The End of an Era - That of The Natural Numbers
in [Math]
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From: MoeBlee on 14 Jun 2010 11:36 On Jun 14, 10:12 am, Aatu Koskensilta <aatu.koskensi...(a)uta.fi> wrote: > Marshall <marshall.spi...(a)gmail.com> writes: > > PS. The urge to intentionally misspell "Koskensilta" in this post was > > just barely suppressed. > > How would you misspell it? KoesKoenSeelta. MoeBlee
From: Marshall on 14 Jun 2010 12:13 On Jun 14, 8:07 am, stevendaryl3...(a)yahoo.com (Daryl McCullough) wrote: > > It's like the Necronomicon to me, a legendary tome that may or > may not actually exist. Maybe that's the real problem. Maybe Nam isn't reading from Shoenfield, but actually from an ancient, corrupted mathematical tome, the Necronamicon, and it is driving him insane. Marshall PS. This time I copied and pasted from Aatu's message.
From: Simplane Simple Plane Simulate Plain Simple on 14 Jun 2010 13:07 On Jun 14, 9:13 am, Marshall <marshall.spi...(a)gmail.com> wrote: > On Jun 14, 8:07 am, stevendaryl3...(a)yahoo.com (Daryl McCullough) > wrote: > {{About|a fictional book|other uses}} {{pp-semi-indef|small=yes|expiry=January 15, 2009}} [[Image:Necronomicon prop.jpg|thumb|right|225px|An artist's interpretation of the Necronomicon.]] The '''''Necronomicon''''' is a [[Fictional book|fictional]] [[grimoire]] appearing in the stories by [[horror fiction|horror]] novelist [[H. P. Lovecraft]] and his followers. It was first mentioned in Lovecraft's [[1924 in literature|1924]]<!--ORIG. PUB. WEIRD TALES FEB. 1924--> short story "[[The Hound]]",<ref>[http:// www.yankeeclassic.com/miskatonic/library/stacks/literature/lovecraft/stories/hound.htm "The Hound", by H. P. Lovecraft] Published February 1924 in "Weird Tales". YankeeClassic.com. Retrieved on January 31, 2009</ref> written in 1922, though its purported author, the "Mad [[Arab]]" [[Abdul Alhazred]], had been quoted a year earlier in Lovecraft's "[[The Nameless City]]".<ref>Though it has been argued that an unnamed copy of the ''Necronomicon'' appears in the 1919 story ''[[The Statement of Randolph Carter]]'', [[S. T. Joshi]] points out that the text in question was "written in characters whose like (narrator [[Randolph Carter]]) never saw elsewhere"--which would not describe any known edition of the ''Necronomicon'', including the one in Arabic, a language Carter was familiar with. S. T. Joshi, "Afterword", ''History of the Necronomicon'', Necronomicon Press.</ref> There was a possible reference to the book in "[[The Statement of Randolph Carter]]" (published in [[1920 in literature|1920]]) though it was not called by name.<ref>H.P. Lovecraft (2008) H.P. Lovecraft: The Fiction, Complete and Unabridged, p. 76-7.</ref> Among other things, the work contains an account of the [[Old One#H. P. Lovecraft|Old Ones]], their history, and the means for summoning them. Other authors such as [[August Derleth]] and [[Clark Ashton Smith]] also cited it in their works; Lovecraft approved, believing such common allusions built up "a background of evil [[verisimilitude]]." Many readers have believed it to be a real work, with booksellers and librarians receiving many requests for it; pranksters have listed it in rare book catalogues, and a student smuggled a card for it into the [[Yale University]] Library's [[card catalog]].<ref>[[L. Sprague de Camp]], ''[[Literary Swordsmen and Sorcerers]]'', p100-1 ISBN 0-87054-076-9</ref> Capitalizing on the notoriety of the fictional volume, real-life [[publisher]]s have printed many books entitled ''Necronomicon'' since Lovecraft's death. {{wikisource|History of the Necronomicon}} ==Origin== How Lovecraft conceived the name "Necronomicon" is not clear â Lovecraft said that the title came to him in a dream.