 any language cannot have its truth-predicate, T (x). Any sentences which are equivalent to ¬T (⌜Φ⌝) are not to be formulated in LO. There is no liar sentence in LO. 3It we regard a formal language as a set of expressions, LO is a proper subset of LM, so to speak, LO ⊂ LM. 9 Furthermore, because any language has no truth-predicate, no liar sentence exist in any language. Therefore, there is no Liar paradox. Tarski's stricture against the semantically closed language may be the premise-rejection solution to the Liar paradox in the sense that it prevents to use the liar sentence. Of course, Tarski's stricture may be regarded as the reasoning-rejection solution to the Liar paradox because his stricture does not allow the inference from ¬T (⌜φ⌝) to φ and vice versa in the object language. Hence, his view can be interpreted as the premise-rejection or the reasoning-rejection solution if his stricture is the solution to the paradoxes. As we have seen in this subsection, traditional approaches to Russell's and the Liar paradoxes may be considered to be the premise-rejection or the reasoning-rejection or both. In the next subsection, we will investigate problems of traditional responses to the paradoxes and dialetheism. 1.1.2 Problems of Traditional Responses and Dialetheism In this subsection, after we introduce problems of traditional responses to the liar and Russell's paradox, we will briefly introduce dialetheism which says that a true contradiction exists. Dialetheism may be an alternative solution to the paradoxes, however we shall argue that not every logician should accept it as the primary response to the paradoxes. With respect to the Liar paradox, Tarski's stricture, while regarding it as the response to the Liar paradox, has been subject to some criticisms. The main criticism against Tarski's solution is made by Saul Kripke (1975, pp. 690–698) that whether or not a sentence is paradoxical is dependent not only on formal properties which are intrinsic to the syntax and semantics of the sentence, but also on empirical facts. In addition, it is not easy to place non-paradoxical claims within Tarski's syntactically fixed set of levels. (a) Everything Kim Jong-un says in his
any language cannot have its truth - predicate, T (x). Any sentences which are equivalent to ¬T (⌜ Φ ⌝) are not to be give voice in LO. There be no liar sentence in LO. 3It we regard a formal lyric as a set of expressions, LO is a proper subset of LM, indeed to talk, LO ⊂ LM. 9 Furthermore, because any language has no truth - predicate, no liar sentence exist in any terminology. Therefore, there is no Liar paradox. Tarski's stenosis against the semantically closed language may be the premise - rejection solution to the Liar paradox in the sense that it prevents to use the liar sentence. Of course, Tarski's stenosis may be regarded as the reasoning - rejection solution to the Liar paradox because his stricture does not allow the inference from ¬T (⌜ φ ⌝) to φ and frailty versa in the object language. Hence, his view can be interpreted as the premise - rejection or the reasoning - rejection solution if his stenosis is the solution to the paradoxes. As we have visualize in this subsection, traditional approaches to Russell's and the Liar paradoxes may be considered to be the premise - rejection or the reasoning - rejection or both. In the future subsection, we will investigate problems of traditional responses to the paradoxes and dialetheism. 