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Topic: Liar paradox

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In the News (Wed 26 Jun 19)

  Liar paradox - Wikipedia, the free encyclopedia
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...".
On that basis, the paradox is blocked by restricting the Rule of Assumptions in Gentzen-style presentations of the sequent-calculus.
The lesson of the liar is that not all assumptions are for free.
en.wikipedia.org /wiki/Liar_paradox   (2512 words)

 Peter Suber, Paradox of Self-Amendment, Section 1
Paradoxes are disturbing because we have difficulty denying them status as meaningful statements subject to the normal rules about contradiction and truth, and we are rarely willing to amend our logical rules merely to accommodate a string of words that twists them up.
Russell's paradox is of the Barber-type, not the Liar-type.
Lawyers under a deadline are normally unaware of the centuries of prior thought on the paradoxes, and in any case might find it irrelevant to the "condensation" of the paradox in their particular case and to the inherited rules under which they must devise a solution.
www.earlham.edu /~peters/writing/psa/sec01.htm   (7901 words)

 Liar Paradox [Internet Encyclopedia of Philosophy]
Most logical paradoxes are based on circular definitions or self-referential statements, and the liar paradox is no exception.
Most logicians want systematic removal of the paradox, but Wittgenstein is content to say that we may need to live with this paradox and to agree never to utter the Liar sentence, especially if it seems that removal of the contradiction could have worse consequences.
Some of the solutions to the Liar Paradox require a revision in classical logic, the formal logic in which sentences of a formal language have exactly two possible truth values (TRUE, FALSE), and in which the usual rules of inference allow one to deduce anything from an inconsistent set of assumptions.
www.utm.edu /research/iep/p/par-liar.htm   (3442 words)

 PARADOX Persistent contradictory opposites create popular hypocritical deception.   (Site not responding. Last check: 2007-09-08)
The fact 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 or false.
There is no paradox because the claim that this statement is false does not lead to a contradiction.
Liar statements and liar-like statements are ungrounded, and therefore have no truth value.
www.unique-design.net /library/paradox.html   (977 words)

 Paradox - Uncyclopedia
Unrequited-Gay-Love Paradox: Say a gay guy is in love with a straight guy, and all he wants is a straight answer.
A Most Ingenious Paradox: This Paradox (a Most Ingenious Paradox):You are the victim of this clumsy arrangement, having been born in leap-year, on the twenty-ninth of February;And so, by a simple arithmetical process, you'll easily discover,That though you've lived twenty-one years, yet, if we go by birthdays, you're only five and a little bit over.
Paradox (Arizona): A place where conspiricy theorists believe there is an alien base, but it doesn't exist.
uncyclopedia.org /wiki/Paradox   (1014 words)

 Math Notes - Set Membership
may help to explain the liar’s paradox, because the truth-teller’s statement evokes much less anxiety but is a statement of essentially the same form as the liar’s statement.
In summary, the obvious interpretation of the liar’s statement can’t be used to represent the liar’s statement suggesting that the liar’s statement is not supported by any traditional system of logic.
In the case of the liar’s paradox, the liar’s side results in a contradiction and the truth-teller’s side does not provide enough information.
home.att.net /~p.konieczko/paradox.html   (1213 words)

 Cretan Paradox
The Cretan Paradox is attributed to the Cretan poet Epimenides [http://en.wikipedia.org/wiki/Epimenides_paradox].
(For one analysis, see http://david.tribble.com/text/liar.htm, but note that that page treats the terms "Epimenides Paradox" and "Liar Paradox" as interchangeable.) But in the historical view, it is more interesting to note that twenty-six centuries ago, careful thinkers were already aware of, and exploring, the limits and limitations of their language and their methods of reasoning.
Even in that form, it is still true that (A) being a liar, even always, doesn't preclude uttering the occasional true statement and (B) the author is implying, especially in the context of the poem, that he himself is excluded.
c2.com /cgi/wiki?CretanParadox   (701 words)

 The Epimenides Paradox
The so-called "Liar Paradox," or "Epimenides Paradox," is really the cornerstone of a whole family of paradoxes of the type known as "liar paradoxes".
Similarly, with the above version of the Epimenides paradox, all that follows is that Epimenides is a liar and that at least one Cretan is truthful.
Now, if Epimenides were the only Cretan, then we would indeed have a paradox, just as we would have if a sole inhabitant of an island of knights and knaves said that all inhabitants of the island were knaves (which would be tantamount to saying that he is a knave, which is impossible).
david.tribble.com /text/liar.htm   (547 words)

