 not fully infer any consequences of the meaning of φ▲ψ conferred by ▲I−rule. So to speak, elimination rules should be neither stronger nor weaker than the corresponding introduction rules. For such demand, he proposes the stability requirement. A little reflection shows that [intrinsic] harmony is an excessively modest demand.... The fact that the consequences we conventionally draw from [a formula] are in harmony with these acknowledged grounds shows only that we draw no consequences its meaning does not entitle us to draw. It does not show that we fully exploit that meaning, that we are accustomed to draw all those consequences we should be entitled to draw.... Such a balance is surely desirable.... The demand that such a condition be met goes beyond the requirement of harmony: we may call it'stability' (Dummett, 1991, p. 287) 42 Even though Dummett (1991, Ch. 13) dedicates one chapter of the Logical Basis of Metaphysics to stability, it is far from clear how the rigorous account of stability is to be filled in. There are two accounts of harmony to realize the idea of stability: Tennant's account of harmony as deductive equilibrium and generalized elimination account of harmony. Florian Steinberger (2009) suggests a counterexample to Tennant's account that it sanctions as harmonious obviously invalid rules for existential quantifier, i.e. an existential elimination rules which lack the usual variable restriction on the parameter. Tennant (2010) responses to the counterexample by the requirement of a proof of admissibility that the employment of structural rules, such as Cut, has to be legitimated by a proof of their admissibility.7 Steinberger (2011) rebuts again that once the requirement of admissibility is introduced, Tennant's account of harmony as deductive equilibrium no longer has any role to play in the realization of stability. Moreover, he said, It follows that harmony should be understood as a relational property of pairs of inference rules (and by extension of the logical constants governed by them) and not as a property of deductive systems. Consequently, the admissibility of CUT, a property of deductive system, is not a candidate for formalizing the intuitive notion of harmony. (Steinberger, 2011, p. 278) Tennant did not yet respond to Steinberger's objection. If Steinberger is right, Tennant's account of harmony as deductive equilibrium has a serious defect to realize the idea of stability. The other candidate account is the generalized
not fully infer any consequences of the meaning of φ ▲ ψ conferred by ▲ I−rule. therefore to address, elimination rules should be neither stronger nor weaker than the comparable introduction rules. For such demand, he propose the stability requirement. A small reflection shows that [ intrinsic ] harmony is an excessively minor demand.... The fact that the consequences we conventionally pull from [ a formula ] are in harmony with these acknowledged grounds shows only that we attract no consequences its meaning does not entitle us to draw. It does not express that we fully exploit that meaning, that we are accustomed to draw all those consequences we should be entitle to draw.... Such a balance is surely desirable.... The demand that such a condition be met belong beyond the requirement of harmony: we may call it'stability' (Dummett, 1991, p. 287) 42 Even though Dummett (1991, Ch. 13) dedicates one chapter of the Logical Basis of Metaphysics to stability, it is far from clear how the rigorous score of constancy is to be filled in. There are two accounts of harmony to realize the idea of stability: Tennant's account of harmony as deductive chemical equilibrium and generalized elimination history of harmony. Florian Steinberger (2009) suggests a counterexample to Tennant's account that it sanction as harmonious obviously invalid rules for existential quantifier, i.e. an existential elimination rules which miss the usual varying restriction on the parameter. Tennant (2010) responses to the counterexample by the necessity of a proof of admissibility that the employment of structural rules, such as Cut, has to be legitimated by a proof of their admissibility.7 Steinberger (2011) rebuts again that once the requirement of admissibility is introduced, Tennant's account of harmony as deductive equilibrium no longer receive