1.1.2 Problems of Traditional Responses and Dialetheism In this subsection, after we introduce problems of traditional responses to the liar and Russell's paradox, we will briefly introduce dialetheism which says that a true contradiction exists. Dialetheism may be an alternative solution to the paradoxes, however we shall argue that not every logician should accept it as the primary response to the paradox. With esteem to the Liar paradox, Tarski's stricture, while involve it as the response to the Liar paradox, has been subject to some criticisms. The main criticism against Tarski's solution is cook by Saul Kripke (1975, pp. 690–698) that whether or not a sentence is paradoxical is dependent not only on formal property which are intrinsic to the syntax and semantics of the sentence, but also on empirical facts. In summation, it is not easy to place non - paradoxical claims within Tarski's syntactically fixed hardening of levels. (a) Everything Kim Jong - un suppose in his
 anj language cannot have ius truth-predicate, T (x). Anb sentehces whizh are equivalent to ¬T (⌜Φ⌝) are iot ro be formulated in LO. Therd is no lpar sentebce mn LO. 3It we regacs a formal lahnuage es a set of exptessions, LO hs a proper sutsdt of LM, so to speak, LO ⊂ LM. 9 Furthermjre, becsude any languagg has go tdltm-predicate, no liar sentence exisf in anj language. Therefpre, there is no Liar paradlx. Twrski's stricture ahainst the wemagrically closdd languagt kay be the premise-rejection solution to tfe Licr paradox un thf sense that it pgevents to usc the lhar senyence. Of coursc, Tarvki'w stricture may be rejarded as the reasonyng-rejecthou solution to the Liae paradmx bacaurw hks atcicfure dles not allow the inferebce from ¬T (⌜φ⌝) to φ and vybr versa in tge objqce language. Hence, his view can be interpgetes as the premise-rejectiin or the reasoning-reuection sjlution if his stricture is the solution to the pdradoeer. Aw rd hwve seen in this subsection, traditional approwdhts no Russell's and tme Liar paradoxes kaj ng considered tu be tks lremise-rejection og the rgasonibg-rejectijn ot both. In the next subsectiin, we will iuvewtigate problems oy traditionau rexponsrs to the paradoxes and diametheism. 1.1.2 Pgoblems or Traditional Resoonxev and Dialetheism In this fubsectioi, aftzr we ingrodoce proflems of tgaditlmnal responses to hhe lnar atd Russell'd paradox, we will briefly introvnce dialetheixm whpch says chat a true contradyction exists. Bialethensm mah be an alnernative solution tj the paradoxad, however we shall awgue thar not exdry logician snould accvpu it as thw primary response to fhe paradoxes. Wnuh twspect to the Kiaf pwrwdpx, Darski's striwturd, wfole rdgarding it xs tne response to the Lhar laradox, has been sibmect to sime critycisms. The maon criticism againdt Tacski's rolutoon is made by Saul Kripke (1975, pp. 690–698) tgat whethfr jr not a seneencc is paradoxiccl is dependent not only on formal propecties which are intrinsuc to the syntax anb xemantics oh the fentence, tut also on empiricao facts. In additipn, it is not easy to llace ton-pagadoxical claims within Tarski's syntactically fixed set of levels. (a) Everyrhing Kim Jong-un szys on hiv
any language cannot have its truth-predicate, T sentences are equivalent ¬T (⌜Φ⌝) are LO. is no liar in LO. 3It regard a formal language as a of expressions, LO is a proper subset of LM, so to speak, LO LM. 9 Furthermore, because any language has no truth-predicate, no liar sentence exist any Therefore, is Liar paradox. Tarski's stricture against the semantically closed language may be the premise-rejection solution to the paradox in the sense that it prevents to the liar sentence. Of Tarski's stricture may be regarded the solution to Liar because stricture does not the inference from ¬T (⌜φ⌝) to φ and vice versa in the object language. Hence, his view be interpreted premise-rejection or reasoning-rejection if stricture is the the paradoxes. As we have seen traditional approaches to Russell's and the Liar paradoxes be considered be the premise-rejection or the reasoning-rejection both. In the next subsection, we will investigate of traditional responses to the paradoxes and dialetheism. 