Table Of ContentStudies in Universal Logic
Daniel Parrochia
Pierre Neuville
Towards
a General Theory
of Classifi cations
StudiesinUniversalLogic
SeriesEditor
Jean-Yves Béziau (Federal University of Rio de Janeiro and Brazilian Research
Council,RiodeJaneiro,Brazil)
EditorialBoardMembers
HajnalAndréka(HungarianAcademyofSciences,Budapest,Hungary)
MarkBurgin(UniversityofCalifornia,LosAngeles,USA)
Ra˘zvanDiaconescu(RomanianAcademy,Bucharest,Romania)
JosepMariaFont(UniversityofBarcelona,Barcelona,Spain)
AndreasHerzig(CentreNationaldelaRechercheScientifique,Toulouse,France)
ArnoldKoslow(CityUniversityofNewYork,NewYork,USA)
Jui-LinLee(NationalFormosaUniversity,HuweiTownship,Taiwan)
LarissaMaksimova(RussianAcademyofSciences,Novosibirsk,Russia)
GrzegorzMalinowski(UniversityofŁódz´,Łódz´,Poland)
DarkoSarenac(ColoradoStateUniversity,FortCollins,USA)
PeterSchröder-Heister(UniversityTübingen,Tübingen,Germany)
VladimirVasyukov(RussianAcademyofSciences,Moscow,Russia)
Thisseriesisdevotedtotheuniversalapproachtologicandthedevelopmentofa
generaltheoryoflogics.Itcoverstopicssuchasglobalset-upsforfundamental
theoremsoflogicandframeworksforthestudyoflogics,inparticularlogical
matrices,Kripkestructures,combinationoflogics,categoricallogic,abstractproof
theory,consequenceoperators,andalgebraiclogic.Itincludesalsobookswith
historicalandphilosophicaldiscussionsaboutthenatureandscopeoflogic.Three
typesofbookswillappearintheseries:graduatetextbooks,researchmonographs,
andvolumeswithcontributedpapers.
Daniel Parrochia (cid:2) Pierre Neuville
Towards
a General Theory
of Classifications
DanielParrochia PierreNeuville
DepartmentofPhilosophy EcoleNationaleSupérieuredesSciences
UniversitéJeanMoulin–LyonIII del’InformationetdelaBibliothèque
Lyon,France Villeurbanne,France
ISBN978-3-0348-0608-4 ISBN978-3-0348-0609-1(eBook)
DOI10.1007/978-3-0348-0609-1
SpringerBaselHeidelbergNewYorkDordrechtLondon
LibraryofCongressControlNumber:2013936647
MathematicsSubjectClassification(2010): 03-XX,03Axx,06-XX,62H30,91C20
©SpringerBasel2013
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“Formal logicisnothingbutthestudyofthe
propertiescommontoallclassifications;it
teachesusthattwosoldierswhoaremembers
ofthesameregimentbelongbythisvery fact
tothesamebrigade,and consequentlytothe
samedivision;andthewholetheoryofthe
syllogismisreducedtothis.Whatis,then,the
conditionnecessary fortherulesofthislogic
tobevalid?Itisthattheclassificationwhich
isadoptedbeimmutable.Welearnthattwo
soldiersare membersofthesameregiment,
and wewanttoconcludethattheyare
membersofthesamebrigade;wehavethe
righttodothisprovided thatduring thetime
spent carryingonourreasoning oneofthe
twomenhasnotbeentransferred fromone
regimenttoanother”.
HenriPoincaré(LastEssays)
“Onemorningatdawn,hemadehiscry
heard, whichistosay, asort ofchirping, or
more ofameowing,ormoreofabarking, or
more ofalowing,well,that’salmostit,a
roar, ormore exactlyatrumpeting,yes,that’s
theword, asort ofchirping.”
EricChevillard(Palafox)
“Thentheclientcamein,toldhimthathe
wantedtowrite;so, thepublicwritertook
fromhisboxapackofallfixedletters,chose
therightoneand copieditdownonthe
paper... Because, infact,allthatmencan
telloneanother,fromcasetocase—the
youngmantohisfiancée,thefathertohis
son,thetradertohiscustomer—wastobe
codifiedunderfiveorsixdifferentpatterns,
wherethere wasnothingtochange, apart
fromthenameandthenumbers.”
PandelisPrevelakis(ChronicleofaCity)
“InChina,apopularnameforthegiant
pandais“large bearcat”(Chinese大熊猫,
pinyindàxióngma¯o),fromdà(大) large,
xióng(熊)bearandma¯o (猫)cat,which
suggests, according totheplaceofthe
adjectivesinChinese,thatpandaswouldbe
cats.Indeed,DNAanalysisshowsthatthe
pandasshare withthebears90percent of
theirgeneticinheritance,andthatthestaying
10percent,ofcourse, doesnotcomefrom
cats.”