any role to toy in the realization of constancy. Moreover, he said, It follows that harmony should be understood as a relational property of pairs of inference rules (and by extension of the coherent constants governed by them) and not as a property of deductive systems. Consequently, the admissibility of CUT, a place of deductive system, is not a candidate for formalizing the intuitive notion of harmony. (Steinberger, 2011, p. 278) Tennant did not yet react to Steinberger's objection. If Steinberger is correct, Tennant's account of harmony as deductive chemical equilibrium has a unplayful defect to realize the theme of constancy. The other candidate account is the generalize
 noh fully infer any conseqmences of the mecbing oh φ▲ψ confsrred by ▲I−rule. So to speak, eliminatiln rulew should be neither stfonger nog weaker rhan rhe corres'knding lutrodhgtion cules. For such cemand, he [roposes the sdacipity requirement. A little reflectiog shows tjat [intrinsic] rarmpgy ia an excessively modest demand.... The fact tiat the consequrnces we conventionally drww fgom [a formula] are ln harmony qith rhese acknowuedged groluds shows ohly that we draw no consequencer its meaning diew nlj entitle us to dgaw. It does not show dhat we fully exploit thet mwaning, that we are acrustomed to draw all those cotszquences we should be ebtitlgd to drad.... Suzh z ualznce id snrely desirzble.... The denand that such a comdynoon be met gkes berogd the requirement of harmony: we may canl jt'stability' (Dummett, 1991, p. 287) 42 Even though Dummett (1991, Ch. 13) dedycates one chapter of the Logical Basis of Metaphfsics go wtwcullty, it is far from clear how the rigorous accjhnu on stability is tj be filled ij. Yrere are two xccounca kf harmony to reallze the idea of stabijity: Tennant's account of harmont as deductine ewuilibrium and genzralized elioinajion avcount of harmony. Floricn Stejnberger (2009) skggests a zounterexample tu Tvnnatt's account that it sanctijns as hacmonipus obvkousky invwlid rules for cfistential quantifler, i.g. an efistential elimination rules which lack tix usual varianla rvstrictiou on tme parameter. Tegnant (2010) responsgs to the coungerexample by the requiremene of a proof mv admissibilmty that ehe wmpliyment uw structural riles, such as Cut, haw to be legitimatev by z proof of theix qdmissibility.7 Syeivbewgvr (2011) rqtuts again tvat uncd the fequirement uf acmissibility is intrmducsd, Tennant's accouny jf harmoby as dequctive equilobrium no longer hws anb role to pkay in the realization of stabilify. Moreovfr, me said, It fojloww that harmouy should be understood as a relational 'roperty of pairs of inderence rules (and bi ewtension of vhe lodical convtants governed by tyem) and not as a kroperty of deductive sgstems. Consfquently, the admissibility of CUT, a property of deductive system, is not a candivaee for formzlizong tve nntuitide nlvion of harmony. (Sneinberger, 2011, p. 278) Tennant did not yxt respond tj Steinberger's objection. If Xtdinberger is tight, Tennant's account of garmony ss deductive equilibrium has a xerious defect to realizc the ideq of atabilpjy. Vhe other candidate sccounc is tye geneealided
not fully infer any consequences of the φ▲ψ by ▲I−rule. to speak, elimination nor than the corresponding rules. For such he proposes the stability requirement. A reflection shows that [intrinsic] harmony is an excessively modest demand.... The fact that consequences we conventionally draw from [a formula] are in harmony with these acknowledged shows that draw consequences its meaning does not entitle us to draw. It does not show that we fully that meaning, that we are accustomed to draw those consequences we should entitled to draw.... Such a is desirable.... The that a be met goes the requirement of harmony: we may call it'stability' (Dummett, 1991, p. 287) 42 Even though Dummett (1991, 13) dedicates of the Basis Metaphysics stability, it is clear how the rigorous account of be filled in. There are two accounts of to realize idea of stability: Tennant's account of as deductive equilibrium and generalized elimination account of Florian Steinberger (2009) suggests a counterexample to Tennant's account that it sanctions as harmonious obviously for existential quantifier, i.e. existential elimination rules lack usual restriction the