 Georges Metanomski LIAR'S "PARADOX"
Liar's "Paradox" has been formulated in Greece about 600 BC so it's reasonable to push it first through the filter of Aristotelian Logic.
The "modern" version of Liar is the following "statement" L: -Which statement?- you may wonder and you would be right: L is NOT a statement.
Liar in its "modern" version "THIS STATEMENT IS FALSE" is not a statement at all thus it cannot be true, nor false, nor a paradox, but just an empty meaningless noise.
evans-experientialism.freewebspace.com /meta_liarsparadox.htm   (1065 words)

 [No title]   (Site not responding. Last check: 2007-09-08)
The liar paradox is an ancient conundrum of logic.
In addition to context diagrams, the mathematical notion of a meta-context is also needed for resolving the liar paradox.
Meta-contextual resolutions of related paradoxes, such as the strengthened liar paradox, are also described.
www.uwec.edu /walkerjs/media/LiarPara.txt   (84 words)

 Liar's Paradox Paper
Neff then introduces the Cretan Liar Paradox ("All Cretans always lie"), which admittedly is not a paradox until reformulated, viz., "This sentence is false." Neff mentions several attempted solutions of the paradox as reformulated--including, notably, Bertrand Russell's theory of types [3]--before attempting his own solution.
A subject/predicate proposition (e.g., 'The Liar is a Thief', 'All cows eat grass'), by predicating certain attributes of the subject-concept's referents, implicitly asserts the existence of the subject-concept's referents.
First of all, the Liar (in the original formulation of the Paradox) was not a concept-stealer.
members.aol.com /REBissell/indexmm9.html   (4854 words)

 Ephilosopher :: Puzzles and Paradoxes :: Classic : The Liar Paradox   (Site not responding. Last check: 2007-09-08)
It is actually one of the simplest paradox to solve as one can work it out just by considering the "simple theory of types" that Russel proposed in the early 20th century.
What I meant by solving this particular paradox, is that Russell provided an opening to attack such problems, and from him, the "liar paradox" per se is no more the focus of studies.
The difficulty most people have with paradoxes like this is that they delude themselves into thinking the words they use to express reality actually denotes whatever reality may or may not actually be.
www.ephilosopher.com /phpBB_14-action-viewtopic-topic-51.html   (2152 words)

 Epimenides paradox - Wikipedia, the free encyclopedia
Alternatively, if, by "liar", we were to mean someone whose statements are usually but not always false, the logical problem would dissolve: Epimenides might usually lie, but on this occasion it might be that he happened to speak the truth.
Paradoxical versions of the Epimenides problem are closely related to a class of more difficult logical problems, including the liar paradox, Russell's paradox, and the Burali-Forti paradox, all of which have self-reference in common with Epimenides.
(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.
en.wikipedia.org /wiki/Epimenides_paradox   (1130 words)

 Liar paradox
The roots of the Liar paradox stretch back to the philosopher Epimenides in the sixth century B.C. Epimenides said: "All Cretans are liars....
However, most formulations of logic define a "liar" as an entity that always produces the negation of the true answer, that is, someone who does nothing but lie.
Even the statement "I am a liar" is not paradoxical; depending on the definition of "liar" it may be true or false.
www.daviddarling.info /encyclopedia/L/Liar_paradox.html   (511 words)

 Liar Paradox [Internet Encyclopedia of Philosophy]
There are many versions of the Paradox in addition to Buridan's and the Liar generated from (1).
Although there are many suggestions for how to deal with the Liar Paradox, most are never developed to the point of giving a formal, symbolic theory.
However, for those who believe the Paradox is not a minor problem but one deserving of immediate attention, there can be no waiting around until the other problems of language are solved independently.
www.mit.edu /people/yandros/phil/liar-paradox-iep.html   (3102 words)

 Liar Paradox - Curiouser.co.uk
If one defines a liar as someone who sometimes tells the truth and sometimes doesn't, one can clearly see that no paradox exists, as the statement "all Cretans are liars" can be true without contradicting the status of the speaker as someone who sometimes lies and sometimes tells the truth.
If "all Cretans are liars" is a lie, then one can logically infer that "Not all Cretans are liars", which means that at least one Cretan tells the truth at least some of the time.
It is known as the Liar Paradox, and is attributed to Eubulides of Miletus, a Greek philosopher who lived in the fourth Century BC.
www.curiouser.co.uk /paradoxes/liar.htm   (584 words)

 Some paradoxes   (Site not responding. Last check: 2007-09-08)
Eubulides, the Megarian sixth century B.C. Greek philosopher, and successor to Euclid, invented the paradox of the liar.
In this paradox, Epimenides, the Cretan, says, "All Cretans are liars." If he is telling the truth he is lying; and if he is lying, he is telling the truth.
The paradox arises from a disguised breach of the arithmetical prohibition on division by zero, occurring at (5): since a = b, dividing both sides by (a - b) is dividing by zero, which renders the equation meaningless.
www.wordsmith.demon.co.uk /paradoxes/index.htm   (3977 words)

