656:"everything I am saying is false") Bhartrhari identifies a hidden parameter that can change unproblematic situations in daily communication into a stubborn paradox. Bhartrhari's solution can be understood in terms of the solution proposed in 1992 by Julian Roberts: "Paradoxes consume themselves. But we can keep apart the warring sides of the contradiction by the simple expedient of temporal contextualisation: what is 'true' with respect to one point in time need not be so in another ... The overall force of the 'Austinian' argument is not merely that 'things change', but that rationality is essentially temporal in that we need time in order to reconcile and manage what would otherwise be mutually destructive states." According to Robert's suggestion, it is the factor "time" which allows us to reconcile the separated "parts of the world" that play a crucial role in the solution of Barwise and Etchemendy. The capacity of time to prevent a direct confrontation of the two "parts of the world" is here external to the "liar". In the light of Bhartrhari's analysis, however, the extension in time that separates two perspectives on the world or two "parts of the world" â the part before and the part after the function accomplishes its task â is inherent in any "function": also the function to signify which underlies each statement, including the "liar". The unsolvable paradox â a situation in which we have either contradiction (
749:. Then the theory at hand, which is assumed to prove certain facts about numbers, also proves facts about its own statements. Questions about the provability of statements are represented as questions about the properties of numbers, which would be decidable by the theory if it were complete. In these terms, the Gödel sentence states that no natural number exists with a certain, strange property. A number with this property would encode a proof of the inconsistency of the theory. If there were such a number then the theory would be inconsistent, contrary to the consistency hypothesis. So, under the assumption that the theory is consistent, there is no such number.
491:
discussing truth values to envision levels of languages, each of which can predicate truth (or falsehood) only of languages at a lower level. So, when one sentence refers to the truth-value of another, it is semantically higher. The sentence referred to is part of the "object language", while the referring sentence is considered to be a part of a "meta-language" with respect to the object language. It is legitimate for sentences in "languages" higher on the semantic hierarchy to refer to sentences lower in the "language" hierarchy, but not the other way around. This prevents a system from becoming self-referential.
826:. However, lacking the intelligence to realize the statement is a paradox, he simply responds, "Um, true. I'll go with true. There, that was easy." and is unaffected. Humorously, all other AIs present barring GLaDOS, all of which are significantly less sentient and lucid than both her and Wheatley, are still killed from hearing the paradox. However, GLaDOS later notes that she almost killed herself from her own attempt to kill Wheatley.
525:) 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 ...".
2398:
2388:
742:, Gödel used a modified version of the liar paradox, replacing "this sentence is false" with "this sentence is not provable", called the "Gödel sentence G". His proof showed that for any sufficiently powerful theory T, G is true, but not provable in T. The analysis of the truth and provability of G is a formalized version of the analysis of the truth of the liar sentence.
706:"A = false" is equivalent to "not A" and therefore the equation is not solvable. This is the motivation for reinterpretation of A. The simplest logical approach to make the equation solvable is the dialetheistic approach, in which case the solution is A being both "true" and "false". Other resolutions mostly include some modifications of the equation;
502:+1 which asserts that the first statement is false." This is a true, meaningful statement about the hierarchy that Tarski defines, but it refers to statements at every level of the hierarchy, so it must be above every level of the hierarchy, and is therefore not possible within the hierarchy (although bounded versions of the sentence are possible).
652:(late fifth century AD) dealt with paradoxes such as the liar in a section of one of the chapters of his magnum opus the VÄkyapadÄ«ya. Bhartrhari's solution fits into his general approach to language, thought and reality, which has been characterized by some as "relativistic", "non-committal" or "perspectivistic". With regard to the liar paradox (
849:, titled "Access Denied", the main character Jesse and their friends are captured by a supercomputer named PAMA. After PAMA controls two of Jesse's friends, Jesse learns that PAMA stalls when processing and uses a paradox to confuse him and escape with their last friend. One of the paradoxes the player can make Jesse say is the liar paradox.
137:(late fifth century AD) was well aware of a liar paradox which he formulated as "everything I am saying is false" (sarvam mithyÄ bravÄ«mi). He analyzes this statement together with the paradox of "unsignifiability" and explores the boundary between statements that are unproblematic in daily life and paradoxes.
809:, the Doctor temporarily stumps the insane computer BOSS by asking it "If I were to tell you that the next thing I say would be true, but that the last thing I said was a lie, would you believe me?" BOSS tries to figure it out but cannot and eventually decides the question is irrelevant and summons security.