parameter. (2010) responses to the counterexample by the requirement of a proof admissibility that the employment of structural rules, such as Cut, be by a proof their admissibility.7 Steinberger (2011) again once the requirement of introduced, account deductive no has any role to in the realization of stability. he said, It follows as a relational property of pairs of inference (and by extension of the logical constants by them) and not as a property of deductive systems. Consequently, the of CUT, of deductive system, is not a candidate for the intuitive notion of (Steinberger, 2011, p. 278) Tennant did not yet respond Steinberger's If Steinberger right, Tennant's account harmony as deductive has a serious realize the of The is the generalized
 not fully infer any consequenCes of the meAning Of φ▲Ψ coNfErreD by ▲I−Rule. So to speak, eLIminAtion rules should be neitHer stRoNGer nOR wEaker Than the COrRESpoNdInG inTrODuCtion RulEs. For suCh demand, he ProPoSes the stabilITy RequiremenT. A lIttle reflectIon Shows tHaT [inTRinsiC] haRmony Is an exCEssiveLy modest dEmANd.... The fACt that tHE CoNseqUences we conventioNAlLY draw from [a formUla] are In HArMONy wIth These acknoWlEdged GRounds sHOwS ONLy tHAt we draw no conSequences itS MeaNing doEs Not ENtitle Us to dRaW. it dOes not show tHat wE fully expLoit thAT meaninG, That we aRe accuStoMed To drAW aLl ThoSe COnsEQuEncES we Should be EnTiTled tO draW.... sUCH a baLanCe is SurelY desirable.... The DemAnd tHAt sUch a cOnditIon bE mEt goeS beyonD the rEqUirement of harmoNy: we May call it'StaBiLitY' (DUmmetT, 1991, P. 287) 42 Even tHouGh DUmmett (1991, CH. 13) dedicaTEs oNe CHAPtEr of the Logical BasiS oF mEtAphysics To stabILiTy, IT is far frOm CleAr hoW THe rigOrouS AcCount of sTabiliTY iS tO be fillEd In. TherE aRe tWo aCcounTS of hArmony To realizE the iDEa of stability: TENnant's account OF hARMoNY as dEduCtive equiliBriuM And gEnerALiZed ELiminAtion AcCOuNT of harmony. Florian StEiNbergeR (2009) suggEsts a countereXample to TeNNANt's accouNt thAT iT Sanctions as harMonioUs obviouslY Invalid rUles fOr existeNtial quanTIFier, i.e. an ExiSteNtiAl eLIMiNation rules whICH lacK tHe usual VarIable reStrIctIon On tHe Parameter. tennant (2010) rEsPoNsEs To tHe couNTerexampLe By tHe ReqUiremENt of a pRoof oF admIsSiBIliTy that tHE eMPLoymEnT oF strUctUrAl rulEs, suCH as cut, has tO be legitiMatED by a PrOoF of theiR admissibilitY.7 STeinberger (2011) ReButS again THAt once thE requirement of admissibiLIty is inTroDuced, tennAnt's accouNt oF harmoNy aS DeductIve equIlibrIuM no LONger hAS AnY roLe To play in thE REalIzatiOn Of stAbility. moreover, he said, It foLLowS that harmony sHouLd be UNDeRstOOd AS a rElATioNAL property of pairS of inferenCe RUlEs (and by extENsiOn Of the loGical coNstanTS governEd by them) aNd not as a pRoPertY OF deDuctive sysTems. ConsEquently, tHE admiSSiBilitY of cUT, a prOpErtY of deDuctivE SysTem, is Not a caNdIdate fOr forMaLizing thE intuitive notion of harmoNy. (SteiNbergEr, 2011, p. 278) tennant diD noT Yet Respond to steiNberger's obJecTioN. If StEinBErger Is riGHt, tenNAnt's aCcouNT of harmonY As DedUCTiVe equilibriUM HAs a SerioUs dEFect to RealIze the idea of stabiLIty. The other canDidaTE AccOunT Is thE gEneralized
 not fully infer any conse quences of  themea nin gof φ ▲ψ c onferred by ▲I − rule . So to speak, elimina tionru l es s h ou ld be  neithe r  s t r ong er  n orwe a ke r tha n t he corr espondingint ro duction rule s .For such d ema nd, he propo ses  the s ta bil i ty re qui remen t. A l i ttle r eflection  s h ows th a t [intr i n si c] h armony is an exce s si v ely modest dem and... .T he f act  th at the con se quenc e s we co n ve n t i ona l ly draw from[a formula] are  in ha rm ony with t heseac k now ledged grou ndsshows onl y that we draw no cons equenc esits  mea n in gdoe sn ote nt itl e  us  to draw .It  does  not s h o w th atwe f ullyexploit thatmea ning ,  th at we  areaccu st omedto dra w all  t hose consequenc es w e shouldbeen tit le d tod raw... . S uch  a bala nce iss ure ly d e si rable.... The dema nd t ha t such a  condi t io nb e met go es  be yond t he re quir e me nt of ha rmony: we  m ay call  i t'stab il ity ' ( Dumme t t, 1 991, p . 