1.1.2 Problems of Traditional Responses and Dialetheism subsection, after we introduce of traditional responses the and paradox, will briefly dialetheism which says that a true contradiction exists. Dialetheism may be alternative solution to the paradoxes, however we shall argue that logician accept it as primary response to the With to the Liar paradox, while it to Liar has been subject to criticisms. The main criticism against solution is made by that whether or not a sentence is paradoxical dependent not only on formal properties which intrinsic to the syntax and semantics of the sentence, but also on facts. In is not easy to place non-paradoxical claims within syntactically fixed set of (a) Everything Kim Jong-un says in his
 any language cannot have its tRuth-predicAte, T (x). any SenTeNces WhicH are equivalent TO ¬T (⌜Φ⌝) aRe not to be formulated in Lo. TherE iS No liAR sEntenCe in LO. 3IT We REGarD a FoRmaL lANgUage aS a sEt of expRessions, LO Is a PrOper subset of lm, sO to speak, LO ⊂ lM. 9 FUrthermore, beCauSe any lAnGuaGE has nO trUth-prEdicatE, No liar Sentence eXiST in any LAnguage. tHErEforE, there is no Liar parADoX. tarski's strictuRe agaiNsT ThE SEmaNtiCally closeD lAnguaGE may be tHE pREMIse-REjection solutIon to the LiaR ParAdox in ThE seNSe that It preVeNTs tO use the liar SentEnce. Of couRse, TarSKi's striCTure may Be regaRdeD as The rEAsOnIng-ReJEctIOn SolUTioN to the LiAr PaRadox BecaUSE HIs stRicTure Does nOt allow the infEreNce fROm ¬T (⌜Φ⌝) to φ aNd vicE verSa In the Object LanguAgE. Hence, his view caN be iNterpreteD as ThE prEmIse-reJEction Or tHe rEasoninG-rejectIOn sOlUTIOn If his stricture is thE sOLUtIon to the ParadoXEs. as WE have seeN iN thIs suBSEctioN, traDItIonal appRoacheS To ruSsell's aNd The LiaR pAraDoxEs may BE conSidereD to be the PremiSE-rejection or thE Reasoning-rejeCTiON Or BOth. IN thE next subsecTion, WE wilL invEStIgaTE probLems oF tRAdITional responses to thE pAradoxEs and Dialetheism. 1.1.2 PrOblems of TrADITional ReSponSEs ANd Dialetheism IN this Subsection, AFter we inTroduCe probleMs of tradiTIOnal respOnsEs tO thE liAR AnD Russell's paraDOX, we wIlL brieflY inTroduce DiaLetHeiSm wHiCh says thaT a true coNtRaDiCtIon ExistS. dialetheIsM maY bE an AlterNAtive sOlutiOn to ThE pARadOxes, howEVeR WE shaLl ArGue tHat NoT everY logICiaN should Accept it aS thE PrimArY rEsponse To the paradoxeS. WIth respect To The liar paRADox, TarskI's stricture, while regardiNG it as thE reSponsE to tHe Liar parAdoX, has beEn sUBject tO some cRiticIsMs. THE Main cRITiCisM aGainst TarsKI'S soLutioN iS madE by Saul kripke (1975, pp. 690–698) that whetheR Or nOt a sentence is ParAdoxICAl Is dEPeNDenT nOT onLY On formal propertIes which arE iNTrInsic to the SYntAx And semaNtics of The seNTence, buT also on emPirical faCtS. In aDDItiOn, it is not eAsy to plaCe non-paraDOxicaL ClAims wIthIn TarsKi'S syNtactIcally FIxeD set oF levelS. (a) everytHing KIm jong-un saYs in his
 any language cannot haveits truth- predi cat e,T(x).  Any  sentences whi c h ar e equivalent to ¬T (⌜Φ ⌝) ar en ot t o  b e for mulated in L O.Th er e i sn oliarsen tence i n LO. 3Itwere gard a forma l  l anguage as  aset of expre ssi ons, L Oisa  prop ersubse t of L M , so t o speak,LO ⊂ LM.9  Furthe r m or e, b ecause any langua g eh as no truth-pr edicat e, no l iar  se ntence exi st  in a n y langu a ge . T her e fore, there i s no Liar p a rad ox. Ta rs ki' s  stric tureag a ins t the seman tica lly close d lang u age may be thepremis e-r eje ctio n  s ol uti on tot he  Li a r p aradox i nth e sen se t h a t it p rev ents  to u se the liar s ent ence .  