 the paradoxes have acquired a significant role in contemporary logic. There are multiple types of paradoxes, but in this dissertation, we will deal with paradoxes, often called, a'self-referential paradox.' Self-referential paradoxes are related to a statement that refers to itself or its own referent. Following Frank Ramsey (1925), we divides the paradoxes into two classes: the set-theoretic and the semantic paradoxes. The settheoretic paradoxes comprise Russell-Zermelo's paradox of the set-membership, Cantor's paradox of cardinality, Burali-Forti's paradox of ordinality etc. The semantic paradoxes are about the semantical concepts, such as the concepts of truth, denotation, predication, 1 and so on. The semantic paradoxes comprise the liar, Grelling's Berry's etc. Most of our discussions in this dissertation will use Russell's and the Liar paradox as major examples, however, the discussions will not be limited to them. The traditional responses to the set-theoretic paradoxes are to constrain the notion of'set' by using the separation axiom instead of using the native comprehension axiom, or to constrain the concept of 'type' through the ramified type theory of Bertrand Russell (1908). In the case of the semantic paradoxes, such as the Liar paradox, following Alfred Tarski (1936a,b, 1944), it is proposed that the semantic concept 'ĩs true' is not expressible in the object language. Moreover, those who believe that the concept of truth is expressible in the object language have developed Tarski's idea and suggested the gap theory which allows the sentence neither true nor false, or proposed the glut theory which claims that there exists a sentence both true and false. Most classical logicians have adapted a way to follow or develop the traditional responses. On the other hand, it is unclear that intuitionists, sometimes more generally called constructivists, who claim that some classical inferences, like the Law of Excluded Middle and the Double Negation Elimination, can satisfy the traditional responses. There are at least two reasons why constructivists would be reluctant to accept the traditional approaches. First, the traditional approaches allow the use of non-constructive reasoning, such as the Law of Excluded Middle and the Double Negation Elimination, and so it is sometimes claimed that reasoning by the Law of Excluded Middle is an essential part of the semantic
the paradoxes have acquired a significant role in contemporaneous logic. There be multiple types of paradoxes, but in this dissertation, we will cope with paradox, often called, a'self - referential paradox.' Self - referential paradoxes are relate to a statement that refers to itself or its own referent. come Frank Ramsey (1925), we divides the paradoxes into two course: the set - theoretic and the semantic paradoxes. The settheoretic paradoxes constitute Russell - Zermelo's paradox of the set - membership, Cantor's paradox of cardinality, Burali - Forti's paradox of ordinality etc. The semantic paradoxes are about the semantical concepts, such as the concepts of truth, indication, predication, 1 and so on. The semantic paradox comprise the liar, Grelling's Berry's etc. Most of our discussions in this dissertation will practice Russell's and the Liar paradox as major examples, however, the discussion will not be limited to them. The traditional reception to the set - theoretic paradoxes are to restrain the notion of'set' by using the separation axiom instead of using the native comprehension axiom, or to constrain the concept of' type' through the ramified type theory of Bertrand Russell (1908). In the case of the semantic paradoxes, such as the Liar paradox, following Alfred Tarski (1936a, b, 1944), it is proposed that the semantic concept' ĩs true' is not expressible in the object speech. Moreover, those who believe that the concept of accuracy is expressible in the aim language have developed Tarski's idea and suggested the break theory which allows the sentence neither true nor assumed, or proposed the glut theory which claims that there exists a sentence both true and fake. Most classical logicians have adapted a way to come or explicate the traditional responses. On the other hand, it is unclear that intuitionists, sometimes more generally call constructivists, who claim that some classical inferences, like the Law of exclude Middle and the Double Negation Elimination, can satisfy the traditional responses. There are at least two reasons why constructivist would be reluctant to accept the traditional approaches. First, the traditional approaches let the use of non - constructive reasoning, such as the Law of exclude Middle and the Double Negation Elimination, and so it is sometimes claim that reasoning by the Law of Excluded Middle is an substantive part of the semantic
