 V1 and some element of V′i) and V ′ i is redundancy-free. Hence, the criterion of common-cause coupling needs to be supplemented by a further criterion, which discriminates between constitutional and non-constitutional (i.e. coincidental) common-cause couplings. We contend that the identifying feature of constitutional common-cause couplings is their unbreakability. That is, if the set An Abductive Theory of Constitution 13 of analyzed variables is expanded, coincidental common-cause couplings may be broken whereas constitutional common-cause couplings will persist across all variable set expansions. More concretely, if a variable V1 and a set V′i coincidentally happen to be common-cause coupled within a set Vi, expansions of Vi by further causes of V1 are bound to unveil, say, surgical causes of V1 that do not induce changes in V′i-to the effect that the common-cause coupling disappears. This is excluded in cases of constitution. The common-cause coupling of a phenomenon Ψ and a constituting set Φ is not a mere contingency of a modeled set V, which contains Ψ and Φ along with a given number of their common causes; rather, it is a structural necessity of the relationship between Ψ and Φ, which not only holds relative to V but also relative to every expansion of V. That means that, even though the constitutional model 3a and the pure causal model 3b in Figure 3 are indistinguishable relative to data on the variables in the set V3 = {IΨ, IΦ,Ψ,Φ1,Φ2,Φ3}, they are not equivalent in their implications for what happens under expansions of V3. Model 3a with its constitutive dependencies entails that the common-cause coupling of Ψ and its constituents cannot be broken by expanding V3, whereas model 3b does not have any such implications. Rather, according to model 3b it is to be expected that, sooner or later, surgical causes of Ψ and Φ1 to Φ3 will be found that break their coupling. These different implications render it possible to choose between constitutional and pure common-cause models. Gradually expanding V3 (in a series of follow-up studies) will yield one of two outcomes: (I) the common-cause coupling of Ψ and Φ = {Φ1,Φ2,Φ3} is broken or (II) it is not broken. In case
V1 and some element of V′i) and V ′ i is redundancy - free. Hence, the criterion of coarse - lawsuit coupling needs to be supplemented by a further standard, which discriminates between constitutional and non - constitutional (i coincident) common - cause couplings. We contend that the identifying feature of speech of constitutional common - cause couplings is their unbreakability. That is, if the jell An Abductive Theory of Constitution 13 of analyzed variables is expanded, coincidental common - campaign couplings may be broken whereas constitutional coarse - cause couplings will persist across all variable stage set expansions. More concretely, if a variable V1 and a set V′i coincidentally happen to be common - lawsuit coupled within a set Vi, expansions of Vi by further causes of V1 are bound to unveil, say, surgical causes of V1 that do not induce changes in V′i - to the effect that the common - cause coupling disappears. This is excluded in cases of constitution. The coarse - cause coupling of a phenomenon Ψ and a constituting typeset Φ is not a bare eventuality of a modeled set V, which contains Ψ and Φ along with a given number of their common causes; preferably, it is a structural necessity of the relationship between Ψ and Φ, which not only holds relative to V but besides relative to every expansion of V. That means that, even though the constitutional model 3a and the pure causal model 3b in Figure 3 are identical proportional to datum on the variables in the set V3 = { IΨ, IΦ, Ψ, Φ1,Φ2,Φ3 }, they are not equivalent in their implications for what happens under expansions of V3. Model 3a with its constitutive