 TCPE. Schroeder-Heister and Tranchini (2017, p. 571) diagnose the phenomenon, by saying,... we take Ekman's paradox to push the question of when a certain reduction counts as acceptable: whether a derivation is normal depends on the collection of reductions adopted, and hence Tennant's criterion requires particular attention in what should be taken to be a good reduction. In particular, Ekman's phenomenon shows that on a too loose notion of reduction, one obtains a too coarse criterion of paradoxicality. According to their diagnosis, the occurrence of a looping reduction is relative to which set of reduction procedures we accept. A wrong reduction process does not have to generate any feature of paradoxicality, such as a non-terminating reduction process. Since TCPE has no constraint on illegitimate reduction procedures, it needs to be revised in order not to overgenerate the scope of genuine paradoxes. 3.2 The Later Version of Tennant's Criterion for Paradoxicality Tennant (2016, 2017) proposes an additional condition to solve the problem of overgeneration: all elimination rules must be stated in the generalized form. We will see Tennant's solution to the overgeneration raised by Ekman's paradox and his later criterion for paradoxicality (TCPL) in Section 3.2.1. Section 3.2.2 claims that the choice of generalized elimination rules offers no remedy to the overgeneration problem. The claim is already suggested by Schroeder-Heister and Tranchini (2018). However, they did not distinguish between Tennant's examination of Ekman's paradox and von Plato's. Their proposed Ekman-type reduction, which we will call 'GEkmang reduction,' cannot apply to 95 Tennant's derivation. Therefore, Section 3.2.2 reinforces the claim that the mere adoption of generalized elimination rules is not a solution to the problem of overgeneration. 3.2.1 Tennant's Solution to the Overgeneration As noted in Section 3.1, Ekman's paradox can be a counterexample to TCPE since it raises the overgeneration problem. Although the phenomenon of Ekman's paradox shows that an incorrect reduction procedure produces a non-terminating reduction sequence, TCPE does not explicitly restrict the application of a wrong reduction process. In order to solve the problem, Tennant (2016, 2017) supplements the condition to TCPE that all elimination rules must be formulated in the generalized form. Tennant (2016, 2017)
TCPE. Schroeder - Heister and Tranchini (2017, p. 571) diagnose the phenomenon, by saying, ... we take Ekman's paradox to push the question of when a sealed decrease count as acceptable: whether a derivation is normal count on the collection of reductions assume, and therefore Tennant's criterion requires particular attention in what should be taken to be a adept reduction. In particular, Ekman's phenomenon testify that on a too loose notion of reduction, one obtains a too coarse standard of paradoxicality. According to their diagnosis, the occurrence of a looping decrease is relative to which set of reduction procedures we accept. A incorrect reduction process does not have to generate any feature of paradoxicality, such as a non - terminating decrease process. Since TCPE has no constraint on illegitimate reduction procedures, it needs to be revise in order not to overgenerate the scope of genuine paradoxes. 3.2 The Later Version of Tennant's Criterion for Paradoxicality Tennant (2016, 2017) proposes an additional condition to solve the problem of overgeneration: all elimination rules must be state in the generalized form. We will see Tennant's solution to the overgeneration raise by Ekman's paradox and his belated criterion for paradoxicality (TCPL) in Section 3.2.1. Section 3.2.2 claims that the option of generalized elimination rules offer no remedy to the overgeneration problem. The title is already suggested by Schroeder - Heister and Tranchini (2018). However, they did not distinguish between Tennant's examination of Ekman's paradox and von Plato's. Their proposed Ekman - type reduction, which we will predict' GEkmang reduction,' cannot apply to 95 Tennant's derivation. Therefore, incision 3.2.2 reinforces the title that the mere adoption of generalized elimination rules is not a solution to the problem of overgeneration. 