Instruct: Given a question, retrieve relevant documents that can help answer the question.
Query: What does a paradox mean?
A paradox is a statement that, despite apparently valid reasoning from true premises, leads to an apparently-self-contradictory or logically unacceptable conclusion.[1][2] A paradox involves contradictory-yet-interrelated elements that exist simultaneously and persist over time.[3][4][5]
Perhaps better put, for "All Cretans are liars" to be a true statement, it does not mean that all Cretans must lie all the time. In fact Cretans could tell the truth quite often but still all be liars in the sense that liars are people prone to deception for dishonest gain. Considering that “All Cretans are liars” has been seen as a paradox only since the 19th century, this seems to resolve the alleged paradox. Of course if ‘all Cretans are continuous liars’ is actually true, then asking a Cretan if they are honest would always elicit the dishonest answer ‘yes’. So arguably the original proposition is not so much paradoxical as invalid. 
Peter Geach describes and rejects four levels of omnipotence. He also defines and defends a lesser notion of the "almightiness" of God.Augustine of Hippo in his City of God writes "God is called omnipotent on account of His doing what He wills" and thus proposes the definition that "Y is omnipotent" means "If Y wishes to do X then Y can and does do X". 
The notion of omnipotence can also be applied to an entity in different ways. An essentially omnipotent being is an entity that is necessarily omnipotent. In contrast, an accidentally omnipotent being is an entity that can be omnipotent for a temporary period of time, and then becomes non-omnipotent. The omnipotence paradox can be applied to each type of being differently.
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.
His works typically offer readers an approachable invitation to the use of semiotics to help explain everyday phenomena. For instance, his book "Quest for Meaning: A Guide to Semiotic Theory and Practice" provides readers with a simple three-fold way of considering semiotic inquiry as trying to answer "What does it Mean? How does it convey meaning? And Why does it mean what it means?" 
In the study of illative (deductive) combinatory logic, Curry in 1941 recognized the implication of the paradox as implying that, without restrictions, the following properties of a combinatory logic are incompatible:Note that unlike the liar paradox or Russell's paradox, Curry's paradox does not depend on what model of negation is used, as it is completely negation-free. Thus paraconsistent logics can still be vulnerable to this paradox, even if they are immune to the liar paradox.
Kierkegaard uses the Doctrine of Recollection as an example of how truth was found in Ancient Greek philosophy and is still found in psychotherapy and modern medicine. Both of these sciences are based on questioning the patient, "Learner", in the hope of jogging their memory about past events. The therapist could ask the right question and not realize he has received the answer he was looking for, this is known as Meno's paradox. Kierkegaard puts his paradox this way, "what a man knows he cannot seek, since he knows it; and what he does not know he cannot seek, since he does not even know for what to seek."
Most commentators on Sen's paradox have argued that Sen's minimal liberalism condition does not adequately capture the notion of individual rights. Essentially what is excluded from Sen's characterization of individual rights is the ability to voluntarily form contracts that lay down one's claim to a right.
The sorites paradox (; sometimes known as the paradox of the heap) is a paradox that arises from vague predicates. A typical formulation involves a heap of sand, from which grains are individually removed. Under the assumption that removing a single grain does not turn a heap into a non-heap, the paradox is to consider what happens when the process is repeated enough times: is a single remaining grain still a heap? If not, when did it change from a heap to a non-heap?
Meno asks Socrates: "And how will you inquire into a thing when you are wholly ignorant of what it is? Even if you happen to bump right into it, how will you know it is the thing you didn't know?" Socrates rephrases the question, which has come to be the canonical statement of the paradox: "[A] man cannot search either for what he knows or for what he does not know[.] He cannot search for what he knows--since he knows it, there is no need to search--nor for what he does not know, for he does not know what to look for."
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.
When asked in 1993 by a "The New York Times" Style reporter what it all meant, Cost said, "If you could give us [Cost and Revs] the meaning of life, I’d give you the meaning of us." At that time the posters included a phone number; those who called heard a woman's recorded voice repeat their questions back to them: "My intuition tells me that you're asking yourselves who are Revs and Cost and what are they doing? What is it? What does it mean? What does it mean? What does it mean?"
Cost and Revs continued to write in New York City with impunity, highly visible examples of the graffiti that Mayor Rudolph Giuliani was determined to eradicate. One letter writer called Cost "probably the worst graffiti vandal in the history of New York."
