movement of constituents.
Paradoxes of material implication
The root of the paradoxes lies in a mismatch between the interpretation of the validity of logical implication in natural language, and its formal interpretation in classical logic, dating back to George Boole's algebraic logic. In classical logic, implication describes conditional if-then statements using a truth-functional interpretation, i.e. "p implies q" is defined to be "it is not the case that p is true and q false". Also, "p implies q" is equivalent to "p is false or q is true". For example, "if it is raining, then I will bring an umbrella", is equivalent to "it is not raining, or I will bring an umbrella, or both". This truth-functional interpretation of implication is called material implication or material conditional.
Conditioning (probability)
In order to avoid paradoxes (such as the Borel's paradox), the following important distinction should be taken into account. If a given event is of nonzero probability then conditioning on it is well-defined (irrespective of any other events), as was noted above. By contrast, if the given event is of zero probability then conditioning on it is ill-defined unless some additional input is provided. Wrong choice of this additional input leads to wrong conditional probabilities (expectations, distributions). In this sense, ""the concept of a conditional probability with regard to an isolated hypothesis whose probability equals 0 is inadmissible."" (Kolmogorov.
Paradoxes of set theory
As with König's paradox, this paradox cannot be formalized in axiomatic set theory because it requires the ability to tell whether a description applies to a particular set (or, equivalently, to tell whether a formula is actually the definition of a single set).
Paradox
Some paradoxes have revealed errors in definitions assumed to be rigorous, and have caused axioms of mathematics and logic to be re-examined. One example is Russell's paradox, which questions whether a "list of all lists that do not contain themselves" would include itself, and showed that attempts to found set theory on the identification of sets with properties or predicates were flawed. Others, such as Curry's paradox, are not yet resolved.
Temporal paradox
A causal loop is a paradox of time travel that occurs when a future event is the cause of a past event, which in turn is the cause of the future event. Both events then exist in spacetime, but their origin cannot be determined. A causal loop may involve an event, a person or object, or information. The terms boot-strap paradox, predestination paradox or ontological paradox are sometimes used in fiction to refer to a causal loop.
Paradox of thrift
The paradox of thrift (or paradox of saving) is a paradox of economics. The paradox states that an increase in autonomous saving leads to a decrease in aggregate demand and thus a decrease in gross output which will in turn lower "total" saving. The paradox is, narrowly speaking, that total saving may fall because of individuals' attempts to increase their saving, and, broadly speaking, that increase in saving may be harmful to an economy. Both the narrow and broad claims are paradoxical within the assumption underlying the fallacy of composition, namely that what is true of the parts must be true of the whole. The narrow claim transparently contradicts this assumption, and the broad one does so by implication, because while individual thrift is generally averred to be good for the economy, the paradox of thrift holds that collective thrift may be bad for the economy.
Paradox
Paradoxes which are not based on a hidden error generally occur at the fringes of context or language, and require extending the context or language in order to lose their paradoxical quality. 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 well-known liar paradox: it is a sentence which cannot be consistently interpreted as either true or false, because if it is known to be false, then it is known that it must be true, and if it is known to be true, then it is known that 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.
Paradox of analysis
One way to resolve this paradox is to redefine what is an analysis. In explaining the paradox, a potential analysis is assumed to be a relation between concepts rather than the verbal expressions used to illustrate them. If the verbal expression is part of the analysis, then we shouldn't expect complete intersubstitutivity even in cases of correct analyses. However, this response seems to move the notion of analysis into mere linguistic definition, rather than doing interesting work with concepts.
No-no paradox
(where we use single quotes to refer to the linguistic expression inside the quotes). Consider however the two sentences:
Paradox of fiction
The paradox of fiction is a philosophical problem about how people can experience strong emotions from purely fictional things, such as art, literature, and imagination. The paradox draws attention to an everyday issue of how people are moved by things which, in some ways, do not exist. Although the ontology of fictional things in general has been discussed in philosophy since Plato, the paradox was first suggested by Colin Radford and Michael Weston in 1975. After Radford and Weston's original paper, they and others have continued the discussion by giving the problem slightly differing formulations and solutions.
Parrondo's paradox
Parrondo's paradox, a paradox in game theory, has been described as: "A combination of losing strategies becomes a winning strategy". It is named after its creator, Juan Parrondo, who discovered the paradox in 1996. A more explanatory description is:
Russell's paradox
A notable exception to the above may be the Grelling–Nelson paradox, in which words and meaning are the elements of the scenario rather than people and hair-cutting. Though it is easy to refute the barber's paradox by saying that such a barber does not (and "cannot") exist, it is impossible to say something similar about a meaningfully defined word.