dependencies entails that the coarse - cause coupling of Ψ and its constituents cannot be broken by boom V3, whereas model 3b does not take any such implications. preferably, according to exemplar 3b it is to be expected that, preferably or later, surgical causes of Ψ and Φ1 to Φ3 will be witness that break their coupling. These different implications supply it possible to choose between constituent and pure common - cause models. Gradually expanding V3 (in a serial of follow - up studies) will give one of two outcomes: (I) the common - cause coupling of Ψ and Φ = { Φ1,Φ2,Φ3 } is broken or (II) it is not broken. In casing
 V1 wnd some element of V′i) akd V ′ i is redunbqncy-frxe. Hencs, the crkterion of common-cause couplmng beeds to be supplemented by a furtheg criteriin, wiich discriminatxa betwecu conabitutnoial and non-consjitutional (i.a. coincidental) cumlon-cause couplings. We contend that ehe idemtlfying feature of bogstifltlonal common-cause couplings is tgeir unureakability. Thst is, if the set An Abductlve Hheory of Constituhion 13 of anqlyzqe variables ks expanded, coincidentzl common-cause couplings may be brokzn whereas xobstljutional comnon-calse couplings will pessist avross all varisblx ser expansions. More conrretely, if a variablg V1 and a vec V′i coincidentally hqppen tm be comoin-cxust cpulled wlthmn a set Vi, expansions of Vi by further csufvx of V1 are bkund tj tnveil, say, surgical causes of V1 that do nof induce changes in V′i-ti the effect that the common-catse coupling disappears. This is excluded in cases of ckvstnbmtiov. Tje common-cause coupling of a phenomenon Ψ and w cpnxtituting set Φ is not a mrrf vjntingency of a modzmes set V, which contwins Ψ agd Φ aoong with a goven number of their common causes; rathvr, ir is a structural uecessity of the relayionship between Ψ and Φ, chich hot only hopds relatjxe to V but also rekadive to txery expansion of V. That mxans chat, evev thpugh tre constitktional model 3a and the oure eausan model 3b ln Figure 3 are indistinguishablx relative to ddta on the rariabkes in the see V3 = {IΨ, IΦ,Ψ,Φ1,Φ2,Φ3}, they cre not zquivauent in thvir implirations for rhat happens gjder expansimns of V3. Modwl 3a with igr constitutive dependenbits entails that the common-camse cuhpling of Ψ and nus xonstituents camnog bq hrpkqt by expanditg V3, whdteas oodel 3b doew not have any such impliwatikns. Rather, accordimg to modeo 3b it if to be expecyed that, sooner or latec, surgmcal csusgs of Ψ and Φ1 to Φ3 will be found tgat break thcir coupling. Ehesc disferent im'lications render it possible to choose uetween constitutional qnd pure common-causg mpdels. Graduelly evpanding E3 (in a series of foloow-up studies) wilk yield one of two oufcomes: (I) thf common-cause coupling of Ψ and Φ = {Φ1,Φ2,Φ3} is broken or (II) it is not broken. In casw
V1 and some element of V′i) and i redundancy-free. Hence, criterion of common-cause by further criterion, which between constitutional and (i.e. coincidental) common-cause couplings. We contend the identifying feature of constitutional common-cause couplings is their unbreakability. That is, if set An Abductive Theory of Constitution 13 of analyzed variables is expanded, coincidental couplings be whereas common-cause couplings will persist across all variable set expansions. More concretely, if a variable V1 and set V′i coincidentally happen to be common-cause coupled a set Vi, expansions Vi by further causes of are to unveil, surgical of that do not changes in V′i-to the effect that the common-cause coupling disappears. This is excluded in cases of constitution. common-cause coupling phenomenon Ψ a set is not a of a modeled set V, which Φ along with a given number of their causes; rather, is a structural necessity of the between Ψ and Φ, which not only holds to V but also relative to every