AChinesestudent(Privateconversation)
Preface
This book is an essay in epistemology of classifications, not a mathematical text-
book or monograph. Except in a few pages, we do not present results of our own.
Whenitisthecase,wemustrecognizetheyareoftenelementaryones.Indeed,our
main purpose is not to provide an exposition of an actual mathematical theory of
classifications, that is, a general theory which would be available to any kind of
them:hierarchicalornothierarchical,ordinaryorfuzzy,overlappingornotoverlap-
ping,finiteorinfinite,andsoon,foundingallpossibledivisionsoftherealworld.
Forthemoment,suchatheoryisbutadream.Weareessentiallylistingquestions.
Our aim is, in fact, to expose the “state of the art” of this moving field and the
philosophy one may eventually adopt to go further. To say a little more, we shall
speakofsomeadvancesmadeinthelastcentury,discussafewtrickyproblemsthat
remaintobesolved,and,aboveall,showtheverywaysopenforthosewhodonot
wishtostayanylongeronthewrongtrack.
Letusbrieflyexplaintheimportanceofthesubject.
ALongHistory
Finite classifications, as an economical way of grouping objects to simplify our
understanding of the world (one may start with this “intuitive” definition), have
been known since Antiquity and may already be found in the writings of Plato or
Aristotle(see[371,376,377,383]).1
1Ofcourse,theviewsofPlatoandAristotleaboutclassificationsareverydifferent.Allalongthe
Dialogues,andespeciallyinthelatestones(Parmenides,Sophist,Politicus,Philaebus...),Plato
obviouslyusedtoclassalotofthings(WaysofLife,PoliticalConstitutions,Pleasures,Arts,Jobs,
KindsofKnowledge,etc.),generallyinrelationwiththe“distance”thatseparatesthemfromtheir
archetypalforms—whichgivessomeorder(orpreorder)onthem.But,asAristotleargues,itis
quiteimpossibletoexplainwhatexactlythisparticipationorimitationis.Thepropertiesthatthe
formshave(eternal,unchanging,transcendent,etc.)arenotcompatiblewithmaterialobjectsand
themetaphorofparticipationorimitationbreaksdowninanumberofcases.Forinstance,what
vii
viii Preface
Though scholastic thought put these classifications to good use, taxonomy as a
fully fledged discipline actually began to develop with the birth of natural science
intheClassicalAge,andwiththeneedtoorganizeflorasandfaunasinconnection
with the growth of human population on earth, in the context of the beginning of
agronomy (see [115, 117]). A century later, following the progress of technology,
Chemistryitselfbegantobeascience.ComingaftertheworksofLavoisierandAu-
gusteLaurent,andalotof,oftenunsuccessful,essays,Mendeleev’sPeriodicTable
of the Elements were given all the credit for winning the victory. Since that time,
all sciences have made use of classifications (especially physics, where important
fieldsneedtobeorganizedbynon-trivialmathematicalstructures:forinstance,dis-
cretegroupsincrystallography,orLiegroupsinquantummechanicsandelementary
particlephysics).
ProgressinLibraryClassifications
At the end of the XIXth century, the development of scientific research, which
raised the question of information storage and retrieval, encouraged the constitu-
tionofvoluminouslibrarycatalogs:e.g.,Dewey’sdecimalclassification,Otletand
La Fontaine’s universal decimal classification (see [138]), Herbert Putnam’s Li-
braryofCongressclassification(see[426]).InthecourseoftheXXthcentury,new
modes of indexing and original classification schedules appeared in this domain
withS.R.Ranganathan(see[411,412])andhisfacetedclassification,while,inthe
middleofthe1950s,aClassificationResearchGroupwasconstitutedandmanyin-
ternationalconferencesonscientificinformationorganized(London1946,Chicago
1950,Dorking1957,Washington1958,Cleveland1959,Elsinore1965...).
Sincethattime,somerareattemptstodevelopaformalizedapproachtoclassi-
fications were made by authors like R.A. Fairthorne, C.N. Mooers, B.C. Vickery
(see[489,490])orJ.Farradane(see[161,162]),theverystartofamathematicsof
classifications having already existed since the end of the 1940s, as mentioned in
a brief paper of the Journal of Symbolic Logic (see [89]) where Alonzo Church’s
review studied the work of R.A. Fairthorne, including discussions of A.B. Agard
Evans,T.H.O’BeirneandE.M.R.Ditmas.2 Infact,thoseresearchesneverreached
thelevelofageneraltheory.
doesitmeanexactlythatawhiteobjectbesaidtoparticipateinorcopytheformofwhiteness?