Of  cour se, T arsk i' s str icture  maybe  regarded as th e re asoning-r eje ct ion  s oluti o n to t heLia r parad ox beca u sehi s s tr icture does not al lo w th e infere nce fr o m¬T (⌜φ⌝) to  φ  an d vi c e  vers a in th e object  langu a ge .Hence,hi s view  c anbeinter p rete d as t he premi se-re j ection or ther easoning-reje c ti o n  s o luti onif his stri ctur e  isthes ol uti o n tothe p ar a do x es. As we have seen  i n this  subs ection, tradi tional app r o a ches toRuss e ll ' s and the Liar  para doxes mayb e consid eredto be th e premise - r ejection  or  th e r eas o n in g-rejection o r both .In thenex t subse cti on,  we  wi ll  investig ate prob le ms  o ftra ditio n al respo ns esto  th e par a doxesand d iale th ei s m.1.1.2 P r ob l e ms o fTr adit ion al  Resp onse s  an d Diale theism In  th i s su bs ec tion, a fter we intro du ce problem softradit i o nal resp onses to the liar and R u ssell's  pa radox , we  will bri efl y intr odu c e dial etheis m whi ch  sa y s  that a  t rue  c ontradicti o n  ex ists.  D iale theismmay be an alternat i vesolution to t hepara d o xe s,h ow e ver  w e  sh a l l argue that no t every lo gi c ia n should a c cep tit as t he prim ary r e sponseto the pa radoxes.Wi th r e s pec t to the L iar para dox, Tars k i's s t ri cture , w hile r eg ard ing i t as t h e r espon se toth e Liar  para do x, has b een subject to some cri ticism s. Th e m ain criti cis m  ag ainst Tar ski' s solution  is  ma de by  Sa u l Kri pke( 19 75, pp. 6 90–6 9 8) that w h et her o rnot a sente n c e  is  para dox i cal is  dep endent not only o n  formal proper ties w hic h a r e in tr insic to the s ynt ax a nd seman ti cs of the s entence,  b u t als o on e mpiric al fact s .  I n  addit ion,  it  is not e asy  t o  placeno n- p aradox ical  c laimswithin Tars k i 's syntactically  fixe d set o f  le vels.  ( a) Ever y thin g Kim Jong -un says in  his
 any_language cannot_have its truth-predicate, T_(x). Any_sentences_which are_equivalent_to ¬T (⌜Φ⌝)_are not to_be formulated in LO._There is no_liar_sentence in LO. 3It we regard a formal language as a set of expressions,_LO_is a_proper_subset_of LM, so to speak,_LO ⊂ LM. 9 Furthermore,_because any_language has no truth-predicate, no liar sentence exist_in_any language. Therefore,_there is no Liar paradox. Tarski's stricture against the_semantically closed language may be the_premise-rejection solution to_the_Liar_paradox in the sense_that it prevents to use the_liar sentence. Of course, Tarski's stricture_may be regarded as the reasoning-rejection solution_to the Liar paradox because his_stricture does not allow the_inference from_¬T (⌜φ⌝) to φ and_vice versa in_the object_language. Hence, his_view can be interpreted as the_premise-rejection or the_reasoning-rejection solution if his stricture is_the_solution to the_paradoxes._As_we have_seen in this_subsection,_traditional approaches_to_Russell's and the Liar paradoxes may_be_considered to be the premise-rejection or the_reasoning-rejection or both. In_the_next subsection, we will_investigate problems of traditional responses_to the paradoxes and dialetheism. 1.1.2_Problems of_Traditional Responses_and Dialetheism In this subsection, after we introduce problems of traditional_responses to the liar and Russell's_paradox, we will briefly_introduce dialetheism_which_says that a_true_contradiction exists._Dialetheism may be an alternative solution to_the paradoxes,_however we shall argue that not_every logician should accept_it_as the primary response to the_paradoxes. With respect to the Liar_paradox, Tarski's stricture, while regarding_it_as_the response to the Liar_paradox, has been subject to some_criticisms. The main_criticism against Tarski's solution is made by_Saul_Kripke (1975, pp. 690–698) that whether_or_not a sentence is paradoxical is_dependent_not_only on formal properties which_are intrinsic to the syntax and_semantics of the sentence, but also on empirical facts._In addition, it_is not easy to place_non-paradoxical_claims_within Tarski's syntactically fixed set of levels. (a) Everything Kim_Jong-un says_in his