Liar paradox
The problem of the liar paradox is that it seems to show that common beliefs about truth and falsity actually lead to a contradiction. Sentences can be constructed that cannot consistently be assigned a truth value even though they are completely in accord with grammar and semantic rules.
List of paradoxes
One class of paradoxes in economics are the paradoxes of competition, in which behavior that benefits a lone actor would leave everyone worse off if everyone did the same. These paradoxes are classified into circuit, classical and Marx paradoxes.
Paradox (disambiguation)
Paradox may also refer to:
Privacy
The privacy paradox is a phenomenon in which online users state that they are concerned about their privacy but behave as if they were not. While this term was coined as early as 1998, it wasn't used in its current popular sense until the year 2000. In his article titled "'Opting In': A Privacy Paradox," John Schwartz wrote that "It's one of the more puzzling conundrums of online life. While companies that capitalize on the Internet's powerful potential to invade privacy are denounced as villains of the information age, millions of people type out highly personal data and send it off to Web sites they've barely heard of, with no strong legal protection against misuse of the information. …The paradox helps illustrate the complexity of the debate over privacy."
Observer's paradox
In the social sciences (and physics and experimental physics), the observer's paradox refers to a situation in which the phenomenon being observed is unwittingly influenced by the presence of the observer/investigator.
Ross–Littlewood paradox
The Ross–Littlewood paradox (also known as the balls and vase problem or the ping pong ball problem) is a hypothetical problem in abstract mathematics and logic designed to illustrate the seemingly paradoxical, or at least non-intuitive, nature of infinity. More specifically, like the Thomson's lamp paradox, the Ross–Littlewood paradox tries to illustrate the conceptual difficulties with the notion of a supertask, in which an infinite number of tasks are completed sequentially. The problem was originally described by mathematician John E. Littlewood in his 1953 book "Littlewood's Miscellany", and was later expanded upon by Sheldon Ross in his 1988 book "A First Course in Probability".
Paradox
Common themes in paradoxes include self-reference, infinite regress, circular definitions, and confusion between different levels of abstraction.
Omnipotence paradox
In other words, the 'limit' on what omnipotence 'can' do is not a "limit" on its actual agency, but an "epistemological boundary" without which omnipotence could not be "identified" (paradoxically or otherwise) in the first place. In fact, this process is merely a fancier form of the classic Liar Paradox: If I say, "I am a liar", then how can it be true if I am telling the truth therewith, and, if I am telling the truth therewith, then how can I be a liar? So, to think that omnipotence is an "epistemological" paradox is like failing to recognize that, when taking the statement, 'I am a liar' self-referentially, the statement is reduced to an actual failure to lie. In other words, if one maintains the supposedly 'initial' position that the necessary conception of omnipotence includes the 'power' to compromise both itself and all other identity, and if one concludes from this position that omnipotence is epistemologically incoherent, then one implicitly is asserting that one's own 'initial' position is incoherent. Therefore, the question (and therefore the perceived paradox) is meaningless. Nonsense does not suddenly acquire sense and meaning with the addition of the two words, "God can" before it. Lewis additionally said that, "Unless something is self-evident, nothing can be proved." This implies for the debate on omnipotence that, "as in matter, so in the human understanding of truth: it takes no true insight to destroy a perfectly integrated structure, and the effort to destroy has greater effect than an equal effort to build; so, a man is thought a fool who assumes its integrity, and thought an abomination who argues for it. It is easier to teach a fish to swim in outer space than to convince a room full of ignorant fools why it cannot be done."
Cellophane paradox
The paradox arises when a firm sells a product with few substitutes, which in turn allows the firm to increase the price of that product. The original reason was that as the price increases, the product will reach a point where it begins to attract more and more substitutes. In technical economic terms, such a product has very low cross-price elasticity of demand. The situation is linked to a United States Supreme Court case and a subsequent response in economic literature.
Newcomb's paradox
In philosophy and mathematics, Newcomb's paradox, also referred to as Newcomb's problem, is a thought experiment involving a game between two players, one of whom purports to be able to predict the future.
EPR paradox
The paradox
Liar paradox
However, that the liar sentence can be shown to be true if it is false and false if it is true has led some to conclude that it is "neither true nor false". This response to the paradox is, in effect, the rejection of the claim that every statement has to be either true or false, also known as the principle of bivalence, a concept related to the law of the excluded middle.