<ref name="HPLA- letters">[http://www.hplovecraft.com/creation/necron/letters.asp Quotes Regarding the Necronomicon from Lovecraftâs Letters]</ref> Although some have suggested that Lovecraft was influenced primarily by [[Robert W. Chambers]]' collection of short stories ''[[The King in Yellow]]'', which centers on a mysterious and disturbing play in book form, Lovecraft is not believed to have read that work until 1927.<ref>Joshi & Schultz, "Chambers, Robert William", ''An H. P. Lovecraft Encyclopedia'', p. 38</ref> Donald R. Burleson has argued that the idea for the book was derived from [[Nathaniel Hawthorne]], though Lovecraft himself noted that "mouldy hidden manuscripts" were one of the stock features of [[Gothic literature]].<ref>Joshi, "Afterword".</ref> Lovecraft wrote<ref>H. P. Lovecraft - Selected Letters V, 418</ref> that the title, as translated from the [[Greek language]], meant "an image of the law of the dead": ''nekros'' - ''νεκÏÏÏ'' ("dead"), ''nomos'' - ''νÏμοÏ'' ("law"), ''eikon'' - ''εικÏν'' ("image").<ref>H. G. Liddell, Robert Scott - Abridged Greek-English Lexicon</ref> [[Robert M. Price]] notes that the title has been variously translated by others as "Book of the names of the dead", "Book of the laws of the dead", "Book of dead names" and "Knower of the laws of the dead". {{Citation needed|date=March 2010}} [[S. T. Joshi]] states that Lovecraft's own etymology is "almost entirely unsound. The last portion of it is particularly erroneous, since ''-ikon'' is nothing more than a neuter adjectival suffix and has nothing to do with ''eikõn'' (image)." Joshi translates the title as "Book considering (or classifying) the dead." <ref>Joshi, S.T. ''The Rise and Fall of the Cthulhu Mythos'' (Mythos Books, 2008) pp. 34-35.</ref> Lovecraft was often asked about the veracity of the ''Necronomicon'', and always answered that it was completely his invention. In a letter to [[Willis Conover]], Lovecraft elaborated upon his typical answer: <blockquote>Now about the ''âterrible and forbidden booksâ'' â I am forced to say that most of them are purely imaginary. There never was any Abdul Alhazred or ''Necronomicon'', for I invented these names myself. [[Robert Bloch]] devised the idea of Ludvig Prinn and his ''[[De Vermis Mysteriis]]'', while the ''[[Book of Eibon]]'' is an invention of [[Clark Ashton Smith]]'s. [[Robert E. Howard]] is responsible for Friedrich von Junzt and his ''[[Unaussprechlichen Kulten]]''.... As for seriously-written books on dark, occult, and supernatural themes â in all truth they donât amount to much. That is why itâs more fun to invent mythical works like the ''Necronomicon'' and ''Book of Eibon''.<ref name="HPLA-letters"/></blockquote> Reinforcing the book's fictionalization, the name of the book's supposed author, Abdul Alhazred, is not even a grammatically correct [[Arabic name]]. The name "Abdul" simply means "the worshiper/slave of...". Standing alone, it would make no sense, as Alhazred is not a last name in the Western sense, but a reference to a person's place of birth.<ref>Petersen, Sandy & Lynn Willis. ''Call of Cthulhu'', p. 189.</ref> ==Fictional history== In 1927, Lovecraft wrote a brief [[pseudo-history]] of the ''Necronomicon'' that was published in 1938, after his death, as ''A History of The Necronomicon''.<ref>[http://www.mythostomes.com/content/ view/12/72/ H. P. Lovecraft's ''History of the Necronomicon'']</ref> This work allowed subsequent fiction writers to remain consistent with Lovecraft's treatment of the ''Necronomicon''.