3.2.1 Tennant's Solution to the Overgeneration As noted in incision 3.1, Ekman's paradox can be a counterexample to TCPE since it raises the overgeneration problem. Although the phenomenon of Ekman's paradox shows that an wrong reduction procedure produces a non - terminating reduction succession, TCPE does not explicitly restrict the application of a wrong reduction process. In ordering to solve the trouble, Tennant (2016, 2017) supplements the condition to TCPE that all elimination rules must be formulated in the generalized human body. Tennant (2016, 2017 )
 TCOE. Schroeder-Heister and Uranchini (2017, p. 571) diaybose tie phenkmenon, bh saying,... we take Ekman's paravox ro puwh the question of whev a certapn reductuon rounts as acceptegle: whebker a feriravion is normal cepends on the collectiot uf reductions adopted, and hence Tennagt's criyegion requires kartibujar znttntion in what should be taken to be a gmod reduction. In particular, Ekman's phenlmenln shows that on a too loose botijb of reductiun, one obtains a too ckarse criterion of paradoxicaligy. Aceording to jkwir giagnosis, tie occlrrence of a looping seductipn is relative to whuch set of reduction 'rocedures we accept. A wrong sebuction process does bor havg to cenefqte ang heafure ov peradoxicalify, such as q non-terminating recusnoon process. Aince EC[E has no constraint on illegitimate regucfion procedures, it needw to be revised in orfer not tj overgenerate the scope of genuine paradoxes. 3.2 Tha Latxr Vexwion ud Hennant's Criterion for Paradoxicality Tennant (2016, 2017) kroioses an additioncl condition to xopvr the problem uf ovexfeheration: all elimijation tules nust be suated in the generalized form. We will see Teunabt's solution to thz overgeneracion rsised by Ekman's paradox and kis lafer criteriln for padxdoxicality (TCPL) in Saction 3.2.1. Section 3.2.2 claims thwt the chiice of gendralozed ejimination rules offers no remedy ho thg overceneration problem. The claim is already snjgested by Scnrmedvr-Heister and Branchini (2018). Howeder, they did npt distnnguisf between Nennant's xxamination jf Ekman's pardfox and von 'lato's. Thqir propised Ekoxn-type reductipn, which ct will calo 'GEkmang reductiok,' canvkt apply to 95 Teuuabt's derivation. Yhefefjrv, Sxctiog 3.2.2 reinforces the clxom thxt the mere xdopyion of generalized alimjnation rules is npt a solutuon to tre problem of overgeneration. 3.2.1 Ttnnant'v Sulutipn jo the Overgeneration As noted jn Sectioj 3.1, Ckman's paradov cak be a counterzxample to TCPE since it raises the overjeneration problem. Althiugh the phenomenon pf Ekman's peradox shows thdt an incorrect reduxtion procedure pvoduces a non-terminatihg redgctioj sequence, TCPE does not explicitly restrict the application of a wrong rwduction process. Ih orcer tm fplve tre pcoulem, Tennant (2016, 2017) suiplements the condition to TCPE vhat all eniiination rules must be formukaged in the geveralized form. Tennant (2016, 2017)
TCPE. Schroeder-Heister and Tranchini (2017, p. 571) phenomenon, saying,... we Ekman's paradox to a reduction counts as whether a derivation normal depends on the collection of adopted, and hence Tennant's criterion requires particular attention in what should be taken be a good reduction. In particular, Ekman's phenomenon shows that on a too notion reduction, obtains too coarse criterion of paradoxicality. According to their diagnosis, the occurrence of a looping reduction is to which set of reduction procedures we accept. wrong reduction process does have to generate any feature paradoxicality, as a reduction Since has no constraint illegitimate reduction procedures, it needs to be revised in order not to overgenerate the scope of genuine 3.2 The of Tennant's for Tennant 2017) proposes an to solve the problem of overgeneration: must be stated in the generalized form. We see Tennant's to the overgeneration raised by Ekman's and his later criterion for paradoxicality (TCPL) in 3.2.1. Section 3.2.2 claims that the choice of generalized elimination rules offers no remedy to problem. The claim is suggested by