590:
propose that the liar sentence (which they interpret as synonymous with the
Strengthened Liar) is ambiguous. They base this conclusion on a distinction they make between a "denial" and a "negation". If the liar means, "It is not the case that this statement is true", then it is denying itself. If it
90:, reportedly stated that "All Cretans are liars." However, Epimenides' statement that all Cretans are liars can be resolved as false, given that he knows of at least one other Cretan who does not lie (alternatively, it can be taken as merely a statement that all Cretans tell lies, not that they tell
490:
diagnosed the paradox as arising only in languages that are "semantically closed", by which he meant a language in which it is possible for one sentence to predicate truth (or falsehood) of another sentence in the same language (or even of itself). To avoid self-contradiction, it is necessary when
310:
If F is assumed to bear a truth value, then it presents the problem of determining the object of that value. But, a simpler version is possible, by assuming that the single word 'true' bears a truth value. The analogue to the paradox is to assume that the single word 'false' likewise bears a truth
196:
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
1432:
recognized that
Bhartrhari "wants to rise at once above all controversies by showing the conditions of possibility of any system of interpretation, rather than to prove the truth of a certain particular system" (Théorie de la connaissance et philosophie de la parole dans le brahmanisme classique,
128:
telling the truth or is he lying? If it is true that every man is a liar, and David's statement, "Every man is a liar" is true, then David also is lying; he, too, is a man. But if he, too, is lying, his statement that "Every man is a liar", consequently is not true. Whatever way you turn the
574:
Kripke proposes a solution in the following manner. If a statement's truth value is ultimately tied up in some evaluable fact about the world, that statement is "grounded". If not, that statement is "ungrounded". Ungrounded statements do not have a truth value. Liar statements and liar-like
285:
The multi-sentence version of the liar paradox generalizes to any circular sequence of such statements (wherein the last statement asserts the truth/falsity of the first statement), provided there are an odd number of statements asserting the falsity of their successor; the following is a
684:
For a better understanding of the liar paradox, it is useful to write it down in a more formal way. If "this statement is false" is denoted by A and its truth value is being sought, it is necessary to find a condition that restricts the choice of possible truth values of A. Because A is
311:
value, namely that it is false. This reveals that the paradox can be reduced to the mental act of assuming that the very idea of fallacy bears a truth value, namely that the very idea of fallacy is false: an act of misrepresentation. So, the symmetrical version of the paradox would be:
55:
is strengthened in order to make it amenable to more rigorous logical analysis. It is still generally called the "liar paradox" although abstraction is made precisely from the liar making the statement. Trying to assign to this statement, the strengthened liar, a classical binary
338:, where the truth values may only be the integer values 0 or 1. In this system, the statement "This statement is false" is no longer paradoxical as it can be assigned a truth value of 0.5, making it precisely half true and half false. A simplified explanation is shown below.
639:
has argued in favour of a non-cognitivist solution to the paradox, suggesting that some apparently well-formed sentences will turn out to be neither true nor false and that "formal criteria alone will inevitably prove insufficient" for resolving the paradox.
614:. Dialetheism is the view that there are true contradictions. Dialetheism raises its own problems. Chief among these is that since dialetheism recognizes the liar paradox, an intrinsic contradiction, as being true, it must discard the long-recognized
947:
St. Jerome, Homily on Psalm 115 (116B), translated by Sr. Marie
Liguori Ewald, IHM, in The Homilies of Saint Jerome, Volume I (1-59 On the Psalms), The Fathers of the Church 48 (Washington, D.C.: The Catholic University of America Press, 1964),
192:
If (A) is false, then "This statement is false" is false. Therefore, (A) must be true. The hypothesis that (A) is false leads to the conclusion that (A) is true, another contradiction. Either way, (A) is both true and false, which is a paradox.
537:
The latter is a simple contradiction of the form "A and not A", and hence is false. There is therefore no paradox because the claim that this two-conjunct Liar is false does not lead to a contradiction. Eugene Mills presents a similar answer.
50:
is the statement of a liar that they are lying: for instance, declaring that "I am lying". If the liar is indeed lying, then the liar is telling the truth, which means the liar just lied. In "this sentence is a lie" the
752:
It is not possible to replace "not provable" with "false" in a Gödel sentence because the predicate "Q is the Gödel number of a false formula" cannot be represented as a formula of arithmetic. This result, known as
714:" and therefore A is false. In computational verb logic, the liar paradox is extended to statements like, "I hear what he says; he says what I don't hear", where verb logic must be used to resolve the paradox.
