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for logics that demand relevant relationships between premise and consequent, unlike classical logic assumed here). The formal statement of the theorem is timeless, eliminating the second objection because the person the statement holds true for at one instant is not necessarily the same person it
324:
So as it was applied here, the statement "if they are drinking, everyone is drinking" was taken to be correct in one case, if everyone was drinking, and in the other case, if they were not drinkingâeven though their drinking may not have had anything to do with anyone else's drinking.
337:"there is a woman on earth such that if she becomes sterile, the whole human race will die out." Smullyan writes that this formulation emerged from a conversation he had with philosopher John Bacon.
650:. In Proceedings of the 14th International Conference on Theorem Proving in Higher Order Logics (TPHOLs '01), Richard J. Boulton and Paul B. Jackson (Eds.). Springer-Verlag, London, UK, 378-394.
333:
Smullyan in his 1978 book attributes the naming of "The
Drinking Principle" to his graduate students. He also discusses variants (obtained by replacing D with other, more dramatic predicates):
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The proof begins by recognizing it is true that either everyone in the pub is drinking, or at least one person in the pub is not drinking. Consequently, there are two cases to consider:
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for the validity of the theorem. And if someone does not drink, then that particular non-drinking individual can be the witness to the theorem's validity.
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348:'s "The quest for correctness" (1996), accompanied by some machine proofs. Since then it has made regular appearance as an example in publications about
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that can be stated as "There is someone in the pub such that, if he or she is drinking, then everyone in the pub is drinking." It was popularised by the
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If and only if there is someone in the pub, there is someone in the pub such that, if they are drinking, then everyone in the pub is drinking
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in formal logic, which states that "If P, then Q" is always true if P is false. (These kinds of statements are said to be
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the others to drink, or that there could be a person such that all through the night that one person were always the
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A slightly more formal way of expressing the above is to say that, if everybody drinks, then anyone can be the
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A "dual" version of the
Principle: "there is at least one person such that if anybody drinks, then he does."
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What is important to the paradox is that the conditional in classical (and intuitionistic) logic is the
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In the setting with empty domains allowed, the drinker paradox must be formulated as follows:
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662:"Searchable Sets, Dubuc-Penon Compactness, Omniscience Principles, and the Drinker Paradox"
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Otherwise at least one person is not drinking. For any nondrinking person, the statement
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Suppose everyone is drinking. For any particular person, it cannot be wrong to say that
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545:. chapter 14. How to Prove Anything. (topic) 250. The Drinking Principle. pp. 209-211.
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The paradox is ultimately based on the principle of formal logic that the statement
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As "Smullyan's âDrinkersâ principle" or just "Drinkers' principle" it appears in
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is true whenever A is false, i.e., any statement follows from a false statement (
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537:
What is the Name of this Book? The Riddle of
Dracula and Other Logical Puzzles
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if that particular person is drinking, then everyone in the pub is drinking
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if that particular person is drinking, then everyone in the pub is drinking
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67:. It seems counterintuitive both that there could be a person who is
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63:
nature of the statement comes from the way it is usually stated in
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53:, who called it the "drinking principle" in his 1978 book
352:; it is sometimes used to contrast the expressiveness of
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H.P. Barendregt (1996). "The quest for correctness".
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75:to drink. The first objection comes from confusing
582:. Stichting Mathematisch Centrum. pp. 54â55.
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321:, this is also a sufficient condition).
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209:drinks, everybody includes that person.
91:The formal statement of the theorem is
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317:is false (in classical logic, but not
88:holds true for at any other instant.
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185:and P is an arbitrary nonempty set.
81:Correlation does not imply causation
450:{\displaystyle \exists x\in P.\ \,}
1036:What the Tortoise Said to Achilles
667:. Computability in Europe 2010: 2.
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171:{\displaystyle \exists x\in P,.\,}
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460:if and only if it is non-empty.
79:statements with causation (see
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302:{\displaystyle A\rightarrow B}
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263:{\displaystyle A\rightarrow B}
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55:What Is the Name of this Book?
1:
660:MartĂn EscardĂł; Paulo Oliva.
240:Explanation of paradoxicality
576:Images of SMC Research 1996
283:. It has the property that
1436:
623:Sets, Logic and Categories
1374:
648:Mizar Light for HOL Light
486:Reification (linguistics)
626:. Springer. p. 91.