<ref>[http:// www.mythostomes.com/content/view/99/72/ A Note About the Necronomicon]</ref> According to this account, the book was originally called ''Al Azif'', an Arabic word that Lovecraft defined as "that nocturnal sound (made by insects) supposed to be the howling of demons". (One Arabic/English dictionary translates ''`AzÄ«f'' as "whistling (of the wind); weird sound or noise".)<ref>''The Hans Wehr Dictionary of Modern Written Arabic'', ed. J.M. Cowan.</ref> In the ''History'', Alhazred is said to have been a "half-crazed [[Arab]]" who worshipped the Lovecraftian entities [[Yog-Sothoth]] and [[Cthulhu]]. He is described as being from [[Sana'a|Sanaa]] in [[Yemen]], and as visiting the ruins of [[Babylon]], the "subterranean secrets" of [[Memphis, Egypt|Memphis]] and the [[Empty Quarter]] of [[Arabia]] (where he discovered the "[[The Nameless City|nameless city]]" below [[Iram of the Pillars|Irem]]). In his last years, he lived in [[Damascus]], where he wrote ''Al Azif'' before his sudden and mysterious death in 738. In subsequent years, Lovecraft wrote, the ''Azif'' "gained considerable, though surreptitious circulation amongst the philosophers of the age." In 950, it was translated into [[Greek language|Greek]] and given the title ''Necronomicon'' by Theodorus Philetas, a fictional scholar from [[Constantinople]]. This version "impelled certain experimenters to terrible attempts" before being "suppressed and burnt" in 1050 by [[Michael I Cerularius|Patriarch Michael]] (an historical figure who died in 1059). After this attempted suppression, the work was "only heard of furtively" until it was translated from Greek into [[Latin]] by [[Ole Worm|Olaus Wormius]]. (Lovecraft gives the date of this edition as 1228, though the real-life Danish scholar Olaus Wormius lived from 1588 to 1624.) Both the Latin and Greek text, the ''History'' relates, were banned by [[Pope Gregory IX]] in 1232, though Latin editions were apparently published in 15th century [[Germany]] and 17th century [[Spain]]. A Greek edition was printed in [[Italy]] in the first half of the 16th century. The [[Elizabethan era|Elizabethan]] magician [[John Dee (mathematician)|John Dee]] (1527-c. 1609) allegedly translated the book — presumably into English — but Lovecraft wrote that this version was never printed and only fragments survive. (The connection between Dee and the ''Necronomicon'' was suggested by Lovecraft's friend [[Frank Belknap Long]].) According to Lovecraft, the Arabic version of ''Al Azif'' had already disappeared by the time the Greek version was banned in 1050, though he cites "a vague account of a secret copy appearing in [[San Francisco]] during the [[Twentieth century|current century]]" that "later perished in fire". The Greek version, he writes, has not been reported "since the burning of a certain [[Salem, Massachusetts| Salem]] man's library in 1692" (an apparent reference to the [[Salem witch trials]]). (In the story ''[[The Diary of Alonzo Typer]]'', the character Alonzo Typer finds a Greek copy.) ==Appearance and contents== The ''Necronomicon'' is mentioned in a number of Lovecraft's short stories and in his novellas ''[[At the Mountains of Madness]]'' and ''[[The Case of Charles Dexter Ward]]''. However, despite frequent references to the book, Lovecraft was very sparing of details about its appearance and contents. He once wrote that "if anyone were to try to write the ''Necronomicon'', it would disappoint all those who have shuddered at cryptic references to it."<ref>Letter to Jim Blish and William Miller, Jr., quoted in Joshi, "Afterword".</ref> In "The Nameless City" ([[1921 in literature|1921]]), a rhyming [[couplet]] that appears at two points in the story is ascribed to Abdul Alhazred: <blockquote>That is not dead which can eternal lie. <br/>And with strange aeons even death may die.