 of outcome (I), the attempt to model the relationship between Ψ and Φ constitutionally is empirically rejected. If, say, a follow-up study reveals a surgical cause of Ψ, Φ is shown not to be a constituting set of Ψ, meaning that the common-cause model prevails. By contrast, outcome (II) gives preference to modeling Φ as a constituting set of Ψ, notwithstanding the fact that the correlations in every expansion of V3 can likewise be reproduced by a mere common-cause model. The reason is that a constitutional model not only reproduces the empirical correlations but also explains why the common-cause coupling of Ψ and Φ is not broken. That is, in case of outcome (II), a constitutional model is preferable over a pure common-cause model because it exceeds the latter in explanatory power. While it is a structural necessity of the constitutional model 3a that Ψ and Φ remain common-cause coupled in all expansions of V3, viz. that outcome (II) obtains, the common-cause model 3b provides no reason whatsoever why surgical causes of Ψ cannot be found. The inference to constitution is thus inherently abductive: constitutional models are preferable over pure causal models because they explain both the highly correlated behavior of phenomena and their constituents as well as the impossibility to de-couple them.9 9Our proposal on how to model the coupling of phenomena and constituents bears certain similarities to Causey's proposal on how to interpret biconditional dependencies used as bridge laws in theory reductions. For Causey (1977, chs. 2, 5), those dependencies express attribute identities if all attempts at causally explaining them have failed-for identity then is the only explanation left standing (Causey 1977, 98-99). (We thank an anonymous reviewer for indicating this parallel to us.) 14 Michael Baumgartner and Lorenzo Casini By letting a complex instance of a variable set Φ designate the occurrence or process (in a particular spatiotemporal region) represented by a complex value assignment Φ1 = φ1,...,Φn = φn to all elements of Φ, we can now introduce the definitional details of our proposed No De-Coupling (NDC) theory of constitutive relevance (where the specificity of the variables is again made explicit): (NDC) Φ1(X1) is constitutively relevant to Ψ(S) if, and only if, there exists a variable set V containing �
of outcome (I), the attempt to model the relationship between Ψ and Φ constitutionally is empirically disapprove. If, suppose, a follow - up study reveals a surgical causal agent of Ψ, Φ is shown not to be a constituting set of Ψ, intend that the coarse - cause exemplar prevails. By contrast, outcome (II) give preference to modeling Φ as a constituting bent of Ψ, notwithstanding the fact that the correlation in every expansion of V3 can likewise be reproduced by a mere common - cause exemplar. The reason is that a constitutional model not entirely reproduces the empirical correlations but also explain why the common - cause coupling of Ψ and Φ is not broken. That is, in case of result (II), a constitutional model is preferable over a pure common - cause model because it exceeds the latter in explanatory power. While it is a structural necessity of the constitutional model 3a that Ψ and Φ remain common - cause coupled in all expansions of V3, viz. that outcome (II) obtains, the coarse - cause model 3b provide no reason whatsoever why surgical causes of Ψ cannot be found. The inference to constitution is therefore inherently abductive: constitutional model are preferable over pure causal models because they excuse both the highly correlated behavior of phenomena and their constituents as well as the impossibility to de - couple them.9 9Our proposal on how to model the coupling of phenomena and constituents bears certain similarity to Causey's proposal on how to rede biconditional dependencies used as bridge laws in theory reductions. For Causey (1977, chs. 2, 5), those colony express attribute identities if all attempt at causally explaining them have failed - for identity then is the only explanation left stand (Causey 1977, 98 - 99). (We thank an anonymous reviewer for indicate this parallel to us .) 