Yablo's paradox
Consider the following infinite set of sentences:Assume there is an "n" such that "S" is true. Then "S" is not true, so there is some "k" > "n" + 1 such that "S" is true. But "S" is not true because "S" is true and "k" > "n". Assuming "S" to be true implies a contradiction: some later "S" is both true and not true. So our assumption is absurd and we must conclude that for each "i", the sentence "S" is not true. But if each "S" is not true, then given that each attributes untruth to later sentences, they are all true. So we have the paradox that each sentence in Yablo's list is true and not true.
Paradoxes of material implication
The paradoxes are logical statements which are true but whose truth is intuitively surprising to people who are not familiar with them. If the terms 'p', 'q' and 'r' stand for arbitrary propositions then the main paradoxes are given formally as follows:
Paradox
Often a seemingly paradoxical conclusion arises from an inconsistent or inherently contradictory definition of the initial premise. In the case of that apparent paradox of a time-traveler killing his own grandfather, it is the inconsistency of defining the past to which he returns as being somehow different from the one which leads up to the future from which he begins his trip, but also insisting that he must have come to that past from the same future as the one that it leads up to.
Icarus paradox
A reason for the paradox is that rationality assumes that more is better, but intensification may be counter-productive.
Epimenides paradox
In that article, Russell uses the Epimenides paradox as the point of departure for discussions of other problems, including the Burali-Forti paradox and the paradox now called Russell's paradox. Since Russell, the Epimenides paradox has been referenced repeatedly in logic. Typical of these references is "Gödel, Escher, Bach" by Douglas Hofstadter, which accords the paradox a prominent place in a discussion of self-reference.
Liar paradox
"A = "A = false""
Lottery paradox
The lottery paradox has become a central topic within epistemology, and the enormous literature surrounding this puzzle threatens to obscure its original purpose. Kyburg proposed the thought experiment to get across a feature of his innovative ideas on probability (Kyburg 1961, Kyburg and Teng 2001), which are built around taking the first two principles above seriously and rejecting the last. For Kyburg, the lottery paradox is not really a paradox: his solution is to restrict aggregation.
Unexpected hanging paradox
The unexpected hanging paradox or hangman paradox is a paradox about a person's expectations about the timing of a future event which they are told will occur at an unexpected time. The paradox is variously applied to a prisoner's hanging, or a surprise school test. It is a particular case of Newcomb's paradox.
Arrow paradox (disambiguation)
Arrow paradox may mean:
Paradox psychology
While there are many treatment theories that address separate aspects of behavior, emotions, and thinking, this approach focuses on the obvious fact that human's entire existence is a 'living paradox'. This paradox is evidenced by the fact that we live in an animal body, but we walk upright with our 'mind in the clouds'; our DNA is programmed to function via instinct, yet we prefer to assert free-will; we are smart enough to 'know better', but quite often repeat past mistakes. As such, it could be argued that the study of 'man as a paradox' is most closely aligned with our 'essence' as a human being.
St. Petersburg paradox
for any "k", since this generates a negatively divergent logarithm in the sum for which can be shown to dominate all other terms in the sum and guarantee that
Pinocchio paradox
The Pinocchio paradox arises when Pinocchio says "My nose grows now" and is a version of the liar paradox. The liar paradox is defined in philosophy and logic as the statement "This sentence is false." Any attempts to assign a classical binary truth value to this statement lead to a contradiction, or paradox. This occurs because if the statement "This sentence is false" is true, then it is false; this would mean that it is technically true, but also that it is false, and so on without end. Although the Pinocchio paradox belongs to the liar paradox tradition, it is a special case because it has no semantic predicates, as for example "My sentence is false" does.
Temporal paradox
A temporal paradox, time paradox, or time travel paradox is a paradox, an apparent contradiction, or a logical contradiction that is associated with the idea of time and time travel. In physics, temporal paradoxes fall into two broad groups: consistency paradoxes exemplified by the grandfather paradox; and causal loops. More broadly, a variation of the Fermi paradox also applies to time travel.
Paradox (literature)
In literature, the paradox is an anomalous juxtaposition of incongruous ideas for the sake of striking exposition or unexpected insight. It functions as a method of literary composition and analysis that involves examining apparently contradictory statements and drawing conclusions either to reconcile them or to explain their presence.