</blockquote> The same couplet appears in "[[The Call of Cthulhu]]" ([[1928 in literature| 1928]]), where it is identified as a quotation from the ''Necronomicon''. This "much-discussed" couplet, as Lovecraft calls it in the latter story, has also been quoted in works by other authors, including [[Brian Lumley]]'s ''The Burrowers Beneath'', which adds a long paragraph preceding the couplet. The ''Necronomicon'' is undoubtedly a substantial text, as indicated by its description in ''[[The Dunwich Horror]]'' ([[1929 in literature| 1929]]). In the story, [[The_Dunwich_Horror#Wilbur_Whateley|Wilbur Whateley]] visits [[Miskatonic University]]'s library to consult the "unabridged" version of the ''Necronomicon'' for a spell that would have appeared on the ''751st'' page of his own inherited, but defective, Dee edition. The ''Necronomicon'''s appearance and physical dimensions are not clearly stated in Lovecraft's work. Other than the obvious black letter editions, it is commonly portrayed as bound in leather of various types and having metal clasps. Moreover, editions are sometimes disguised. In ''The Case of Charles Dexter Ward'', for example, John Merrit pulls down a book labelled ''Qanoon-e-Islam'' from [[Cthulhu Mythos biographies#Curwen, Joseph|Joseph Curwen]]âs bookshelf and discovers to his disquiet that it is actually the ''Necronomicon''. In the [[The Evil Dead (franchise)|Evil Dead]] series of movies, a [[Necronomicon Ex-Mortis|similar book]] is described as "Bound in human flesh and inked in blood, it contains bizarre burial rituals and demon resurrection passages. It was never meant for the world of the living." Many commercially available versions of the book fail to include any of the contents that Lovecraft describes. The [[Simon Necronomicon| Simon ''Necronomicon'']] in particular has been criticized for this.<ref>[http://www.mythostomes.com/content/view/16/69/ The Simon ''Necronomicon''], a review.</ref> ==Locations== According to Lovecraft's "History of the ''Necronomicon''", copies of the original ''Necronomicon'' were held by only five institutions worldwide: * The [[British Museum]] * The [[Bibliothèque nationale de France]] * [[Widener Library]] of [[Harvard University]] in [[Cambridge, Massachusetts]] * The [[Universidad de Buenos Aires|University of Buenos Aires]] * The library of the fictional [[Miskatonic University]] in the also fictitious [[Arkham]], [[Massachusetts]] The last institution holds the Latin translation by Olaus Wormius, printed in [[Spain]] in the 17th century. Other copies, Lovecraft wrote, were kept by private individuals. Joseph Curwen, as noted, had a copy in ''The Case of Charles Dexter Ward'' (1941). A version is held in [[Kingsport (Lovecraft)| Kingsport]] in "[[The Festival (short story)|The Festival]]" ([[1925 in literature|1925]]). The provenance of the copy read by the narrator of "[[Nameless City|The Nameless City]]" is unknown; a version is read by the protagonist in "The Hound" ([[1924 in literature|1924]]). ==Hoaxes and alleged translations== Although Lovecraft insisted that the book was pure invention (and other writers invented passages from the book in their own works), there are accounts of some people actually believing the ''Necronomicon'' to be a real book. Lovecraft himself sometimes received letters from fans inquiring about the ''Necronomicon''<nowiki>'</nowiki>s authenticity. [[Practical joke| Pranksters]] occasionally listed the ''Necronomicon'' for sale in book store newsletters or inserted phony entries for the book in [[Library catalog|library card catalogues]] (where