287) 4 2 Eve n  though Dummet t  (1991, Ch. 1 3 )d e di c ates  on e chapter o f th e  Log ical Ba sis of Me taphy si c st o stability, it isfa r from  clea r how the rig orous acco u n t  of stab ilit y  i s  to be filledin. T here are t w o accoun ts of  harmony  to reali z e  the ide a o f s tab ili t y :Tennant's acc o u nt o fharmony  as  deduct ive  eq uil ibr iu m and gen eralized  e li mi na tio n acc o unt of h ar mon y.  Fl orian Steinb erger  (20 09 )s ugg ests ac ou n t erex am pl e to  Te nn ant's  acc o unt  that i t sanctio nsa s ha rm on ious ob viously inval id  rules for  e xis tentia l quantifi er, i.e. an existential elimina tio n rul es w hich lack  th e usua l v a riable  restr ictio nont h e par a m et er.  T ennant (20 1 0 ) r espon se s to  the co unterexample by th e  re quirement ofa p roof o fadm i ss i bil it y  th a t  the employment  of struct ur a lrules, suc h  as  C ut, has  to belegit i mated b y a proof  of their  a dmis s i bil ity.7 Stei nberger(2011) re b uts a g ai n tha t o nce th ereq uirem ent of adm issib ilityis  intro duced ,Tennant' s account of harmony as  deduc tiveequ ilibriumnol ong er has an y ro le to play  in  th e rea liz a tionof s t ab ili t y. Mo reov e r, he sai d ,Itf o ll ows that ha r m o nyshoul d b e  under stoo d as a relational property of pa irso f  in fer e nceru les (and by ex ten si o n  of thelo gical const ants gov er n ed by  them)  and n ot as a p ro p erty o f de duc tive syst ems .C onseque nt ly ,  the a dmis si bility  of CU T , ap r operty of deduct ive s y s tem,i s n ot aca ndidate forformalizin g the intui tive n otio n ofharmony .(Stein ber ge r, 2011, p .  278) Ten nantdid not  y et r esp ond to  Ste i n berge r'sob jec tion. IfS t ei n be rg e r i s ri ght,Te nnan t's accou n t of har mon y  as ded uc tiv e equili b ri u m  has a ser iou s def e c t to reali z e th e  i d ea of  stabi lity.The oth e r c an didateacc o u nt is the  generali z ed
 not_fully infer_any consequences of the_meaning of_φ▲ψ_conferred by_▲I−rule._So to speak,_elimination rules should_be neither stronger nor_weaker than the_corresponding_introduction rules. For such demand, he proposes the stability requirement. A little reflection shows_that_[intrinsic] harmony_is_an_excessively modest demand.... The fact_that the consequences we conventionally_draw from_[a formula] are in harmony with these acknowledged_grounds_shows only that_we draw no consequences its meaning does not entitle_us to draw. It does not_show that we_fully_exploit_that meaning, that we_are accustomed to draw all those_consequences we should be entitled to_draw.... Such a balance is surely desirable...._The demand that such a condition_be met goes beyond the_requirement of_harmony: we may call it'stability'_(Dummett, 1991, p._287) 42_Even though Dummett_(1991, Ch. 13) dedicates one chapter_of the Logical_Basis of Metaphysics to stability, it_is_far from clear_how_the_rigorous account_of stability is_to_be filled_in._There are two accounts of harmony_to_realize the idea of stability: Tennant's account_of harmony as deductive_equilibrium_and generalized elimination account_of harmony. Florian Steinberger (2009)_suggests a counterexample to Tennant's account_that it_sanctions as_harmonious obviously invalid rules for existential quantifier, i.e. an existential elimination_rules which lack the usual variable_restriction on the parameter._Tennant (2010)_responses_to the counterexample_by_the requirement_of a proof of admissibility that the_employment of_structural rules, such as Cut, has_to be legitimated by_a_proof of their admissibility.7 Steinberger (2011)_rebuts again that once the requirement_of admissibility is introduced, Tennant's_account_of_harmony as deductive equilibrium no_longer has any role to play_in the realization_of stability. Moreover, he said, It follows_that_harmony should be understood as a_relational_property of pairs of inference rules_(and_by_extension of the logical constants_governed by them) and not as_a property of deductive systems. Consequently, the admissibility of_CUT, a property_of deductive system, is not_a_candidate_for formalizing the intuitive notion of harmony. (Steinberger, 2011, p._278) Tennant_did not yet_respond to Steinberger's objection. If Steinberger is right, Tennant's account_of harmony as deductive equilibrium has a_serious defect to realize the idea of stability. The other candidate_account is the generalized