expansion of V. That means that, even though model 3a and the causal model 3b Figure are relative data on variables in the set V3 = {IΨ, IΦ,Ψ,Φ1,Φ2,Φ3}, they are not in their implications for what happens under expansions of V3. with constitutive dependencies entails the common-cause coupling of and constituents cannot be broken V3, model have such Rather, according to model it is to be expected sooner or later, surgical to Φ3 will be found that break their These different implications render it possible to between constitutional and pure common-cause models. Gradually expanding V3 (in a series follow-up studies) one of two outcomes: (I) the common-cause coupling Ψ and Φ = is broken or (II) it is not broken. In
 V1 and some element of V′i) and V ′ i iS redundancY-free. henCe, tHe CritErioN of common-cause COuplIng needs to be supplementEd by a FuRTher CRiTerioN, which dIScRIMinAtEs BetWeEN cOnstiTutIonal anD non-constiTutIoNal (i.e. coincidENtAl) common-caUse Couplings. We cOntEnd thaT tHe iDEntifYinG featUre of cONstituTional comMoN-Cause cOUplings IS ThEir uNbreakability. That IS, iF The set An AbductIve TheOrY Of cONstItuTion 13 of analYzEd varIAbles is EXpANDEd, cOIncidental comMon-cause couPLinGs may bE bRokEN whereAs conStITutIonal common-CausE couplingS will pERsist acROss all vAriablE seT exPansIOnS. MOre CoNCreTElY, if A VarIable V1 anD a SeT V′i coInciDENTAlly HapPen tO be coMmon-cause coupLed WithIN a sEt Vi, eXpansIons Of vi by fUrther CauseS oF V1 are bound to unvEil, sAy, surgicaL caUsEs oF V1 That dO Not indUce ChaNges in V′I-to the eFFecT tHAT ThE common-cause coupliNg DISaPpears. ThIs is exCLuDeD In cases oF cOnsTituTIOn. The CommON-cAuse coupLing of A PhEnOmenon Ψ AnD a consTiTutIng Set Φ iS Not a Mere coNtingencY of a mODeled set V, which COntains Ψ and Φ aLOnG WItH A givEn nUmber of theiR comMOn caUses; RAtHer, IT is a sTructUrAL nECessity of the relatioNsHip betWeen Ψ And Φ, which not oNly holds reLATIve to V buT alsO ReLAtive to every exPansiOn of V. That mEAns that, eVen thOugh the cOnstitutiONAl model 3a And The PurE caUSAl Model 3b in FigurE 3 ARe inDiStinguiShaBle relaTivE to DatA on ThE variableS in the seT V3 = {iΨ, iΦ,ψ,Φ1,φ2,Φ3}, tHey arE Not equivAlEnt In TheIr impLIcatioNs for What HaPpENs uNder expANsIONs of v3. MOdEl 3a wIth ItS consTituTIve DependeNcies entaIls THat tHe CoMmon-cauSe coupling of Ψ AnD its constiTuEntS cannoT BE broken bY expanding V3, whereas model 3B Does not HavE any sUch iMplicatioNs. RAther, aCcoRDing to Model 3b It is tO bE exPECted tHAT, sOonEr Or later, surGICal CauseS oF Ψ anD Φ1 to Φ3 wiLl be found that break THeiR coupling. ThesE diFferENT iMplICaTIonS rENdeR IT possible to chooSe between cOnSTiTutional anD PurE cOmmon-caUse modeLs. GraDUally exPanding V3 (iN a series oF fOlloW-UP stUdies) will yIeld one oF two outcoMEs: (I) thE CoMmon-cAusE couplInG of ψ and Φ = {φ1,Φ2,Φ3} is bROkeN or (II) It is noT bRoken. IN case
 V1 and some element of V′ i) and V ′  i is  re dun da ncy- free . Hence, the c r iter ion of common-cause co uplin gn eeds to  be s uppleme n te d byafu rth er cr iteri on,  whichdiscrimina tes  b etween const i tu tional and  no n-constituti ona l (i.e .coi n ciden tal ) com mon-ca u se cou plings. W ec ontend that th e id enti fying feature ofc on s titutional com mon-ca us e  c o u pli ngs  is theirun break a bility. Th a t is, if the set An  AbductiveT heo ry ofCo nst i tution  13 o fa nal yzed variab lesis expand ed, co i ncident a l commo n-caus e c oup ling s  m ay  be  b r oke n  w her e asconstitu ti on al co mmon - c a u se c oup ling s wil l persist acr oss  all var iable  setexpa ns ions.  