181:where D is an arbitrary
16:Apparent logical paradox
955:Paradoxes of set theory
680:Cite journal requires
451:
329:History and variations
303:
264:
216:is formally true: its
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646:Freek Wiedijk. 2001.
452:
304:
265:
173:
48:mathematical logician
1321:Kavka's toxin puzzle
1093:Income and fertility
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319:intuitionistic logic
287:
281:material conditional
248:
222:material implication
98:
980:Temperature paradox
903:Free choice paradox
767:Fitch's knowability
350:automated reasoning
29:drinker's principle
23:(also known as the
1356:Prisoner's dilemma
1042:Heat death paradox
1030:Unexpected hanging
995:Chicken or the egg
447:
367:A set P satisfies
299:
273:ex falso quodlibet
260:
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33:drinking principle
1420:Logical paradoxes
1402:
1401:
1073:Arrow information
633:978-1-85233-056-9
589:978-90-6196-462-9
481:List of paradoxes
430:
394:
25:drinker's theorem
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1193:Service recovery
1047:Olbers's paradox
747:Buridan's bridge
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592:. Archived from
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531:Raymond Smullyan
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360:Non-empty domain
354:proof assistants
309:is true only if
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77:formal "if then"
65:natural language
51:Raymond Smullyan
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1227:Decision theory
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346:H.P. Barendregt
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96:
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85:Relevance logic
59:The apparently
44:predicate logic
21:drinker paradox
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599:on 2015-07-11
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543:Prentice Hall
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1178:Productivity
1158:Mandeville's
999:
950:Opposite Day
878:Burali-Forti
873:Bhartrhari's
673:cite journal
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601:. Retrieved
594:the original
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28:
24:
20:
18:
1276:Condorcet's
1128:Giffen good
1088:Competition
842:White horse
817:Omnipotence
203:that person
61:paradoxical
1409:Categories
1351:Prevention
1341:Parrondo's
1331:Navigation
1316:Inventor's
1311:Hedgehog's
1271:Chainstore
1254:Population
1249:New states
1183:Prosperity
1163:Mayfield's
1005:Entailment
985:Barbershop
898:Epimenides
603:2012-10-27
502:References
218:antecedent
1366:Willpower
1361:Tolerance
1336:Newcomb's
1301:Fredkin's
1188:Scitovsky
1108:Edgeworth
1103:Easterlin
1068:Antitrust
965:Russell's
960:Richard's
933:Pinocchio
888:Crocodile
807:Newcomb's
777:Goodman's
772:Free will
757:Epicurean
728:paradoxes
420:∈
414:∀
411:→
384:∈
378:∃
294:→
255:→
207:everybody
183:predicate
141:∈
135:∀
132:→
108:∈
102:∃
41:classical
31:, or the
1394:Category
1291:Ellsberg
1143:Leontief
1123:Gibson's
1118:European
1113:Ellsberg
1083:Braess's
1078:Bertrand
1056:Economic
990:Catch-22
970:Socratic
812:Nihilism
782:Hedonism
742:Analysis
726:Notable
620:(1999).
533:(1978).
475:See also
1296:Fenno's
1261:Arrow's
1244:Alabama
1234:Abilene
1213:Tullock
1168:Metzler
1010:Lottery
1000:Drinker
943:Yablo's
938:Quine's
893:Curry's
856:Logical
832:Sorites
822:Preface
802:Moore's
787:Liberal
762:Fiction
234:witness
205:drinks
69:causing
37:theorem
35:) is a
1203:Thrift
1173:Plenty
1148:Lerner
1138:Jevons
1133:Icarus
1063:Allais
1025:Ross's
863:Barber
847:Zeno's
792:Meno's
630:
586:
549:
429:
393:
189:Proofs
27:, the
1306:Green
1286:Downs
1218:Value
1153:Lucas
1020:Raven
928:No-no
883:Court
868:Berry
665:(PDF)
597:(PDF)
580:(PDF)
1384:List
1208:Toil
923:Card
918:Liar
686:help
628:ISBN
584:ISBN
547:ISBN
73:last
19:The
276:).
83:or
39:of
1411::
677::
675:}}
671:{{
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541:.
510:^
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426:.
423:P
417:y
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396:[
390:.
387:P
381:x
315:A
311:B
297:B
291:A
258:B
252:A
165:.
162:]
159:)
156:y
153:(
150:D
147:,
144:P
138:y
129:)
126:x
123:(
120:D
117:[
114:,
111:P
105:x
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