it may be checked out to one '[[Abdul Alhazred|A. Alhazred]]', ostensibly the book's author and original owner). The Widener Library at Harvard, which is supposed to have a copy of the "Necronomicon" according to Lovecraft's stories, has a catalog entry telling the seeker to "inquire at desk". While the stories surrounding the ''Necronomicon'' claim that it is an extremely powerful and dangerous book (one that would not be safe just sitting on a shelf, where anyone could read it), it is equally possible that the listing has a much more mundane purpose â several (equally fictional) versions of the book do exist, and (since books such as the ''Necronomicon'' are frequently stolen from the shelves) the entry may simply be an attempt to prevent theft. Similarly, the [[University of Tromsø|university library of Tromsø]], Norway, lists a translated version of the Necronomicon, attributed to Petrus de Dacia and published in 1994, although the document is listed as "unavailable".<ref>[http://ask.bibsys.no/ask/action/show? pid=970451504&kid=biblio Necronomicon.]</ref> In 1973, Owlswick Press issued an edition of the ''Necronomicon'' written in an indecipherable, apparently fictional language known as "Duriac".<ref>[http://www.mythostomes.com/content/view/14/69/ ''Al Azif: The Necronomicon'', a Review (Owlswick/Wildside Edition)]</ref> This was a limited edition of 348. The book contains a brief introduction by [[L. Sprague de Camp]]. The line between fact and fiction was further blurred in the late 1970s when a book purporting to be a translation of the "real Necronomicon" was published. This book, by the pseudonymic "Simon," had little connection to the fictional [[Lovecraft Mythos]] but instead was based on [[Mesopotamian mythology|Sumerian mythology]]. It was later dubbed the "[[Simon Necronomicon]]". Going into trade paperback in 1980 it has never been out of print and has sold 800,000 copies by 2006 making it the most popular Necronomicon to date. {{Citation needed|date=July 2008}} Despite its contents, the book's marketing focused heavily on the Lovecraft connection and made sensational claims made for the book's magical power. The blurb states it was "potentially, the most dangerous Black Book known to the Western World". Three additional volumes have since been published — ''The Necronomicon Spellbook'', a book of [[pathworking]]s with the 50 names of [[Marduk]]; ''Dead Names: The Dark History of the Necronomicon'', a history of the book itself and of the late 1970s New York occult scene; and ''The Gates Of The Necronomicon'', instructions on pathworking with the Simon Necronomicon. A hoax version of the ''Necronomicon'', edited by [[George Hay (writer)|George Hay]], appeared in [[1978 in literature|1978]] and included an introduction by the paranormal researcher and writer [[Colin Wilson]]. [[David Langford]] described how the book was prepared from a computer analysis of a discovered "cipher text" by [[John Dee (mathematician)|Dr. John Dee]]. The resulting "translation" was in fact written by [[occult]]ist [[Robert Turner]], but it was far truer to the Lovecraftian version than the Simon text and even incorporated quotations from Lovecraft's stories in its passages. Wilson also wrote a story, "The Return of the Lloigor", in which the [[Voynich manuscript]] turns out to be a copy of the ''Necronomicon''. With the success of the Simon Necronomicon the controversy surrounding the actual existence of the Necronomicon was such that a detailed book, ''[[The Necronomicon Files]]'', was published in 1998 attempting to prove once and for all the book was pure fiction. It covered the well-known Necronomicons in depth, especially the Simon one, along with a number of more obscure ones. It was reprinted and expanded in 2003.