Mustwethinkthattheformofwhitenessiswhiteitself?Howcouldtherebewhitenesswithout
anythingwhichwouldbewhite?Whatcanawhiteobjectandtheformofwhitenessbesaidto
haveincommon?AccordingtoAristotle([9],I,9),theformsfailtoexplainhowtherecouldbe
permanenceandorderintheworld.Farmore,intheviewoftheStagyrite,theycannotexplain
anythingatallinourmaterialworld.
2Inthisperiod,thatfollowedthesecondworldwar,thegrowthofinformationbegantonecessitate
coordination (see, for instance, [130] and [131]). A decade later, information science was still
lookingforalanguage(see[350]),andaneffectivepractice(see[163]).
Preface ix
InEurope,especiallywithintheappliedfieldsoflibrary,lifesciencesandsocial
studies,anumberofpapersonclassificationresearchwerepublishedduringthenext
twentyyearsinInternationalClassification,theGermanjournalfoundedin1973by
DrIngetrautDahlberg.3
Atthesametime,researchmadeprogressinFrancewithscholarslikedeGrolier
([211])whopublishedsomemasterpapersinafamousFrenchlibraryreview(see
[212])orZ.Dobrowolski(see[132]),agreattaxonomistinthefieldoftechnology.
However,mostofthesepaperswerenotactuallyconcernedwithamathematics
of classifications and, around the 1990s, the interest in classifications themselves
tendsapparentlytodecline,thetitleofDahlberg’sjournalsoonbeingchangedinto
Knowledge Organization, a much more general and up-to-date topic. The subse-
quentarrivalofthedesktopcomputer,followedbythegrowthofnetworksprovid-
ingaccesstoanalmostincrediblequantityandvarietyofresources,stillkeptaway
from a purely algebraic approach to the problem, automatic clustering and analy-
sis of data being essentially reduced—especially in France—to multidimensional
appliedstatistics(see[36–38,83,257]).
Curiously, until recently, library scientists were not necessarily very aware of
these mathematical developments in classification science (see [386]). Some time
ago,mostofthem,indeed,continuedtoworkwithtraditionalformsoflibraryclas-
sifications.Forexample,inhisVocabulaireélémentairedesclassifications,theBel-
gianlibrarianAndréCanonnestillspeaksoftheCDUofOtletandLaFontaine(or
their followers), and of the Bibliographic Classification of Bliss, as good classifi-
cations(Bliss’sone,thoughnotperfect,beingforhim,undertheformofBC2(the
newBlissclassification),the“bestintheworld”,atleastatthetime(see[76],19)).
He was even considering that such classifications, thanks to their analytical divi-
sions, anticipate in fact some aspects of Ranganathan’s faceted classification.4 On
the other side, those who were concerned with advanced studies in classification
theory tried essentially to convince professionals that it is possible to improve the
Colon Classification of Ranganathan (see, for instance, [226, 346]), which tries to
gobeyondenumerativeorsemi-enumerativeclassificationschemesalreadyinuse,5
3Forabriefhistoryofclassifications,fromtheviewpointoflibrarysciences,seethepapersofthis
author,forinstance[118]or[119].Forrecenttransformationsofthelibrarydomain,seeParrochia
[382,385].
4Letusgiveasimpleexample:intheUDC,insteadofforeseeing,inthesameclass,indexesdenot-
ingpermanentorrecurrentconcepts—forinstance,the“gothic”intheFine-Artsclass(7)—,one
mayapply,exceptincertaincircumstances,theanalyticaldivision033.5forindicating“gothic”,
aconceptwhichnever appears,asamatteroffact,inprimitiveorderivedclasses.Soonewill
neverfind“gothicarchitecture”nor“gothicchurches”intheArchitectureclass(72),butonewill
beallowedtoconstructthosesymbolsbyaddingtotheindexestheappropriateanalyticaldivision:
72.033.5,“gothicarchitecture”;726.6.033.5:“gothicchurches”(see[76],70).
5DeweyDecimalClassification(DDC)orLibraryofCongressClassification(LCC)areenumer-
ative systems which start with a list of possible subjects, each with a corresponding number,
whosedivisions areoftenarrangedin a hierarchicmanner, frommost generaltomost specific.
In those systems, each document (book, paper, webpage, etc.) to be cataloged is then assigned
oneofthenumbersinthescheme.Bliss’sclassification,becauseofthepossiblecombinationsof