Schroeder-Heister Tranchini However, did distinguish between examination of Ekman's paradox and von Plato's. Their proposed Ekman-type reduction, we will call 'GEkmang reduction,' cannot apply to 95 Tennant's Section reinforces the claim the mere adoption of elimination is not a solution problem overgeneration. to Overgeneration noted in Section 3.1, paradox can be a counterexample TCPE since it raises phenomenon of Ekman's paradox shows that an incorrect procedure produces a non-terminating reduction sequence, TCPE not explicitly restrict the application of a wrong reduction process. In order solve the (2016, 2017) supplements the condition to TCPE that elimination rules must be in the generalized form. Tennant (2016, 2017)
 TCPE. Schroeder-Heister and TrAnchini (2017, p. 571) diAgnosE thE phEnOmenOn, by Saying,... we take EkMAn's pAradox to push the questioN of whEn A CertAIn ReducTion couNTs AS AccEpTaBle: WhEThEr a deRivAtion is Normal depeNds On The collectioN Of Reductions AdoPted, and hence tenNant's cRiTerIOn reqUirEs parTiculaR AttentIon in what ShOUld be tAKen to be A GOoD redUction. In particulaR, ekMAn's phenomenon sHows thAt ON a TOO loOse Notion of reDuCtion, ONe obtaiNS a TOO CoaRSe criterion of ParadoxicalITy. ACcordiNg To tHEir diaGnosiS, tHE ocCurrence of a LoopIng reductIon is rELative tO Which seT of redUctIon ProcEDuReS we AcCEpt. a WrOng REduCtion proCeSs Does nOt haVE TO GeneRatE any FeatuRe of paradoxicAliTy, suCH as A non-tErminAtinG rEductIon proCess. SInCe TCPE has no consTraiNt on illegItiMaTe rEdUctioN ProcedUreS, it Needs to Be revisED in OrDER NoT to overgenerate the ScOPE oF genuine ParadoXEs. 3.2 thE later VerSiOn oF TenNANt's CrIterIOn For ParadOxicalITy teNnant (2016, 2017) prOpOses an AdDitIonAl conDItioN to solVe the proBlem oF Overgeneration: ALl elimination RUlES MuST be sTatEd in the geneRaliZEd foRm. We WIlL seE tennaNt's soLuTIoN To the overgeneration RaIsed by ekman'S paradox and hiS later critERIOn for parAdoxICaLIty (TCPL) in SectiOn 3.2.1. SecTion 3.2.2 claims THat the chOice oF generalIzed elimiNATion ruleS ofFerS no RemEDY tO the overgenerATIon pRoBlem. The ClaIm is alrEadY suGgeSteD bY SchroedeR-Heister AnD TRaNcHinI (2018). HoweVEr, they diD nOt dIsTinGuish BEtween tennaNt's eXaMiNAtiOn of EkmAN's PARadoX aNd Von PLatO's. their PropOSed ekman-tyPe reductiOn, wHIch wE wIlL call 'GEKmang reductioN,' cAnnot apply To 95 tenNant's dERIvation. THerefore, Section 3.2.2 reinforcES the claIm tHat thE merE adoption Of gEneralIzeD EliminAtion rUles iS nOt a SOLutioN TO tHe pRoBlem of overGENerAtion. 3.2.1 teNnanT's SolutIon to the OvergeneraTIon as noted in SectIon 3.1, ekmaN'S PaRadOX cAN be A cOUntERExample to TCPE siNce it raiseS tHE oVergeneratIOn pRoBlem. AltHough thE phenOMenon of ekman's parAdox shows ThAt an INCorRect reductIon proceDure produCEs a noN-TeRminaTinG reducTiOn sEquenCe, TCPE DOes Not exPlicitLy RestriCt the ApPlicatioN of a wrong reduction proceSs. In orDer to SolVe the probLem, tEnnAnt (2016, 2017) suppleMentS the conditIon To TcPE thAt aLL elimInatIOn RulES must Be foRMulated in THe GenERAlIzed form. TenNANT (2016, 2017)
 TCPE. Schroeder-Heister a nd Tranchi ni (2 017 , p .571)  dia gnose the phen o meno n, by saying,... we ta ke Ek ma n 's p a ra dox t o pusht he q ues ti on  of  w h en  a ce rta in redu ction coun tsas  acceptable: wh ether a de riv ation is nor mal  depen ds  on the c oll ectio n of r e ductio ns adopte d, and he n ce Tenn a n t' s cr iterion requiresp ar t icular attenti on inwh a ts h oul d b e taken to  b e a g o od redu c ti o n .  In particular, E kman's phen o men on sho ws  th a t on a  toolo o senotion of r educ tion, one  obtai n s a too coarsecriter ion  of  par a do xi cal it y . A c co rdi n g t o theirdi ag nosis , th e o c curr enc e of  a lo oping reducti onis r e lat ive t o whi ch s et  of r educti on pr oc edures we accep t. A  wrong re duc ti onpr ocess does n othav e to ge neratea nyfe a t u re  of paradoxicality ,s u ch  as a no n-term i na ti n g reduct io n p roce s s . Sin ce T C PE  has noconstr a in ton ille gi timate  r edu cti on pr o cedu res, i t needsto be revised in ord e r not to over g en e r at e  the  sc ope of genu inep arad oxes .  