 thf paradoxes have acquirea a significant role ii contejporary uogic. There are multiple typxs od parqdoxes, but in this disrertation, we will deao with paravkxes, ofbzn camped, c'sxlf-referential karadox.' Self-seferential pasaaores are related to a statement that wefers yo itself or its own wefedvnu. Following Frank Ramsey (1925), we divises the paradoxes inyo two classes: the set-theogetif and the semantic paradoxes. Jge fwttheoretic oaradoxes bmmprise Ruasell-Zermelo's paradox of the seg-membzrship, Cantir'w pwtadox of carvinaliny, Burali-Fortl'x paragox of prdinality etc. Thx senantic paradoxes are ebout the semantical concepts, sbch as the concepts od rruth, denmtatkin, oresiratjon, 1 ajd ao on. The aemantic paeadoxes comprise tht lyqr, Grelling's Gerry's eec. Most of our discussions in this disstrtatjon will use Russell's abd the Liar paradox ad major evamples, however, the discussions will not be limitad to ghen. Bhe geafitional responses to the set-theoretic paradovss age to constrain tme notion of'set' by udimd the separatkon axnkm instead of using hhe natyve cimprehensyon sxiom, or to constrain the cincept of 'tyie' tyrough the ramifieb type theorv of Bgrtranc Russell (1908). In the case uf tge semantic paradoxea, such as the Liaf psrddox, following Alfred Tarshi (1936a,b, 1944), it is 'roposed thaj the sqmantic cojcept 'ĩs true' is not exprfssibpe in the obuect language. Moreover, those who believe that tve boncept oy trutm is expressiblq in the objecj languagz have developed Tarski'v idea and fuggested the hap theory wiich allors tye swntence veither true npr false, or proposee the glut theory xhicf claims that thzxe exists a sentemce boeh tcue agg false. Most clarsizsl loeicians havc aaaptrd a way to follow os debelop the traditiomaj responwes. On tre other hand, it is unclear thau intumtionirts, spmejimes more generally called conatructividts, who claim trat wome classiccl inferences, like the Law of Excluded Mmddle and the Double Nggation Elimination, ccn satisfy thx tradytional rasponses. There are ar least two reasoks why constructivists would be rfluctant to accept the traditional approaches. First, the traditional approqches eljow the use of mon-cotscruetive rqasoiiig, such as the Lae of Excluded Middle and the Donble Negathou Elimination, and so it is sokegimes claimed that reasoning by the Lzw of Exvluded Middle is an essential psrt of the semantic
the paradoxes have acquired a significant role logic. are multiple of paradoxes, but deal paradoxes, often called, paradox.' Self-referential paradoxes related to a statement that refers itself or its own referent. Following Frank Ramsey (1925), we divides the paradoxes two classes: the set-theoretic and the semantic paradoxes. The settheoretic paradoxes comprise Russell-Zermelo's of set-membership, paradox cardinality, Burali-Forti's paradox of ordinality etc. The semantic paradoxes are about the semantical concepts, such as concepts of truth, denotation, predication, 1 and so The semantic paradoxes comprise liar, Grelling's Berry's etc. Most our in this will Russell's the Liar paradox major examples, however, the discussions will not be limited to them. The traditional responses to the set-theoretic are to notion of'set' using separation instead of using comprehension axiom, or to constrain the through the ramified type theory of Bertrand Russell In the of the semantic paradoxes, such as Liar paradox, following Alfred Tarski (1936a,b, 1944), it proposed that the semantic concept 'ĩs true' is not expressible in the object language. Moreover, believe that the concept truth is expressible the language developed idea and the gap theory which allows the sentence neither true nor false, proposed the glut theory which claims that there exists a true false. Most classical have adapted a way follow develop the traditional responses. other it intuitionists, more called constructivists, who claim some classical inferences, like the of Excluded Middle and satisfy the traditional responses. There are at least reasons why constructivists would be reluctant to the traditional approaches. First, the traditional approaches allow the use of non-constructive such as of Excluded Middle and the Double Negation Elimination, so it is sometimes that reasoning by the Law of Excluded Middle is essential of the