Liberal paradox
The liberal paradox, also Sen paradox or Sen's paradox, is a logical paradox discovered by Amartya Sen which purports to show that no social system can simultaneously
This paradox is contentious because it appears to contradict the classical liberal claim that markets are both Pareto efficient and respect individual freedoms.
Paradox of competition
Paradox of competition in economics names a model of a situation where measures, which offer a competitive advantage to an individual economic entity, lead to nullification of advantage if all others behave in the same way. In some cases the finite state is even more disadvantageous for everybody than before (for the totality as well as for the individual). The term "Paradox of competition" () was coined by German economist Wolfgang Stützel. It is about a case of a rationality trap.
No-no paradox
The No–no paradox is a distinctive paradox belonging to the family of the semantic paradoxes (like the Liar paradox). It derives its name from the fact that it consists of two sentences each simply denying what the other says.
Twin paradox
In physics, the twin paradox is a thought experiment in special relativity involving identical twins, one of whom makes a journey into space in a high-speed rocket and returns home to find that the twin who remained on Earth has aged more. This result appears puzzling because each twin sees the other twin as moving, and so, according to an incorrect and naive application of time dilation and the principle of relativity, each should paradoxically find the other to have aged less. However, this scenario can be resolved within the standard framework of special relativity: the travelling twin's trajectory involves two different inertial frames, one for the outbound journey and one for the inbound journey, and so there is no symmetry between the spacetime paths of the twins. Therefore, the twin paradox is not a paradox in the sense of a logical contradiction.
Simpson's paradox
Simpson's paradox (or Simpson's reversal, Yule–Simpson effect, amalgamation paradox, or reversal paradox), is a phenomenon in probability and statistics, in which a trend appears in several different groups of data but disappears or reverses when these groups are combined.
This result is often encountered in social-science and medical-science statistics and is particularly problematic when frequency data is unduly given causal interpretations. The paradoxical elements disappear when causal relations are brought into consideration. It has been used to try to inform the non-specialist or public audience about the kind of misleading results mis-applied statistics can generate. Martin Gardner wrote a popular account of Simpson's paradox in his March 1976 Mathematical Games column in "Scientific American".
Knower paradox
The knower paradox is a paradox belonging to the family of the paradoxes of self-reference (like the liar paradox). Informally, it consists in considering a sentence saying of itself that it is not known, and apparently deriving the contradiction that such sentence is both not known and known.
Barbershop paradox
The barbershop paradox was proposed by Lewis Carroll in a three-page essay titled "A Logical Paradox", which appeared in the July 1894 issue of "Mind". The name comes from the "ornamental" short story that Carroll uses to illustrate the paradox (although it had appeared several times in more abstract terms in his writing and correspondence before the story was published). Carroll claimed that it illustrated "a very real difficulty in the Theory of Hypotheticals" in use at the time. Modern logicians would not regard it as a paradox but simply as a logical error.
Grelling–Nelson paradox
The Grelling–Nelson paradox is an antinomy, or a semantic self-referential paradox, concerning the applicability to itself of the word "heterological", meaning "inapplicable to itself". It was formulated in 1908 by Kurt Grelling and Leonard Nelson, and is sometimes mistakenly attributed to the German philosopher and mathematician Hermann Weyl.
It is thus occasionally called Weyl's paradox and Grelling's paradox. It is closely related to several other well-known paradoxes, in particular, the barber paradox and Russell's paradox.
Bhartṛhari
In a section of the chapter on Relation Bhartrhari discusses the liar paradox and identifies a hidden parameter which turns an unproblematic situation in daily life into a stubborn paradox. In addition, Bhartrhari discusses here a paradox that has been called "Bhartrhari's paradox" by Hans and Radhika Herzberger. This paradox arises from the statement "this is unnameable" or "this is unsignifiable".
Russell's paradox
There are some versions of this paradox that are closer to real-life situations and may be easier to understand for non-logicians. For example, the barber paradox supposes a barber who shaves all men who do not shave themselves and only men who do not shave themselves. When one thinks about whether the barber should shave himself or not, the paradox begins to emerge.