862:
Robert Earl Keen's song "The Road Goes On and On" alludes to the paradox. The song is widely believed to be written as part of Keen's feud with Toby Keith, who is presumably the "liar" Keen refers to.
506:
is credited with identifying this incompleteness in Tarski's hierarchy in his highly cited paper "Outline of a theory of truth," and it is recognized as a general problem in hierarchical languages.
129:
proposition, the conclusion is a contradiction. Since David himself is a man, it follows that he also is lying; but if he is lying because every man is a liar, his lying is of a different sort.
282:
Assume (D1) is false. Then (D2) is false. This would mean that (D1) is true. Thus (D1) is both true and false. Either way, (D1) is both true and false â the same paradox as (A) above.
610:
and other logicians, including J. C. Beall and
Bradley Armour-Garb, have proposed that the liar sentence should be considered to be both true and false, a point of view known as
189:
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.
301:
Assume (E1) is false. Then (E2) is true, which means (E3) is false, and hence (E1) is true. Either way, (E1) is both true and false â the same paradox as with (A) and (D1).
927:
399:
477:
445:
1535:
622:
propositions are true. Since trivialism is an intuitively false view, dialetheists nearly always reject the explosion principle. Logics that reject it are called
595:, that the "denial liar" can be true without contradiction while the "negation liar" can be false without contradiction. Their 1987 book makes heavy use of
779:
The liar paradox is occasionally used in fiction to shut down artificial intelligences, who are presented as being unable to process the sentence. In the
692:
If some statement, B, is assumed to be false, one writes, "B = false". The statement (C) that the statement B is false would be written as "C = 'B = false
1834:
304:
There are many other variants, and many complements, possible. In normal sentence construction, the simplest version of the complement is the sentence:
67:
If "this sentence is false" is true, then it is false, but the sentence states that it is false, and if it is false, then it must be true, and so on.
145:
141:
1982:
1579:
John
Buridan on Self-Reference : Chapter Eight of Buridan's Sophismata, with a Translation, and Introduction, and a Philosophical Commentary
618:, which asserts that any proposition can be deduced from a contradiction, unless the dialetheist is willing to accept trivialism â the view that
355:
1510:
1288:
1213:. Seventy-Second Annual Meeting American Philosophical Association, Eastern Division. Vol. 72. Journal of Philosophy. pp. 690â716.
727:
2422:
1250:
237:
has, that the statement is both true and false. Nevertheless, even Priest's analysis is susceptible to the following version of the liar:
1179:
2432:
1725:
1695:
1676:
1404:
2043:
754:
2012:
1849:
1655:
1586:
1390:
1318:
1774:
549:
argued that whether a sentence is paradoxical or not can depend upon contingent facts. If the only thing Smith says about Jones is
1035:
2268:
172:. Sentences can be constructed that cannot consistently be assigned a truth value even though they are completely in accord with
208:
The proposal that the statement is neither true nor false has given rise to the following, strengthened version of the paradox:
859:" alluded to the paradox when the narrator ends the song by stating "I'll lie again and again and I'll keep lying, I promise".
923:
781:
144:
for at least five centuries, starting from late 9th century, and apparently without being influenced by any other tradition.
109:, who lived in the 4th century BC. Eubulides reportedly asked, "A man says that he is lying. Is what he says true or false?"
79:(c. 600 BC) has been suggested as an example of the liar paradox, but they are not logically equivalent. The semi-mythical
2261:
734:
which state inherent limitations of sufficiently powerful axiomatic systems for mathematics. The theorems were proven by
2085:
1545:
739:
298:
Assume (E1) is true. Then (E2) is false, which means (E3) is true, and hence (E1) is false, leading to a contradiction.
1915:
871:
494:
However, this system is incomplete. One would like to be able to make statements such as "For every statement in level
596:
702:
This is an equation from which the truth value of A = "this statement is false" could hopefully be obtained. In the
279:
Assume (D1) is true. Then (D2) is true. This would mean that (D1) is false. Therefore, (D1) is both true and false.
2037:
1977:
1036:"The Early Arabic Liar:The Liar Paradox in the Islamic World from the Mid-Ninth to the Mid-Thirteenth Centuries CE"
886:
202:
2105:
1920:
2080:
757:, was discovered independently by Gödel (when he was working on the proof of the incompleteness theorem) and by
2200:
856:
1013:
363:
2328:
2288:
2165:
1962:
1880:
1784:
1779:
1718:
1502:
665:
456:
418:
2205:
2095:
615:
518:
198:
571:
soft on crime, then both Smith's remark about Jones and Jones's last remark about Smith are paradoxical.
2246:
2190:
2075:
1910:
1804:
1008:[Paradox and Perspectivism in Bhartrhari's Language Philosophy: Language, Thought and Reality].
845:
2363:
2348:
2323:
2318:
2170:
270:
There are also multi-sentence versions of the liar paradox. The following is the two-sentence version:
1275:. Logic, Epistemology, and the Unity of Science. Vol. 36. Dordrecht: Springer. pp. 211â243.
334:, the truth value of a statement can be any real number between 0 and 1 both inclusive, as opposed to
2368:
2353:
2343:
2308:
2256:
2185:
2100:
1972:
1967:
1890:
1885:
1814:
1006:"Paradoxe et perspectivisme dans la philosophie de langage de Bhartrhari: langage, pensée et réalité"
106:
517:
asserts that there is nothing paradoxical about the liar paradox. His claim (which he attributes to
2130:
2090:
2054:
1987:
1854:
1824:
1819:
1789:
1754:
1749:
636:
592:
910:
2401:
2358:
2338:
2278:
2251:
2049:
2002:
1992:
1905:
1769:
1711:
1623:
1479:
1429:
1351:
1222:
1145:
1137:
1102:
983:
975:
881:
731:
76:
2303:
1950:
1945:
1935:
1900:
1809:
1246:
768:
746:
1075:
Zach Weber, Guillermo Badia and
Patrick Girard (2015). "What is an Inconsistent Truth Table?".
591:
means, "This statement is not true", then it is negating itself. They go on to argue, based on
2391:
2373:
2313:
2293:
2283:
2210:
2195:
2115:
2110:
1940:
1895:
1764:
1651:
1644:
1582:
1506:
1396:
1386:
1314:
1309:
1284:
1164:
823:
822:
attempts to use the "this sentence is false" paradox to kill another artificial intelligence,
738:
in 1931, and are important in the philosophy of mathematics. Roughly speaking, in proving the
149:
113:
2333:
2298:
2273:
2225:
2150:
2125:
2120:
2032:
2022:
1997:
1615:
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1380:
1343:
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1214:
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1092:
1084:
967:
686:
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2215:
2175:
2017:
2007:
1844:
1839:
1829:
1794:
1690:
1520:
1376:
1304:
805:
664:) â arises, in case of the liar and other paradoxes such as the unsignifiability paradox (
587:
2427:
2180:
2155:
2145:
2140:
2070:
1870:
1759:
1042:
891:
703:
624:
405:
264:
260:
1120:
HĂĄjek, P.; Paris, J.; Shepherdson, J. (Mar 2000). "The Liar
Paradox and Fuzzy Logic".
958:
Jan E.M. Houben (1995). "Bhartrhari's solution to the Liar and some other paradoxes".
767:
has since sketched an alternative proof of the first incompleteness theorem that uses
2416:
2160:
2027:
1875:
1603:
1540:
1355:
1165:"Computation of fuzzy truth values for the liar and related self-referential systems"
1106:
987:
764:
758:
735:
607:
487:
335:
234:
169:
102:
61:
1497:
Crossley, J.N.; Ash, C.J.; Brickhill, C.J.; Stillwell, J.C.; Williams, N.H. (1972).
1483:
286:
three-sentence version, with each statement asserting the falsity of its successor:
1957:
1930:
1686:
1627:
1149:
852:
790:
707:
522:
514:
160:
The problem of the liar paradox is that it seems to show that common beliefs about
1088:
1280:
1271:
Glanzberg, Michael (2015-06-17). "Complexity and
Hierarchy in Truth Predicates".
2135:
1634:
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1206:
876:
611:
583:
546:
503:
409:
331:
57:
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to confuse and ultimately disable an android holding them captive. In the 1973
696:". Now, the liar paradox can be expressed as the statement A, that A is false:
1347:
799:
794:
649:
134:
83:
80:
31:
672:) and its extension in time, by accepting a simultaneous, opposite function (
341:
Let the truth value of the statement "This statement is false" be denoted by
1428:
ed. by Eli Franco and Karin
Preisendanz, Amsterdam â Atlanta: Rodopi, 1997;
165:
121:
17:
839:
The next thing I say to you will be true / The last thing I said was false.
814:
771:
rather than the liar paradox to construct a true but unprovable formula.