<ref>Dan and John Wisdom Gonce III. 2003. ''The Necronomicon Files''. Boston: Red Wheel Weiser.</ref> In 2004, ''Necronomicon: The Wanderings of Alhazred'', by occultist [[Donald Tyson]], was published by [[Llewellyn Worldwide]]. The Tyson Necronomicon is generally thought to be closer to Lovecraft's vision than other published versions. Donald Tyson has clearly stated that the ''Necronomicon'' is fictional, but that has not prevented his book from being the center of some controversy.<ref>[http:// www.mythostomes.com/content/view/97/72/ Keys to Power beyond Reckoning: Mysteries of the Tyson ''Necronomicon'']</ref> Tyson has since published ''[[Alhazred (novel)|Alhazred]]'', a novelization of the life of the ''Necronomicon'''s author. Historical "Books of the Dead", such as the [[ancient Egypt]]ian ''[[Book of the Dead]]'' or the [[Tibet]]an ''[[Bardo Thodol]]'', are sometimes described as "real Necronomicons." They should not be confused with the Lovecraft ''Necronomicon'', since their contents are meant to be read to and remembered by the dead, rather than to be used by the living to summon the dead. Lovecraft may have been inspired by these books. ==The Astral Necronomicon== [[Kenneth Grant]], the British occultist, disciple of [[Aleister Crowley]], and head of the [[Typhonian Ordo Templi Orientis]] suggested in his book ''The Magical Revival'' (1972) that there was an unconscious connection between Crowley and Lovecraft. He thought they both drew on the same occult forces; Crowley via his magic and Lovecraft through the dreams which inspired his stories and the Necronomicon. Grant claimed that the Necronomicon existed as an [[astral]] book as part of the [[Akashic records]] and could be accessed through [[ritual magic]] or in dreams. Grant's ideas on Lovecraft were featured heavily in the introduction to the [[Simon Necronomicon]] and also have been backed by [[Donald Tyson]]; but Lovecraft, a strict materialist, would likely have been outraged. Like any claim based purely on supernatural evidence, Grant's ideas cannot be proved or disproved and have added further confusion to the issue.<ref>Harms, Dan and John Wisdom Gonce III. 2003. ''The Necronomicon Files''. Boston: Red Wheel Weiser. 103 </ref> ==In popular culture== {{Main|Cthulhu Mythos in popular culture}} The Necronomicon makes minor appearances in many films and television shows and a few video games. It is listed in the in-character bibliography of ''[[Eaters of the Dead]]'' by [[Michael Crichton]]. ==Commercially available versions== * ''Al Azif: The Necronomicon'' by [[L. Sprague de Camp]] (1973, ISBN 1-58715-043-3) * ''[[Simon Necronomicon|Necronomicon]]'' by "Simon" (1980, ISBN 0-380-75192-5) * ''The Gates of the Necronomicon'' by "Simon" (2006, ISBN 0-06-089006-1) * ''[[Necronomicon (H. R. Giger)|H.R. Giger's Necronomicon]]'' by [[H.R. Giger]] (1991, ISBN 0-9623447-2-9) * ''Necronomicon II'' by H.R. Giger * ''Necronomicon: A Study in the Forbidden Magic of Lovecraft & the Great Mystery of Stargates'' (Greek edition, 2008) by George Ioannidis * ''The Necronomicon'' edited by George Hay (1993, ISBN 1-871438-16-0) * ''Necronomicon: The Wanderings Of Alhazred'' by [[Donald Tyson]] (2004, ISBN 0-7387-0627-2) *''Necronomicon Plush Book'' by Toy vault (not an actual book, but rather a novelty collectible parodying the format of children's pop-up books). ==See also== * [[Cthulhu Mythos arcane literature]] * [[Cthulhu Mythos in popular culture]] * [[Anthropodermic bibliopegy]] * [[False document]] * [[Grimoire]] * [[Necronomicon Press]] * [[Simon Necronomicon]] ==Notes== {{reflist|2}} ==References== {{refbegin}} ===Primary sources=== *{{cite book|first=Howard P.