 The Liar Paradox
The Liar Paradox is among the simplest of paradoxes.
The Liar Paradox is sometimes referred to as “EpimenidesParadox”, after the sixth-century B.C. Cretan who asserted that all Cretans are liars.
What he says can’t be true, for if Cretans are always liars, and he is a Cretan, then he must be lying, in which case his statement is false.
www.logicalparadoxes.info /liar.html   (310 words)

 Diagonal Method and the Russell Paradox
The Russell Paradox is the new name given to the liar's paradox.
The form of the paradox of greatest interest to this story occurs with all inclusive sets like the set of all sets.
Although contemplating the liar's paradox is generally a waste of time, Russell realized that any new foundational theory would have to face the issue.
descmath.com /diag/russell.html   (1268 words)

 Mormon Philosophy & Theology
It got me thinking about the Liar's Paradox which is the grand daddy of all the semantic paradoxes.
But it has already violated the given that every statement is true or false, which gives the Liar Paradox its sting -- and in violating it, paradoxically it takes on a truth value and thus conforms to it.
But we have to be careful because in the context of the Liar's paradox I believe indeterminacy means something quite different from what Peirce means by it.
www.lextek.com /clark/10568.html   (1597 words)

 Curry's Paradox (Stanford Encyclopedia of Philosophy)
Curry's paradox, so named for its discoverer, namely Haskell B. Curry, is a paradox within the family of so-called paradoxes of self-reference (or paradoxes of circularity).
Like the liar paradox (e.g., ‘this sentence is false’) and Russell's paradox, Curry's paradox challenges familiar naive theories, including naive truth theory (unrestricted T-schema) and naive set theory (unrestricted axiom of abstraction), respectively.
Unlike the liar and Russell paradoxes Curry's paradox is negation-free; it may be generated irrespective of one's theory of negation.
plato.stanford.edu /entries/curry-paradox   (2107 words)

 Paradoxes: The Liar and Some Relatives
More precisely, the paradox can be resolved in one of these ways, but only at the price of falling into some related paradox.
Indeed, if I am correct, the paradox cannot be resolved – cannot in a way that does not engender further paradoxes, that is – because in it, we are struggling with the boundaries of our conceptual scheme and attempting incoherently to both remain within it and to stand outside it.
You apparently think we can avoid the paradox by claiming that “This sentence is false” is meaningless and therefore, neither true nor false.
personal.bgsu.edu /~roberth/liar.html   (800 words)

 The Liar's Paradox, Contradiction, and Truth - Page 2 - SciForums.com
However, one half of the liar's paradox actually is a liar's paradox itself, if phrased slightly differently: This statement is false.
Well, it seems to me that the statement doesn't have a subject that can be true or false, so the statement is neither true nor false but a poorly constructed assertion.
It is neither a true statement, nor a false statement, nor a paradoxical statement.
www.sciforums.com /showthread.php?p=1192151   (1877 words)

The second reason (that formalizing a natural language might not "preserve its naturalness") is not compelling, but the first reason, the Liar Paradox as emphasized by Andrea A., is serious: So long as the Liar is unattended to, a Davidsonian truth definition for English will itself contain a contradiction.
(2) Tarskian universality is suspect, precisely because it is implicated in the Liar Paradox.
I mentioned a third response in class: that the Liar Paradox is a paradox in its own right.
www.unc.edu /~ujanel/DavLiar.htm   (689 words)

 The Liar's Paradox, Contradiction, and Truth - SciForums.com
Now when considering this, I came to a revelation: Is not the liar's paradox simply an instance where one is testing the Law of Non-Contradiction by postulating a contradictory statement?
Rather, it is like the Liar's Paradox, which would simulteneously be true and false.
When you have the time to give more of a response, what do you think of my argument to show that the Liar's Paradox is basically an example of postulating a contradiction and that its unresolvability reveals that all truthful statements must be resolvable and that all unresolvable statements are in fact not truthful?
www.sciforums.com /showthread.php?p=1177271   (4577 words)

 The Revision Theory of Truth (Stanford Encyclopedia of Philosophy)
It has long been known that the sentence, (1), produces a paradox, the so-called liar's paradox: it seems impossible consistently to maintain that (1) is true, and impossible consistently to maintain that (1) is not true.
This is a formalization of the liar's paradox, with the sentence ¬Tλ as the offending liar's sentence.
The liar sentence X is, unsurprisingly, neither stably true nor stably false: the liar sentence is unstable.
plato.stanford.edu /entries/truth-revision   (7128 words)

 Liar Paradox - Curiouser.co.uk
A statement made by him is believed to be the oldest of logical paradoxes.
His statement therefore implies that he was a liar himself.
This elliminates questions about the nature of liars, such as whether a liar ALWAYS lies.
www.curiouser.co.uk /puzzles/liar.htm   (307 words)

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