Moreconcr et ely, if a varia bleV1 and aset  V ′ico incid e ntally  ha ppe n to be  common - cau se c o up led within a set V i, e xp ansionsof Vib yfu r ther cau se s o f V1 a re bo undt ounveil,say, s u rg ic al caus es  of V1  t hat  do  noti nduc e chan ges in V ′i-to the effect tha t  the common-c a us e co u plin g d isappears.This is e xclu d ed  in cases  of c on s ti t ution. The common-c au se cou pling  of a phenome non Ψ anda c onstitut ings et Φ is not a mer e con tingency o f  a model ed se t V, whi ch contai n s  Ψ and Φ  al ong  wi tha gi ven number of t heir  c ommon c aus es; rat her , i t i s a  s tructural  necessi ty  o fth e r elati o nship be tw een  Ψ  an d Φ,w hich n ot on ly h ol ds rel ative t o  V b ut a ls orela tiv eto ev erye xpa nsion o f V. That  me a ns t ha t,  even t hough the con st itutionalmo del  3a an d the pure  causal model 3b in Fig u re 3 ar e i ndist ingu ishable r ela tive t o d a ta onthe va riabl es  in t he se t V3  ={I Ψ, IΦ,Ψ,Φ1 , Φ 2,Φ 3}, t he y ar e not e quivalent in their imp lications for  wh at h a p pe nsu nd e r e xp a nsi o n s of V3. Model3a with it sc on stitutived epe nd enciesentails  that the com mon-cause  coupling  o f Ψa n d i ts constit uents ca nnot be b r okenb yexpan din g V3,wh ere as mo del 3b doe s not  havean y such  impl ic ations.Rather, according to mo del 3b  it i s t o be expe cte d  th at, soone r or  later, su rgi cal  caus eso f Ψ a nd Φ 1  t o Φ 3  will  bef ound that br eak t he ir coupling . T hes e dif fer e nt imp lica tions render it p o ssible to choo se b e t wee n c o nsti tu tional and pur e c om m o n-causemo dels. Gradu ally exp an d ing V 3 (ina seri es of f o l lo w -up st udie s)will yiel d o ne of twoou tc o mes: ( I) t he  commo n-caus e  cou p l ing of Ψ and Φ =  {Φ1, Φ 2 ,Φ3}i s b roken  o r (II)i t is  not broke n. In case
 V1_and some_element of V′i) and_V ′_i_is redundancy-free._Hence,_the criterion of_common-cause coupling needs_to be supplemented by_a further criterion,_which_discriminates between constitutional and non-constitutional (i.e. coincidental) common-cause couplings. We contend that the identifying_feature_of constitutional_common-cause_couplings_is their unbreakability. That is,_if the set An Abductive_Theory of_Constitution 13 of analyzed variables is expanded, coincidental_common-cause_couplings may be_broken whereas constitutional common-cause couplings will persist across all_variable set expansions. More concretely, if_a variable V1_and_a_set V′i coincidentally happen_to be common-cause coupled within a_set Vi, expansions of Vi by_further causes of V1 are bound to_unveil, say, surgical causes of V1_that do not induce changes_in V′i-to_the effect that the common-cause_coupling disappears. This_is excluded_in cases of_constitution. The common-cause coupling of a_phenomenon Ψ and_a constituting set Φ is not_a_mere contingency of_a_modeled_set V,_which contains Ψ_and_Φ along_with_a given number of their common_causes;_rather, it is a structural necessity of_the relationship between Ψ_and_Φ, which not only_holds relative to V but_also relative to every expansion of_V. That_means that,_even though the constitutional model 3a and the pure causal model_3b in Figure 3 are indistinguishable_relative to data on_the variables_in_the set V3_=_{IΨ, IΦ,Ψ,Φ1,Φ2,Φ3},_they are not equivalent in their implications_for what_happens under expansions of V3. Model_3a with its constitutive_dependencies_entails that the common-cause coupling of_Ψ and its constituents cannot be_broken by expanding V3, whereas_model_3b_does not have any such_implications. Rather, according to model 3b_it is to_be expected that, sooner or later, surgical_causes_of Ψ and Φ1 to Φ3_will_be found that break their coupling._These_different_implications render it possible to_choose between constitutional and pure common-cause_models. Gradually expanding V3 (in a series of follow-up_studies) will yield_one of two outcomes: (I)_the_common-cause_coupling of Ψ and Φ = {Φ1,Φ2,Φ3} is broken or_(II) it_is not broken._In case