|last=Lovecraft|year=1985|title=At the Mountains of Madness and Other Novels|editor=S. T. Joshi (ed.) | edition=7th corrected printing|publisher=Arkham House|location=Sauk City, WI|isbn=0-87054-038-6}} Definitive version. **''The Case of Charles Dexter Ward''<!--NOT A TYPO - A NOVELLA, HENCE ITALICS--> **"The Statement of Randolph Carter" *{{cite book|first=Howard P.|last=Lovecraft|year=1986|title=Dagon and Other Macabre Tales|editor=S. T. Joshi (ed.) |edition=9th corrected printing|publisher=Arkham House|location=Sauk City, WI| isbn=0-87054-039-4}} Definitive version. **"The Festival" **"The Hound" **"The Nameless City" *{{cite book|first=Howard P.|last=Lovecraft|year=1984|title=The Dunwich Horror and Others|editor=S. T. Joshi (ed.) |edition=9th corrected printing|publisher=Arkham House|location=Sauk City, WI| isbn=0-87054-037-8}} Definitive version. **"The Dunwich Horror" *{{cite book|first=Howard P|last=Lovecraft|title=[http:// www.mythostomes.com/content/view/12/72/ A History of The Necronomicon]| publisher=Necronomicon Press|location=West Warwick, RI| isbn=0-318-04715-2|year=1980}} ===Secondary sources=== *{{cite book | last=Joshi | first=S. T. | authorlink=S. T. Joshi | coauthors=David E. Schultz | title=An H. P. Lovecraft Encyclopedia | location=Westport, CT | publisher=Greenwood Press | year=2001 | isbn=0-313-31578-7}} *{{cite web |url=http://www.mythostomes.com/content/view/14/69/ | title=Wildside/Owlswick Necronomicon |date=2006-12-19 |dateformat=mdy| accessdate=March 3, 2007 }} *{{cite book | last=Hill | first=Gary | title=The Strange Sound of Cthulhu: Music Inspired by the Writings of H. P. Lovecraft | publisher=Music Street Journal | year=2006 | isbn=978-1-84728-776-2}} * {{cite book | last =Petersen | first =Sandy | authorlink =Sandy Petersen | coauthors =[[Lynn Willis]], [[Keith Herber]], [[William Workman]], [[William Hamblin]], [[Mark Morrison]], [[Lee Gibbons]] | title =[[Call of Cthulhu (role-playing game)|Call of Cthulhu]] | publisher =[[Chaosium|Chaosium Inc.]] | year=1994 | isbn = 0-933635-86-9 }} {{refend}} ==External links== *[http://www.reocities.com/clorebeast/necpage.htm "The Dan Clore Necronomicon Page"], Everything You Never Wanted to Know about the Necronomicon (Al Azif) of the Mad Arab Abdul Alhazred but Weren't Afraid Enough to Know Better than to Ask! *[http://www.mythostomes.com/content/view/12/72/ "History of the ''Necronomicon''"], by H. P. Lovecraft *[http://www.mythostomes.com/component/option,com_mambowiki/Itemid,55/ "The ''Wikinomicon''"], an online Necronomicon that anyone can edit. <!-- "Category:Fictional books" IS ALREADY A PARENT OF THE CATEGORY BELOW--> {{H.P. Lovecraft}} [[Category:Fictional books within the Cthulhu Mythos]] [[Category:Grimoires]] [[ar:اÙعزÙÙ (Ùتاب)]] [[ca:Necronomicon]] [[de:Necronomicon]] [[el:ÎεκÏονομικÏν]] [[es:Necronomicón]] [[eo:Necronomicon]] [[eu:Nekronomikon]] [[fr:Necronomicon]] [[ko:ë¤í¬ë¡ë ¸ë¯¸ì½]] [[hr:Necronomicon]] [[it:Necronomicon]] [[la:Necronomicon]] [[hu:Howard Phillips Lovecraft#Necronomicon]] [[nl:Necronomicon]] [[ja:ãã¯ãããã³ã³]] [[pl:Necronomicon]] [[pt:Necronomicon]] [[ru:ÐекÑономикон]] [[simple:Necronomicon]] [[sk:Nekronomikon]] [[fi:Necronomicon]] [[sv:Necronomicon]] [[tr:Necronomicon]] > > > > It's like the Necronomicon to me, a legendary tome that may or > > may not actually exist. > > Maybe that's the real problem. Maybe Nam isn't reading from > Shoenfield, but actually from an ancient, corrupted mathematical > tome, the Necronamicon, and it is driving him insane. > > Marshall > > PS. This time I copied and pasted from Aatu's message.