177:
105:. One version of the liar paradox is attributed to the Greek philosopher
979:
1735:
1619:
1599:. MIT Press. Especially chapter 9. ISBN 0262611082, ISBN 978-0262611084
1226:
1141:
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52:
1240:
1238:
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1474:
1457:
819:
87:
1703:
1218:
1133:
1570:
Greenough, P. M. (2001). " Free
Assumptions and the Liar Paradox,"
1444:
The Logic of Reflection. German Philosophy in the Twentieth Century
1005:
148:
could have been the first logician to identify the liar paradox as
1671:
267:), the dialetheic approach can overcome this version of the Liar.
259:, it is a paradox. However, it has been argued that by adopting a
222:. Since this is what (B) itself states, it means that (B) must be
161:
125:
35:
1799:
1400:
830:
1707:
710:
claims that the equation should be "A = 'A = false and A = true
575:
statements are ungrounded, and therefore have no truth value.
1247:"Liar Paradox: Section 4.3.1 Tarski's hierarchy of languages"
745:
To prove the first incompleteness theorem, Gödel represented
1589:. Buridan's detailed solution to a number of such paradoxes.
1245:
Beall, Jc; Glanzberg, Michael; Ripley, David (2016-12-12) .
1334:
Mills, Eugene (1998). "A simple solution to the Liar".
247:
and false, then (C) is only false. But then, it is not
233:
Another reaction to the paradox of (A) is to posit, as
1424:
Jan E. M. Houben, "Bhartrhari's Perspectivism (1)" in
1385:. New York: Oxford University Press. pp. 6, 188.
1658:. A collection of logic puzzles exploring this theme.
1458:"Computational verb systems: The paradox of the liar"
1446:. New Haven and London: Yale University Press. p. 43.
689:
it is possible to give the condition by an equation.
459:
421:
366:
183:
The simplest version of the paradox is the sentence:
1057:
1055:
555:
and Jones says only these three things about Smith:
2234:
2063:
1863:
1742:
1572:
American Philosophical Quarterly 38/2, pp. 115-135.
1313:. MIT Press. section 9.6 "A. N. Prior's Solution".
1172:
Journal of Multiple-Valued Logic and Soft Computing
534:
This statement is true and this statement is false.
404:by generalizing the NOT operator to the equivalent
528:Thus the following two statements are equivalent:
471:
439:
393:
349:
1536:"Fightin' Words: Robert Earl Keen v. Toby Keith"
1163:Kehagias, Athanasios; Vezerides, K. (Aug 2006).
909:Epimenides paradox has "All Cretans are liars."
668:), when abstraction is made from this function (
552:A majority of what Jones says about me is false.
498:of the hierarchy, there is a statement at level
118:
1367:
1365:
1201:
1199:
1719:
8:
1462:International Journal of Intelligent Systems
722:
1382:The Liar: An Essay on Truth and Circularity
1061:Andrew Irvine, "Gaps, Gluts, and Paradox",
2387:
1726:
1712:
1704:
1606:(1984). "The Logic of Paradox Revisited".
1310:Theories of Truth: A Critical Introduction
999:
997:
1473:
1096:
458:
420:
365:
230:and is now true, another paradox arises.
1065:, supplementary vol. 18 (1992), 273â299
1034:Ahmed Alwishah and David Sanson (2009).
567:If Smith really is a big spender but is
122:I said in my alarm, Every man is a liar!
902:
564:Everything Smith says about me is true.
142:liar paradox in early Islamic tradition
1433:Paris â La Haye: Mouton, 1964, p. 263)
317:The preceding statement is false. (G2)
314:The following statement is false. (G1)
276:The preceding statement is false. (D2)
273:The following statement is true. (D1)
7:
723:Gödel's first incompleteness theorem
263:relational semantics (as opposed to
1696:Stanford Encyclopedia of Philosophy
1677:Internet Encyclopedia of Philosophy
2044:What the Tortoise Said to Achilles
1077:Australasian Journal of Philosophy
648:The Indian grammarian-philosopher
133:The Indian grammarian-philosopher
112:The paradox was once discussed by
25:
1534:Cohen, Jason (January 25, 2012).
240:This statement is only false. (C)
97:The paradox's name translates as
2397:
2396:
2386:
1685:Beall, J C; Glanzberg, Michael.
1273:Unifying the Philosophy of Truth
730:are two fundamental theorems of
1407:from the original on 2020-04-22
1253:from the original on 2021-01-12
1185:from the original on 2021-07-08
1016:from the original on 2022-05-15
930:from the original on 2012-11-11
789:", the liar paradox is used by
755:Tarski's undefinability theorem
728:Gödel's incompleteness theorems
579:Jon Barwise and John Etchemendy
218:nor false, then it must be not
211:This statement is not true. (B)
186:A: This statement (A) is false.