In a 1955 article in the philosophy journal "Mind", J. L. Mackie tried to resolve the paradox by distinguishing between first-order omnipotence (unlimited power to act) and second-order omnipotence (unlimited power to determine what powers to act things shall have). An omnipotent being with both first and second-order omnipotence at a particular time might restrict its own power to act and, henceforth, cease to be omnipotent in either sense. There has been considerable philosophical dispute since Mackie, as to the best way to formulate the paradox of omnipotence in formal logic.Another common response is that since God is supposedly omnipotent, the phrase "could not lift" does not make sense and the paradox is meaningless. This may mean that the complexity involved in rightly understanding omnipotence—contra all the logical details involved in misunderstanding it—is a function of the fact that omnipotence, like infinity, is perceived at all by contrasting reference to those complex and variable things, "which it is not". An alternative meaning, however, is that a non-corporeal God cannot lift anything, but can raise it (a linguistic pedantry)—or to use the beliefs of Hindus (that there is one God, who can be manifest as several different beings) that whilst it is possible for God to do all things, it is not possible for all his incarnations to do them. As such, God could create a stone so heavy that, in one incarnation, he couldn't lift it, yet could do something that an incarnation that "could" lift the stone could not.
Wittgenstein's work expresses the omnipotence paradox as a problem in semantics—the study of how we give symbols meaning. (The retort "That's only semantics," is a way of saying that a statement only concerns the definitions of words, instead of anything important in the physical world.) According to the "Tractatus," then, even attempting to formulate the omnipotence paradox is futile, since language cannot refer to the entities the paradox considers. The final proposition of the "Tractatus" gives Wittgenstein's dictum for these circumstances: "What we cannot speak of, we must pass over in silence".
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.
The first paradox (the Liar) is probably the most famous, and is similar to the famous paradox of Epimenides the Cretan. The second, third and fourth paradoxes are variants of a single paradox and relate to the problem of what it means to "know" something and the identity of objects involved in an affirmation (compare the masked man fallacy). The fifth and sixth paradoxes are also a single paradox and is usually thought to relate to the vagueness of language. The final paradox attacks presumptions involved in a proposition, and is related to the syllogistic fallacy.
Bock responded to the paradox by positing that both statisticians in the scenario are correct once the question being asked is clarified. The first statistician (who compares group means and distributions) is asking "are there differences in average weight gain?", whereas the second is asking "what are the differences in 
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".
Quine's paradox is a paradox concerning truth values, stated by Willard Van Orman Quine. It is related to the liar paradox as a problem, and it purports to show that a sentence can be paradoxical even if it is not self-referring and does not use demonstratives or indexicals (i.e. it does not explicitly refer to itself). The paradox can be expressed as follows:
Saket Suman of "Business Standard" wrote in his review: "What Tharoor does, and succeeds in doing, is show his readers what Modi said and says, and what he and his government did during the four years of their rule so far." Anirudh Madhavan of "The Week" wrote: "Tharoor echoes the sentiments of the many who oppose Modi, but does so with academic rigour."
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.
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.
Paradoxical motion is a late sign of flail segment; therefore, an absence of paradoxical motion does not mean the patient does not have a flail segment.
"Chorus"
Oh what does it mean when the pubs are all packed at five-thirty?
Oh what does it mean when we're all having fish for our tea?
Oh what does it mean when Top of the Pops is on the telly?
Oh yes, the weekend's nearly here;
So sing along with meeee-ee hee hee...
The Grelling–Nelson paradox arises when we consider the adjective "heterological". One can ask: Is "heterological" a heterological word?
If the answer is "no", then "heterological" is autological. This leads to a contradiction, for in this case "heterological" does not describe itself: it must be a heterological word.
But if the answer is "yes", then "heterological" is heterological. This again leads to a contradiction, because if the word "heterological" describes itself, it is autological.The paradox can be eliminated, without changing the meaning of "heterological" where it was previously well-defined, by modifying the definition of "heterological" slightly to hold all nonautological words except "heterological". But "nonautological" is subject to the same paradox, for which this evasion is not applicable because the rules of English uniquely determine its meaning from that of "autological". A similar slight modification to the definition of "autological" (such as declaring it false of "nonautological" and its synonyms) might seem to correct that, but the paradox still obtains for synonyms of "autological" and "heterological" such as "selfdescriptive" and "nonselfdescriptive", whose meanings also would need adjusting, and the consequences of those adjustments would then need to be pursued, and so on. Freeing English of the Grelling–Nelson paradox entails considerably more modification to the language than mere refinements of the definitions of "autological" and "heterological", which need not even be in the language for the paradox to arise. The scope of these obstacles for English is comparable to that of Russell's paradox for mathematics founded on sets.