No-no paradox
Generally speaking, the paradox instantiates the problem of determining the status of ungrounded sentences that are not inconsistent. More in particular, the paradox presents the challenge of expanding one’s favourite theory of truth with further principles which either express the symmetry intuition against possibilities 3. and 4. or make them acceptable in spite of their intuitive repugnancy. Because (N) and (N) do not lead to inconsistency, a certain strand in the discussion of the paradox has been willing to assume both the relevant instances of (T) and classical logic, thereby deriving the conclusion that either possibility 3. or possibility 4. holds. Such conclusion has in turn been taken to have momentous consequences for certain influential philosophical theses. Consider, for example, the thesis of truthmaker maximalism:
Potato paradox
Expanding brackets and simplifying
Paradox of fiction
The basic paradox is as follows:The paradox is that all three premises seem to be true, but can not logically be true at the same time. If any two points (e.g. 1 and 3) are taken to be true, then the third (e.g. 2) must either be false or else produce a contradiction.
Banach–Tarski paradox
and
Paradox of analysis
The paradox of analysis is a paradox that concerns how an analysis can be both correct and informative. Although the problem takes its origin from the conflict in Plato's "Meno", it was formulated in its complete form by philosopher G. E. Moore in his book "Principia Ethica", and first named by C. H. Langford in his 1942 article "The Notion of Analysis in Moore's Philosophy".
Liar paradox
If (A) is true, then "This statement is false" is true. Therefore, (A) must be false. The hypothesis that (A) is true leads to the conclusion that (A) is false, a contradiction.
List of paradoxes
However, some of these paradoxes qualify to fit into the mainstream perception of a paradox, which is a self-contradictory result gained even while properly applying accepted ways of reasoning. These paradoxes, often called "antinomy," point out genuine problems in our understanding of the ideas of truth and description.These paradoxes have in common a contradiction arising from either self-reference or circular reference, in which several statements refer to each other in a way that following some of the references leads back to the starting point.
Cantor's paradox
This paradox is named for Georg Cantor, who is often credited with first identifying it in 1899 (or between 1895 and 1897). Like a number of "paradoxes" it is not actually contradictory but merely indicative of a mistaken intuition, in this case about the nature of infinity and the notion of a set. Put another way, it is paradoxical within the confines of naïve set theory and therefore demonstrates that a careless axiomatization of this theory is inconsistent.
Foundations of mathematics
The name ""paradox"" should not be confused with "contradiction". A contradiction in a formal theory is a formal proof of an absurdity inside the theory (such as ), showing that this theory is inconsistent and must be rejected. But a paradox may be either a surprising but true result in a given formal theory, or an informal argument leading to a contradiction, so that a candidate theory, if it is to be formalized, must disallow at least one of its steps; in this case the problem is to find a satisfying theory without contradiction. Both meanings may apply if the formalized version of the argument forms the proof of a surprising truth. For instance, Russell's paradox may be expressed as "there is no set of all sets" (except in some marginal axiomatic set theories).
Necktie paradox
The necktie paradox is a puzzle or paradox within the subjectivistic interpretation of probability theory. It is a variation (and historically, the origin) of the two-envelope paradox.
Banach–Tarski paradox
where the notation "aS"("a") means take all the strings in "S"("a") and concatenate them on the left with "a".
Mechanical paradox
The mechanical paradox is an apparatus for studying physical paradoxes.
Parrondo's paradox
However, when these two losing games are played in some alternating sequence - e.g. two games of A followed by two games of B (AABBAABB...), the combination of the two games is, paradoxically, a "winning" game. Not all alternating sequences of A and B result in winning games. For example, one game of A followed by one game of B (ABABAB...) is a losing game, while one game of A followed by two games of B (ABBABB...) is a winning game. This coin-tossing example has become the canonical illustration of Parrondo's paradox – two games, both losing when played individually, become a winning game when played in a particular alternating sequence. The apparent paradox has been explained using a number of sophisticated approaches, including Markov chains, flashing ratchets, Simulated Annealing and information theory. One way to explain the apparent paradox is as follows:
Wollheim's paradox
Wollheim's paradox is a problem in political philosophy that points to an inherent contradiction in the concept of democracy. The paradox highlights the fact that a person can simultaneously advocate two conflicting policy options A and B, provided that the person believes that democratic decisions should be followed. The paradox was formulated by the British philosopher Richard Wollheim in 1962 in an article entitled "A paradox in the theory of democracy".
Paradox
W. V. Quine (1962) distinguished between three classes of paradoxes:
Paradox
Other paradoxes involve false statements ("'impossible' is not a word in my vocabulary", a simple paradox) or half-truths and the resulting biased assumptions. This form is common in howlers.
Allais paradox
Allais presented his paradox as a counterexample to the independence axiom.