1649:What Is the Name of This Book?
1608:Journal of Philosophical Logic
1063:Canadian Journal of Philosophy
926:. About.com (New York Times).
782:Star Trek: The Original Series
388:
382:
226:. Since initially (B) was not
1:
1122:The Journal of Symbolic Logic
1089:10.1080/00048402.2015.1093010
643:
1281:10.1007/978-94-017-9673-6_10
1211:Outline of a theory of truth
960:Journal of Indian Philosophy
740:first incompleteness theorem
676:) undoing the previous one.
140:There was discussion of the
2423:Communication of falsehoods
1499:What is mathematical logic?
1041:. p. 1. Archived from
1012:(in French) (19): 173â199.
1010:Bulletin d'Ătudes Indiennes
597:non-well-founded set theory
450:from which it follows that
307:This statement is true. (F)
201:, a concept related to the
2449:
2433:Self-referential paradoxes
1639:Papers in Logic and Ethics
1501:. London-Oxford-New York:
887:Performative contradiction
843:In the seventh episode of
818:, artificial intelligence
644:Bhartrhari's perspectivism
251:. Since initially (C) was
203:law of the excluded middle
2382:
1581:, Cambridge Univ. Press,
1004:Jan E.M. Houben (2001).
924:"Paradoxes of Eubulides"
531:This statement is false.
412:, the statement becomes
394:{\displaystyle x=NOT(x)}
357:. The statement becomes
156:Explanation and variants
1963:Paradoxes of set theory
1503:Oxford University Press
1442:Roberts, Julian. 1992.
1348:10.1023/a:1004232928938
872:HilbertâBernays paradox
812:In the 2011 video game
660:) or infinite regress (
561:Smith is soft on crime.
558:Smith is a big spender.
1577:Hughes, G. E. (1992).
837:, includes the lyrics
616:principle of explosion
519:Charles Sanders Peirce
473:
441:
395:
351:
199:principle of bivalence
131:
101:(ÏΔÏ
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1456:Yang, T. (Sep 2001).
1336:Philosophical Studies
846:Minecraft: Story Mode
747:statements by numbers
654:sarvam mithyÄ bravÄ«mi
474:
472:{\displaystyle x=0.5}
442:
440:{\displaystyle x=1-x}
396:
352:
27:Paradoxical assertion
2329:Kavka's toxin puzzle
2101:Income and fertility
666:Bhartrhari's paradox
457:
419:
364:
345:
321:Possible resolutions
265:functional semantics
146:NaáčŁÄ«r al-DÄ«n al-áčŹĆ«sÄ«
107:Eubulides of Miletus
48:antinomy of the liar
1988:Temperature paradox
1911:Free choice paradox
1775:Fitch's knowability
1048:on August 16, 2011.
593:situation semantics
168:actually lead to a
2364:Prisoner's dilemma
2050:Heat death paradox
2038:Unexpected hanging
2003:Chicken or the egg
1620:10.1007/bf00453020
1505:. pp. 52â53.
1430:Madeleine Biardeau
1426:Beyond Orientalism
972:10.1007/bf01880219
882:Knights and Knaves
775:In popular culture
732:mathematical logic
469:
437:
391:
214:If (B) is neither
77:Epimenides paradox
2410:
2409:
2081:Arrow information
1670:Dowden, Bradley.
1645:Smullyan, Raymond
1597:Theories of Truth
1512:978-0-19-888087-5
1290:978-94-017-9672-9
922:Andrea Borghini.
680:Logical structure
295:E1 is false. (E3)
292:E3 is false. (E2)
289:E2 is false. (E1)
114:Jerome of Stridon
99:pseudĂłmenos lĂłgos
16:(Redirected from
2440:
2400:
2399:
2390:
2389:
2201:Service recovery
2055:Olbers's paradox
1755:Buridan's bridge
1728:
1721:
1714:
1705:
1700:
1691:Zalta, Edward N.
1681:
1631:
1593:Kirkham, Richard
1558:
1557:
1555:
1553:
1544:. Archived from
1531:
1525:
1524:
1494:
1488:
1487:
1477:
1475:10.1002/int.1049
1468:(9): 1053â1067.
1453:
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1416:
1415:
1413:
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1369:
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1359:
1342:(2/3): 197â212.
1331:
1325:
1324:
1305:Kirkham, Richard
1301:
1295:
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1259:
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1178:(5â6): 539â559.