14 Michael Baumgartner and Lorenzo Casini By let a complex instance of a variable star set Φ designate the occurrence or process (in a finical spatiotemporal region) represented by a complex value assignment Φ1 = φ1,... ,Φn = φn to all elements of Φ, we can now insert the definitional details of our project No De - Coupling (NDC) theory of constitutive relevance (where the specificity of the variables is again made explicit ): (NDC) Φ1(X1) is constitutively relevant to Ψ(S) if, and merely if, there exists a variable put V containing �
 of outcome (I), the attempt tu model the relcrionshmp betwsen Ψ and Φ constitutionally is empirirallt rejtbted. If, say, a follow-uo study rvveals a wurgmcal cause of Ψ, Φ ma shown not tk be c ronstituting sej of Ψ, meaninc that the comkov-ccuse model prevails. By contrast, outcjme (II) biges preference to kjdeljng Φ as a constituting set of Ψ, notsithstaiding the fact yhat the correlations in egery expansion of V3 caj likewise ve rqproduced by x mere common-cause modgl. The reason is that a constitugionak model noj knpi reproduces the vmpirical corvvlationv but akso explains wmy thx conmon-cause coupling of Ψ and Φ is not brokgn. That is, iu case of outcome (II), q xonsthtuthonau moael ix lreferwblx over a pude common-cayse model because iu evbreds the latfer in evplanatory power. While it is a structurdl hecessity of the constirutional model 3a that Ψ and Φ reiain common-cause coupled in all expansions of V3, vhz. thet ouucime (IK) ohtains, the common-cause model 3b provides no rewaom ehatsoever why surgical csudex of Ψ cannot bg found. Ths inference to condtitutijn is thus inhtrentky abductive: constitutional models are irefwrable over pure ccusal models becsuse yhey explain both the hnghly dorrelated hehavior kw phenomena and ghepr cmnstituents as well as the impossibmlity to de-cuuplg them.9 9Jur proposwl on how to model the clupliug of phenomena and constituents bears certain similarities jo Wauvey's pro'osal pn how to intqrpret bicondijional de'endenzies used zs bridje laws in treory reductimjs. For Causeb (1977, chs. 2, 5), ehosw dependenckds express atttibute idvnuities if qll attempts at camsalli sxplaining them hace failed-for idrntkty tjei is eve only expldnatkon keft rtanding (Camseh 1977, 98-99). (Ee thank an anonymouv rebiewer for indicatonn this patallel to us.) 14 Michael Naumgartner and Logenzo Carini Ny jetting a complex instance of z variablf sct Φ designate the occurrence pr process (in a particular spatiotemporel region) represented bt a complex value axxignment Φ1 = φ1,...,Φi = φn tj all elekents of Φ, we can now introduce the deninitional details of kur prmposef No De-Coupling (NDC) theory of constitutive relevance (where the specificitt of tie variables js abain kabe zxplicie): (NDR) Φ1(E1) is constitutiveky relevant to Ψ(S) if, and only if, there efifts a variable set V containone �
of outcome (I), the attempt to model between and Φ is empirically rejected. reveals surgical cause of Φ is shown to be a constituting set of meaning that the common-cause model prevails. By contrast, outcome (II) gives preference to Φ as a constituting set of Ψ, notwithstanding the fact that the correlations every of can be reproduced by a mere common-cause model. The reason is that a constitutional model not only the empirical correlations but also explains why the coupling of Ψ and is not broken. That is, case outcome (II), constitutional is over a pure model because it exceeds the latter in explanatory power. While it is a structural necessity of the model 3a and Φ common-cause in expansions of V3, outcome (II) obtains, the common-cause model reason whatsoever why surgical causes of Ψ cannot found. The to constitution is thus inherently abductive: models are preferable over pure causal models because explain both the highly correlated behavior of phenomena and their constituents as well as the de-couple them.9 9Our proposal how to model coupling phenomena constituents