Maiers, Jerald E.

Maiers, Martin J.

English

eScholarship - University of California

UC MercedProceedings of the Annual Meeting of the Cognitive Science SocietyTitleFuzzy Logic vs Pre-Logic: Zadeh vs Levy-BruhlPermalinkhttps://escholarship.org/uc/item/3tz352c7JournalProceedings of the Annual Meeting of the Cognitive Science Society, 18(0)AuthorsMaiers, Jerald E.Maiers, Martin J.Publication Date1996 Peer reviewedeScholarship.org Powered by the California Digital LibraryUniversity of CaliforniaFuzz y Logi c v s Pre-Logic :  Zade h v s Levy-Bruh l Jerald E. Maiers* and Martin J. Maiers ** •Medica l  Suppor t  Services ,  110 0 Commerce Drive ,  Racine ,  WI  5340 6 ••Advance d Bioscience s Computin g Center ,  Universit y  o f  Minnesota ,  St .  Paul ,  M N 5510 8 (maiersSexecpc.com ) Introductio n I n 196 5 Loft i  Zade b introduce d a n innovativ e engineerin g notion ,  fuzz y se t  theory .  Zadeh' s approac h was essentiall y  rejecte d b y th e mai n strea m engineerin g communitie s o f  Europ e an d America .  Fo r  2 5 years ,  ther e wer e onl y a  smal l  se t  o f  wester n fuzz y logi c researchers . But  i n th e lat e 80' s fuzz y se t  theor y reache d Japa n an d Chin a wher e i t  produce d a  fur y o f  activity ,  includin g heav y govenmie m fundin g o f  researc h an d a  resultan t  larg e industr y o f  fuzz y products .  Ther e hav e bee n "cultura l theories "  offere d fo r  th e vivi d differenc e i n th e respons e t o thi s mathematica l  theory ,  bu t  ther e i s a n underlyin g explanatio n lie s i n th e wor k o f  a n earl y Cognitiv e Scientist . Zadeh - Fuzzy Logic Zadeh' s outline d a  radica l  ne w approac h t o mathematic s and ,  b y extension ,  t o logic .  Classica l  o r  cris p se t  theor y i s base d o n th e concep t  tha t  a n elemen t  i s eithe r  a  member  o f a se t  o r  i t  i s  not .  I n classi c se t  theor y ther e migh t  b e a  se t  o f person s si x fee t  tal l  o r  over .  Eac h individua l  i s  eithe r  i n tha t  se t  o r  not .  Fuzz y se t  theor y i s base d o n th e concep t tha t  an d elemen t  ha s a  degre e o f  membershi p i n a  set .  I n thi s approac h a n elemen t  i s  a  m e m b er  o f  a  se t  t o som e degree ;  bu t  a n elemen t  i s als o no t  a  member  o f  th e se t  t o some degree .  I n fuzz y se t  theor y ther e migh t  b e a  se t  o f  tal l persons .  O n th e 0  t o 1  membershi p scal e Zade h devise d a perso n si x fee t  tal l  migh t  b e a  m e m b er  t o a  . 8 degree . Sinc e se t  theor y i s fundamenta l  t o mathematics ,  a  chang e fro m cris p set s t o fuzz y sets ,  implie d a  reformulatio n o f mathematics .  I n a  simila r  way ,  ̂ zz y premise s implie d a reformulatio n o f  logic .  Th e notio n o f  a n elemen t  havin g bot h membershi p an d non-membershi p lead s t o a  ftizzy logi c tha t  doe s no t  suppor t  a  principl e o f  contradiction . L e v y - B r u h l  -  Pre-logi c I n 191 0 Lucia n L6vy-Bruh l  lai d th e foundatio n fo r  th e field of  Cognitiv e Anthropolog y i n H o w Native s Thin k wit h hi s descriptio n o f  th e pre-logi c natur e o f  non-wester n thought . Thi s boo k alon g wit h bi s fou r  other s o n th e sam e topi c focu.se d o n modellin g th e menta l  function s o f  non -European s base d o n ethnographi c studies . L^vy-Bruhl' s  se t  ou t  t o presen t  "th e mos t  genera l  law s particula r  t o th e mentalit y o f  primitives .  (1985 ,  pl4). " The mos t  genera l  la w h e identifie d wa s th e "la w o f participation. "  whic h h e describe s b y sayin g "i n th e collectiv e representation s o f  primitiv e mentality ,  objects , beings ,  phenomen a ca n b e . .  bot h themselve s an d somethin g othe r  tha n themselve s (1985 ,  p76). "  A n exampl e Levy-Bnih l  offer s i s tha t  a  perso n ca n b e bot h a human an d a  bir d a t  th e sam e time . L6vy-Bruh l  contrast s th e abstrac t  natur e o f  categorie s tha t  ar e use d i n wester n versu s non-wester n thought :  'Th e conditio n o f  ou r  abstractio n i s th e logica l  homogeneit y o f th e concept s whic h permit s o f  thei r  combinations .  N o w thi s homogeneit y i s  closel y boun d u p wit h th e homogeneou s representation s o f  space .  I f  th e pre-logica l mind ,  o n th e contrary ,  imagine s th e variou s region s i n spac e a s differin g i n quality ,  abstraction s a s w e usuall y conceiv e o f  i t  become s ver y difficul t  t o suc h a  min d (1985 , pl21). " L6vy-Bnih l  describe s th e absenc e o f  th e principl e o f contradictio n a s a  majo r  contras t  betwee n pre-logi c an d wester n logic .  H e says ,  "th e oppositio n betwee n th e on e and th e many ,  th e sam e an d another ,  an d s o fort h doe s no t impos e upo n thi s mentalit y th e necessit y o f  affirmin g on e of  th e term s i f  th e othe r  b e denie d o r  vis a vers a (1985 , p77) "  H e goe s o n t o say ,  "I t  i s  no t  antilogical ;  i t  i s no t alogica l  either .  B y designatin g i t  'prelogical '  I  merel y wis h t o stat e tha t  i t  doe s no t  bin d itsel f  d o w n t o contradictio n (1985 ,  p78). " Contrast of Fuzzy Logic and Pre-Logic L6vy-Bruh l  contraste d th e wester n "  logica l  homogeneit y o f th e concepts "  wit h th e non-wester n pre-logica l  concept s base d o n "th e variou s region s i n spac e a s differin g i n quality. "  Lik e Zadeh' s fuzz y concepts ,  Ldvy-Bruhl' s  pre -logi c concept s involv e som e degre e o f  membershi p an d non-membership .  A n d jus t  a s ther e i s n o principl e o f contradictio n possibl e i n fuzz y logic ,  L^vy-Bruh l  identifie d th e lac k o f  contradictio n a s on e o f  it s mos t  significan t characteristic s o f  "native "  pre-logic . The pre-logi c whic h L6vy-Bruh l  foun d characterizin g non-wester n thought ,  i s homologou s t o Zadeh' s fuzz y logic . Thi s analysi s suggest s a  cognitiv e scienc e hypothesi s fo r th e differentia l  respons e t o fuzz y logi c i n tha t  th e contemporar y engineer s o f  th e Pacifi c  R i m wer e mor e pre -logica l  tha n thei r  wester n counterparts .  Empirica l  researc h woul d b e require d t o actuall y tes t  thi s notion . I n hi s conclusio n L^vy-Bruhl' s  insightfull y suggeste d tha t  al l  human s shar e a  mentalit y tha t  "i s bot h logica l  an d pre-logical. "  I t  woul d seem ,  i n vie w o f  th e practica l implication s o f  th e initia l  rejectio n o f  fuzz y logi c b y wester n engineering ,  tha t  thi s questio n coul d b e o f  genera l interes t  t o Cognitiv e Science . Levy-Bruhl, L, 1985, How Natives Think, Princeton Universit y Press ,  NJ . Zadeh ,  L. ,  1965 ,  "Fuzz y sets, "  Informatio n an d Control , 8:338-353 . 801 

Fuzzy Logic vs Pre-Logic: Zadeh vs Levy-Bruhl

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Fuzzy Logic vs Pre-Logic: Zadeh vs Levy-Bruhl

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