1169:
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687:self-referential
478:
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150:self-referential
38:, the classical
21:
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2441:
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2413:
2412:
2411:
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2378:
2289:Decision-making
2235:Decision theory
2230:
2059:
1983:Hilbert's Hotel
1916:GrellingâNelson
1859:
1738:
1732:
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1377:John Etchemendy
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868:
806:The Green Death
777:
769:Berry's paradox
725:
720:
711:
700:
699:A = "A = false"
693:
682:
646:
634:
632:Non-cognitivism
605:
588:John Etchemendy
581:
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255:and is now not
243:If (C) is both
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2206:St. Petersburg
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1835:Rule-following
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1817:
1812:
1807:
1802:
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1760:Dream argument
1757:
1752:
1746:
1744:
1740:
1739:
1733:
1731:
1730:
1723:
1716:
1708:
1702:
1701:
1687:"Liar Paradox"
1682:
1672:"Liar Paradox"
1665:
1664:External links
1662:
1660:
1659:
1642:
1632:
1614:(2): 153â179.
1604:Priest, Graham
1600:
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1319:
1296:
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1263:
1232:
1209:(1975-11-06).
1195:
1155:
1128:(1): 339â346.
1112:
1067:
1051:
1026:
993:
966:(4): 381â401.
950:
940:
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901:
899:
896:
895:
894:
892:Self-reference
889:
884:
879:
874:
867:
864:
855:'s 1994 song "
776:
773:
724:
721:
719:
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704:Boolean domain
698:
681:
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633:
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625:paraconsistent
604:
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406:Zadeh operator
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44:liar's paradox
26:
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2334:Morton's fork
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2247:Apportionment
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2112:
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2106:DownsâThomson
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2031:
2029:
2026:
2024:
2023:Plato's beard
2021:
2019:
2016:
2014:
2011:
2009:
2006:
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1994:
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1921:KleeneâRosser
1919:
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1845:Theseus' ship
1843:
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1833:
1831:
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1805:Mere addition
1803:
1801:
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1745:
1743:Philosophical
1741:
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1656:0-671-62832-1
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1587:0-521-28864-9
1584:
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1573:
1569:
1568:
1563:
1548:on 2015-10-03
1547:
1543:
1542:
1541:Texas Monthly
1537:
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1320:0-262-61108-2
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765:George Boolos
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760:
759:Alfred Tarski
756:
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743:
741:
737:
733:
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637:Andrew Irvine
631:
629:
627:
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617:
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609:
608:Graham Priest
602:
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594:
589:
585:
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576:
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505:
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492:
489:
488:Alfred Tarski
483:Alfred Tarski
482:
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411:
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336:Boolean logic
333:
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305:
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235:Graham Priest
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209:
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184:
181:
179:
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170:contradiction
167:
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155:
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151:
147:
143:
138:
136:
130:
127:
123:
117:
116:in a sermon:
115:
110:
108:
104:
103:Ancient Greek
100:
95:
93:
89:
85:
82:
78:
70:
68:
65:
63:
62:contradiction
59:
54:
49:
45:
41:
37:
33:
19:
2354:Preparedness
2186:Productivity
2166:Mandeville's
1958:Opposite Day
1925:
1886:Burali-Forti
1881:Bhartrhari's
1694:
1675:
1648:
1641:. Duckworth.