certain similarities Causey's proposal on how to interpret biconditional dependencies used as bridge in theory reductions. For Causey (1977, chs. 2, 5), those attribute if all attempts causally explaining them have identity is the only explanation (Causey 98-99). anonymous for this parallel to us.) Michael Baumgartner and Lorenzo Casini letting a complex instance designate the occurrence or process (in a particular region) represented by a complex value assignment = φ1,...,Φn = φn to all elements of Φ, we can now the definitional our proposed No De-Coupling (NDC) theory of constitutive (where the specificity of variables is again made explicit): (NDC) Φ1(X1) is constitutively to if, and if, there exists variable set V �
 of outcome (I), the attempt to modEl the relatIonshIp bEtwEeN Ψ anD Φ coNstitutionally IS empIrically rejected. If, say, a FolloW-uP StudY ReVeals A surgicAL cAUSe oF Ψ, φ iS shOwN NoT to be A coNstitutIng set of Ψ, mEanInG that the commON-cAuse model pRevAils. By contraSt, oUtcome (iI) GivES prefEreNce to ModeliNG Φ as a cOnstitutiNg SEt of Ψ, nOTwithstANDiNg thE fact that the correLAtIOns in every expaNsion oF V3 CAn LIKewIse Be reproducEd By a meRE common-CAuSE MOdeL. the reason is thAt a constituTIonAl modeL nOt oNLy reprOduceS tHE emPirical corrElatIons but alSo explAIns why tHE common-Cause cOupLinG of Ψ ANd φ iS noT bROkeN. thAt iS, In cAse of outCoMe (iI), a coNstiTUTIOnal ModEl is PrefeRable over a purE coMmon-CAusE modeL becaUse iT eXceedS the laTter iN eXplanatory power. whilE it is a strUctUrAl nEcEssitY Of the cOnsTitUtional Model 3a tHAt Ψ AnD φ REmAin common-cause coupLeD IN aLl expansIons of v3, ViZ. tHAt outcomE (Ii) obTainS, THe comMon-cAUsE model 3b pRovideS No ReAson whaTsOever wHy SurGicAl cauSEs of ψ cannoT be found. the inFErence to constiTUtion is thus inHErENTlY AbduCtiVe: constitutIonaL ModeLs arE PrEfeRAble oVer puRe CAuSAl models because they ExPlain bOth thE highly correlAted behaviOR OF phenomeNa anD ThEIr constituents As welL as the impoSSibility To de-cOuple theM.9 9Our propoSAL on how to ModEl tHe cOupLINg Of phenomena anD COnstItUents beArs Certain SimIlaRitIes To causey's prOposal on HoW tO iNtErpRet biCOnditionAl DepEnDenCies uSEd as brIdge lAws iN tHeORy rEductioNS. FOR causEy (1977, ChS. 2, 5), thoSe dEpEndenCies EXprEss attrIbute idenTitIEs if AlL aTtempts At causally expLaIning them hAvE faIled-foR IDentity tHen is the only explanation LEft stanDinG (CausEy 1977, 98-99). (We Thank an anOnyMous reVieWEr for iNdicatIng thIs ParALLel to US.) 14 miChaEl baumgartneR ANd LOrenzO CAsinI By lettIng a complex instancE Of a Variable set Φ dEsiGnatE THe OccURrENce Or PRocESS (in a particular sPatiotempoRaL ReGion) represENteD bY a complEx value AssigNMent Φ1 = φ1,...,ΦN = φn to all eLements of φ, wE can NOW inTroduce the DefinitiOnal detaiLS of ouR PrOposeD No de-CoupLiNg (NdC) theOry of cONstItutiVe releVaNce (wheRe the SpEcificitY of the variables is again mAde expLicit): (nDC) φ1(X1) is constItuTIveLy relevanT to Ψ(s) if, and only If, tHerE exisTs a VAriabLe seT v cOntAIning �
 of outcome (I), the attem pt to mode l the  re lat io nshi p be tween Ψ and Φc onst itutionally is empiric allyre j ecte d .If, s ay, a f o ll o w -up  s tu dyre v ea ls asur gical c ause of Ψ,  Φis  shown not t o  b e a consti tut ing set of Ψ , m eaning  t hat the c omm on-ca use mo d el pre vails. By  c o ntrast ,  outcom e (I I) g ives preference t o  m o deling Φ as aconsti tu t in g set  of  Ψ, notwit hs tandi n g the f a ct t h att he correlatio ns in every exp ansion  o f V 3  can l ikewi se bereproducedby a  mere com mon-ca u se mode l . The r easonistha t ac on st itu ti o nal mo del not  only re pr od ucesthee m p i rica l c orre latio ns but also e xpl ains why  thecommo n-ca us e cou plingof Ψan d Φ is not brok en.That is,inca seof  outc o me (II ),a c onstitu tionalm ode li s pr eferable over a pu re c om mon-caus e mode l  b ec a use it e xc eed s th e latte r in ex planator y powe r .Wh ile itis  a str uc tur alneces s ityof the  constit ution a l model 3a tha t  Ψ and Φ rema i nc o mm o n-ca use  coupled in  all expa nsio n sofV 3, vi z. th at ou t come (II) obtains,th e comm on-ca use model 3bprovides n o r eason wh atso e ve r  why surgicalcause s of Ψ can n ot be fo und.The infe rence toc o nstituti onisthu s i n h er ently abducti v e : co ns titutio nal  models  ar e p ref era bl e over pu re causa lmo de ls  be cause they exp la inbo ththe h i ghly c orrel ated  b eh a vio r of ph e no m e na a nd  t heir  co ns titue ntsa s w ell asthe impos sib i lity  t ode-coup le them.9 9Ou rproposal o nhow  to mo d e l the co upling of phenomena and constit uen ts be arscertain s imi lariti est o Caus ey's p ropos al  on h ow to i nt erp re t bicondit i o nal  depe nd enci es used  as bridge laws in the ory reduction s.ForC a us ey( 19 7 7,ch s . 2 , 5), those depen dencies ex pr e ss  attribute ide nt ities i f all a ttemp t s at ca usally ex plainingth em h a v e f ailed-foridentity  then ist he on l yexpla nat ion le ft  st andin g (Cau s ey1977,  98-99 ).  (We t hankan  anonymo us reviewer for indicat ing th is pa ral lel to us .)1 4 M ichael Ba umga rtner andLor enz o Cas ini By le ttin g  a  co m plexinst a nce of av ar iab l e  s et Φ design a t e  th e occ urr e nce or  pro cess (in a partic u lar spatiotemp oral r egi on) repr es ented by a com ple xv a lue assi gn ment Φ1 = φ 1,...,Φn  = φn to  all e lement s of Φ, w ec an now  int rod uce the d efi ni t ional d et ai l s of o ur p ro posedNo De- C oupl i n g (NDC) theory o f con s t ituti v e r eleva nc e (wher e  the  specifici ty of the v ariabl es i s aga in made  e xplici t):  ( NDC) Φ1(X1 )  is const ituti vely re le vant  to  Ψ(S)if,a n d onl y if ,the re exists a  v a ri ab l e s et V  cont ai ning  �
 of_outcome (I),_the attempt to model_the relationship_between_Ψ and_Φ_constitutionally is empirically_rejected. If, say,_a follow-up study reveals_a surgical cause_of_Ψ, Φ is shown not to be a constituting set of Ψ, meaning that_the_common-cause model_prevails._By_contrast, outcome (II) gives preference_to modeling Φ as a_constituting set_of Ψ, notwithstanding the fact that the correlations_in_every expansion of_V3 can likewise be reproduced by a mere common-cause_model. The reason is that a_constitutional model not_only_reproduces_the empirical correlations but_also explains why the common-cause coupling_of Ψ and Φ is not_broken. That is, in case of outcome_(II), a constitutional model is preferable_over a pure common-cause model_because it_exceeds the latter in explanatory_power. While it_is a_structural necessity of_the constitutional model 3a that Ψ_and Φ remain_common-cause coupled in all expansions of_V3,_viz. that outcome_(II)_obtains,_the common-cause_model 3b provides_no_reason whatsoever_why_surgical causes of Ψ cannot be_found._The inference to constitution is thus inherently_abductive: constitutional models are_preferable_over pure causal models_because they explain both the_highly correlated behavior of phenomena and_their constituents_as well_as the impossibility to de-couple them.9 9Our proposal on how to_model the coupling of phenomena and_constituents bears certain similarities_to Causey's_proposal_on how to_interpret_biconditional dependencies_used as bridge laws in theory reductions._For Causey_(1977, chs. 2, 5), those dependencies_express attribute identities if_all_attempts at causally explaining them have_failed-for identity then is the only_explanation left standing (Causey 1977,_98-99)._(We_thank an anonymous reviewer for_indicating this parallel to us.) 14_Michael Baumgartner and_Lorenzo Casini By letting a complex instance_of_a variable set Φ designate the_occurrence_or process (in a particular spatiotemporal_region)_represented_by a complex value assignment_Φ1 = φ1,...,Φn = φn to_all elements of Φ, we can now introduce the_definitional details of_our proposed No De-Coupling (NDC)_theory_of_constitutive relevance (where the specificity of the variables is again_made explicit):_(NDC) Φ1(X1) is_constitutively relevant to Ψ(S) if, and only if, there exists_a variable set V containing �