From: Nam Nguyen on 14 Jun 2010 22:29 Daryl McCullough wrote: > Nam Nguyen says... >> Daryl McCullough wrote: >>> Nam Nguyen says... >>>> Daryl McCullough wrote: >>>>> No, it doesn't, but I don't actually care what Shoenfield or Tarski >>>>> said. What I care about is having a non-stupid definition of "truth >>>>> in a model" that applies to models with empty domain. >>>> But you shouldn't have worried about that: because that "non-stupid >>>> definition" could only render falsehood. >>> No, a nonstupid definition of "truth in a model" makes >>> some statements true, and the rest false. >> The caveat here is when I said "could only render falsehood" I meant >> that only in the cases you had refereed as "models with empty domain". > > Right you have a definition which is nonstupid for models with nonempty > domain, but is stupid for models with empty domain. I'd prefer a definition > that is nonstupid in all cases. > >>> I've explained it before. I'm interested in *submodels*. Suppose you >>> start with a structure S for a language L and you restrict attention to >>> a substructure S' for a sublanguage L' in the following way: >>> >>> The domain U' of S' consists of all elements of S that satisfy some >>> unary predicate D(x). >> We can just top it right here. If the U of S is empty, so is the U' of >> S': what is the point of going further? > > The interesting case is the one in which U is nonempty, but U' > may or may not be empty. But you keep forgetting that the case under debate here is the degenerated case where U is empty! > > If U and U' are both nonempty, then we have, for any > Phi(x) that does not involve quantifiers: > > "Ax Phi(x)" is true in the structure with domain U' > <-> > "Ax D(x) -> Phi(x)" is true in the structure with domain U. But what does this have to do with my particular case when U = {}? (Your "U and U' are both nonempty" above!) > > There is no reason not to allow this same equivalence to hold > in the case in which D(x) is universally false (in which case, > U' is empty). But again you're not talking about the case U = {}, using set membership! > > There is just no technical justification for your definition. Unless you're talking about the same case that U = {}, I can't understand what you're talking about. > > You claim that it's following Tarski and/or Schoenfield. I > don't believe you. You misunderstood one or both of them. > > It's possible that they gave a definition of "truth in a model" > that only applies to models with nonempty domain. But how would you go from that possibility (and that's just a possibility) to a meta level conclusion that there's _no other context_ in FOL that x=x is false? > What I doubt > very seriously is that they gave a definition that applies > to all models (empty domain or not) but which gives all sentences > the value "false" in the case of the empty model. But why would you have such doubt in the first place, while there are facts that wouldn't support your position, such as if there's no contingent truth there's no logical truth, as I explained before and as Shoenfield implicitly alluded to it in his condition iii? > That would be stupid. It's all definition and correct inference that would matter. You have to prove that when U = {} it'd be impossible to conclude x=x could be false using strictly unformalized set membership. Given most of authors and credible links avoid this situation, I'm not confident at all _you_ would be able to prove that, while they themselves have kept silent! You certainly can try but it'd be to no avail until you recognize you're actually dealing with the degenerated case, which from what you said above you doesn't seem you've recognized so.
From: Nam Nguyen on 14 Jun 2010 22:36
Marshall wrote: > On Jun 13, 9:32 am, Nam Nguyen <namducngu...(a)shaw.ca> wrote: >> In all that _Marshall still doesn't have any valid argument_ for his statement >> that x=x is true in _all_ contexts of FOL reasoning. > > It's true in all contexts in which there isn't anything that is not > equal to > itself. Can you find a context where x is not equal to x? Please show > me an x, any x, that is not equal to itself. Go on, Potato Chip, > show me one. So, Marhsall, does the-thing-that-doesn't-equal-itself equal itself, mathematically speaking? |