1638:
1611:
1607:
1596:
1578:
1571:
1550:. Retrieved
1546:the original
1539:
1529:
1498:
1492:
1465:
1461:
1451:
1443:
1438:
1425:
1420:
1409:. Retrieved
1381:
1339:
1335:
1329:
1308:
1299:
1272:
1266:
1255:. Retrieved
1210:
1207:Kripke, Saul
1187:. Retrieved
1175:
1171:
1158:
1125:
1121:
1115:
1080:
1076:
1070:
1062:
1043:the original
1029:
1018:. Retrieved
1009:
963:
959:
953:
943:
932:. Retrieved
917:
905:
861:
853:Rollins Band
851:
844:
842:
838:
834:
828:
813:
811:
804:
798:
791:Captain Kirk
780:
778:
763:
751:
744:
726:
718:Applications
708:Arthur Prior
701:
691:
683:
673:
669:
661:
657:
653:
647:
635:
623:
619:
606:
582:
573:
568:
566:
554:
545:
536:
527:
523:John Buridan
515:Arthur Prior
513:
510:Arthur Prior
499:
495:
493:
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195:
191:
188:
182:
159:
139:
132:
119:
111:
98:
96:
91:
74:
66:
47:
43:
40:liar paradox
39:
29:
18:Liar Paradox
2284:Condorcet's
2136:Giffen good
2096:Competition
1850:White horse
1825:Omnipotence
1635:A. N. Prior
1373:Jon Barwise
877:Insolubilia
835:Enough Said
612:dialetheism
603:Dialetheism
584:Jon Barwise
547:Saul Kripke
542:Saul Kripke
504:Saul Kripke
410:fuzzy logic
332:fuzzy logic
326:Fuzzy logic
60:leads to a
58:truth value
2417:Categories
2359:Prevention
2349:Parrondo's
2339:Navigation
2324:Inventor's
2319:Hedgehog's
2279:Chainstore
2262:Population
2257:New states
2191:Prosperity
2171:Mayfield's
2013:Entailment
1993:Barbershop
1906:Epimenides
1564:References
1521:0251.02001
1411:2016-02-22
1257:2021-01-16
1189:2021-02-17
1098:2292/30988
1020:2018-08-04
934:2012-09-04
911:Titus 1:12
800:Doctor Who
795:Harry Mudd
736:Kurt Gödel
650:Bhartrhari
261:two-valued
135:Bhartrhari
84:Epimenides
32:philosophy
2374:Willpower
2369:Tolerance
2344:Newcomb's
2309:Fredkin's
2196:Scitovsky
2116:Edgeworth
2111:Easterlin
2076:Antitrust
1973:Russell's
1968:Richard's
1941:Pinocchio
1896:Crocodile
1815:Newcomb's
1785:Goodman's
1780:Free will
1765:Epicurean
1736:paradoxes
1356:169981769
1107:170137819
988:170337976
785:episode "
662:anavasthÄ
432:−
2402:Category
2299:Ellsberg
2151:Leontief
2131:Gibson's
2126:European
2121:Ellsberg
2091:Braess's
2086:Bertrand
2064:Economic
1998:Catch-22
1978:Socratic
1820:Nihilism
1790:Hedonism
1750:Analysis
1734:Notable
1647:(1986).
1637:(1976).
1595:(1992).
1552:July 12,
1484:41448750
1405:Archived
1401:86031260
1379:(1989).
1307:(1992).
1251:Archived
1180:Archived
1083:(3): 7.
1014:Archived
980:23447805
928:Archived
866:See also
824:Wheatley
815:Portal 2
178:semantic
2304:Fenno's
2269:Arrow's
2252:Alabama
2242:Abilene
2221:Tullock
2176:Metzler
2018:Lottery
2008:Drinker
1951:Yablo's
1946:Quine's
1901:Curry's
1864:Logical
1840:Sorites
1830:Preface
1810:Moore's
1795:Liberal
1770:Fiction
1693:(ed.).
1628:2442524
1227:2024634
1150:6865763
1142:2586541
803:serial
787:I, Mudd
670:vyÄpÄra
658:virodha
180:rules.
174:grammar
166:falsity
94:lies).
71:History
53:paradox
2211:Thrift
2181:Plenty
2156:Lerner
2146:Jevons
2141:Icarus
2071:Allais
2033:Ross's
1871:Barber
1855:Zeno's
1800:Meno's
1654:
1626:
1585:
1519:
1509:
1482:
1399:
1389:
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1317:
1287:
1225:
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833:song,
820:GLaDOS
88:Cretan
2428:Lying
2314:Green
2294:Downs
2226:Value
2161:Lucas
2028:Raven
1936:No-no
1891:Court
1876:Berry
1689:. In
1624:S2CID
1480:S2CID
1352:S2CID
1223:JSTOR
1183:(PDF)
1168:(PDF)
1146:S2CID
1138:JSTOR
1103:S2CID
1046:(PDF)
1039:(PDF)
984:S2CID
976:JSTOR
898:Notes
408:from
162:truth
126:David
124:" Is
36:logic
2392:List
2216:Toil
1931:Card
1926:Liar
1652:ISBN
1583:ISBN
1554:2021
1507:ISBN
1397:LCCN
1387:ISBN
1315:ISBN
1285:ISBN
857:Liar
831:Devo
829:The
793:and
586:and
521:and
257:true
253:true
249:true
245:true
228:true
224:true
220:true
216:true
176:and
164:and
92:only
86:, a
81:seer
75:The
34:and
1616:doi
1517:Zbl
1470:doi
1344:doi
1277:doi
1215:doi
1130:doi
1093:hdl
1085:doi
968:doi
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620:all
569:not
467:0.5
330:In
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