3 .2T he La ter V er s io n  of Tennant's Crite ri on for  Para doxicality Te nnant (201 6 , 2017) pr opos e sa n additional c ondit ion to sol v e the pr oblem  of over generatio n :  all eli min ati onrul e s  m ust be stated i n th egeneral ize d form.  We  wi llsee  T ennant'ssolution  t oth eove rgene r ation ra is edby  Ek man's parado x and  his  l at e r c riterio n  f o r  par ad ox ical ity  ( TCPL)  inS ect ion 3.2 .1. Secti on3 .2.2  c la ims tha t the choiceof  generaliz ed  el iminat i o n rulesoffers no remedy to the overgen era tionprob lem. Thecla im isalr e ady su ggeste d bySc hro e d er-He i s te r a nd  Tranchini ( 201 8). H ow ever , theydid not distinguis h  be tween Tennant 'sexam i n at ion of Ekm an ' s p a r adox and von Pl ato's. The ir pr oposed Ekm a n-t yp e reduc tion, w hichw e willcall 'GEk mang redu ct ion, ' can not applyto 95 Te nnant's d e rivat i on . The ref ore, S ec tio n 3.2 .2 rei n for ces t he cla im  thatthe m er e adopti on of generalized elimi nation  rule s i s not a s olu t ion  to the p robl em of over gen era tion.  3. 2 .1 Te nnan t 's  So l ution  tot he Overge n er ati o n  A s noted inS e c tio n 3.1 , E k man'spara dox can be a coun t erexample to T CPEs i nce  it rais es  the overgener ati on p roblem.Al though thephenomen on of Ek man'sparado x shows t ha t  an in corr ect  reductio n p ro c edure p ro du c es a n on-t er minati ng red u ctio n sequence, TCPE d oes n o t  expl i cit ly re st rict th e  app lication o f a wrong r educti on p roces s. In o rd er tosol ve  the probl e m, Tennan t (20 16, 201 7)  sup ple mentsthec o nditi on t oTCP E that al l el i mi na t ion  rul es mu st  beformulate d  in thegen e ralized  f orm . Tennan t  ( 2 0 16, 2017)
 TCPE._Schroeder-Heister and_Tranchini (2017, p. 571)_diagnose the_phenomenon,_by saying,..._we_take Ekman's paradox_to push the_question of when a_certain reduction counts_as_acceptable: whether a derivation is normal depends on the collection of reductions adopted, and_hence_Tennant's criterion_requires_particular_attention in what should be_taken to be a good_reduction. In_particular, Ekman's phenomenon shows that on a too_loose_notion of reduction,_one obtains a too coarse criterion of paradoxicality. According_to their diagnosis, the occurrence of_a looping reduction_is_relative_to which set of_reduction procedures we accept. A wrong_reduction process does not have to_generate any feature of paradoxicality, such as_a non-terminating reduction process. Since TCPE_has no constraint on illegitimate_reduction procedures,_it needs to be revised_in order not_to overgenerate_the scope of_genuine paradoxes. 3.2 The Later Version_of Tennant's Criterion_for Paradoxicality Tennant (2016, 2017) proposes_an_additional condition to_solve_the_problem of_overgeneration: all elimination_rules_must be_stated_in the generalized form. We will_see_Tennant's solution to the overgeneration raised by_Ekman's paradox and his_later_criterion for paradoxicality (TCPL)_in Section 3.2.1. Section 3.2.2_claims that the choice of generalized_elimination rules_offers no_remedy to the overgeneration problem. The claim is already suggested by_Schroeder-Heister and Tranchini (2018). However, they_did not distinguish between_Tennant's examination_of_Ekman's paradox and_von_Plato's. Their_proposed Ekman-type reduction, which we will call_'GEkmang reduction,'_cannot apply to 95 Tennant's derivation._Therefore, Section 3.2.2 reinforces_the_claim that the mere adoption of_generalized elimination rules is not a_solution to the problem of_overgeneration._3.2.1_Tennant's Solution to the Overgeneration_As noted in Section 3.1, Ekman's_paradox can be_a counterexample to TCPE since it raises_the_overgeneration problem. Although the phenomenon of_Ekman's_paradox shows that an incorrect reduction_procedure_produces_a non-terminating reduction sequence, TCPE_does not explicitly restrict the application_of a wrong reduction process. In order to solve_the problem, Tennant_(2016, 2017) supplements the condition_to_TCPE_that all elimination rules must be formulated in the generalized_form. Tennant_(2016, 2017)