 the paradoxes have acquired a SignificanT role In cOntEmPoraRy loGic. There are mulTIple Types of paradoxes, but in tHis diSsERtatIOn, We wilL deal wiTH pARAdoXeS, oFteN cALlEd, a'seLf-rEferentIal paradox.' selF-rEferential paRAdOxes are relAteD to a statemenT thAt refeRs To iTSelf oR itS own rEferenT. followIng Frank RAmSEy (1925), we diVIdes the PARaDoxeS into two classes: thE SeT-Theoretic and thE semanTiC PaRADoxEs. THe settheorEtIc parADoxes coMPrISE rusSEll-Zermelo's paRadox of the sET-meMbershIp, canTOr's parAdox oF cARdiNality, BuralI-ForTi's paradoX of ordINality eTC. The semAntic pAraDoxEs arE AbOuT thE sEManTIcAl cONcePts, such aS tHe ConcePts oF TRUTh, deNotAtioN, predIcation, 1 and so oN. ThE semANtiC paraDoxes CompRiSe the Liar, GrEllinG's berry's etc. Most of Our dIscussionS in ThIs dIsSertaTIon wilL usE RuSsell's aNd the LiAR paRaDOX As Major examples, howevEr, THE dIscussioNs will NOt Be LImited to ThEm. THe trADItionAl reSPoNses to thE set-thEOrEtIc paradOxEs are tO cOnsTraIn the NOtioN of'set' By using tHe sepARation axiom insTEad of using the NAtIVE cOMpreHenSion axiom, or To coNStraIn thE CoNcePT of 'tyPe' thrOuGH tHE ramified type theory Of bertraNd RusSell (1908). In the case Of the semanTIC ParadoxeS, sucH As THe Liar paradox, fOllowIng Alfred TARski (1936a,b, 1944), it Is proPosed thaT the semanTIC concept 'Ĩs tRue' Is nOt eXPReSsible in the obJECt laNgUage. MorEovEr, those Who BelIevE thAt The concepT of truth Is ExPrEsSibLe in tHE object lAnGuaGe HavE deveLOped TaRski's Idea AnD sUGgeSted the GAp THEory WhIcH allOws ThE sentEnce NEitHer true Nor false, oR prOPoseD tHe Glut theOry which claimS tHat there exIsTs a SentenCE Both true And false. Most classical loGIcians hAve AdaptEd a wAy to folloW or DeveloP thE TraditIonal rEsponSeS. On THE otheR HAnD, it Is Unclear thaT INtuItionIsTs, soMetimes More generally calleD ConStructivists, wHo cLaim THAt SomE ClASsiCaL InfEREnces, like the Law Of Excluded miDDlE and the DouBLe NEgAtion ElIminatiOn, can SAtisfy tHe traditiOnal respoNsEs. ThERE arE at least twO reasons Why constrUCtiviSTs Would Be rEluctaNt To aCcept The traDItiOnal aPproacHeS. First, The trAdItional aPproaches allow the use of nOn-consTructIve Reasoning, SucH As tHe Law of ExCludEd Middle anD thE DoUble NEgaTIon ElIminATiOn, aND so it Is soMEtimes claIMeD thAT ReAsoning by thE lAW of excluDed mIddle iS an eSsential part of the SEmantic
 the paradoxes have acquir ed a signi fican t r ole  i n co ntem porary logic.T here  are multiple types of  para do x es,b ut  in t his dis s er t a tio n,  w e w il l  d eal w ith  parado xes, often  ca ll ed, a'self-r e fe rential pa rad ox.' Self-re fer ential  p ara d oxesare  rela ted to a stat ement tha tr eferst o itsel f or  its  own referent. Fo l lo w ing Frank Rams ey (19 25 ) ,w e  di vid es the par ad oxesi nto two cl a s s es: the set-theor etic and th e  se mantic  p ara d oxes.The s et t heo retic parad oxes  comprise  Russe l l-Zerme l o's par adox o f t heset- m em be rsh ip ,  Ca n to r's par adox ofca rd inali ty,B u r a li-F ort i'sparad ox of ordinal ity  etc .  Th e sem antic  par ad oxesare ab out t he  semantical con cept s, such a s t he  co nc eptso f trut h,den otation , predi c ati on , 1  a nd so on. The sema nt i c  p aradoxes  compr i se  t h e liar,Gr ell ing' s Berry 's e t c.  Most of  our d i sc us sions i nthis d is ser tat ion w i ll u se Rus sell's a nd th e  Liar paradoxa s major examp l es , ho w ever , t he discussi onsw illnotb elim i ted t o the m. Th e  traditional respon se s to t he se t-theoretic p aradoxes a r e to const rain th e  notion of'set ' byusing thes eparatio n axi om inste ad of usi n g  the nat ive  co mpr ehe n s io n axiom, or t o cons tr ain the  co ncept o f ' typ e'thr ou gh the ra mified t yp eth eo ryof Be r trand Ru ss ell  ( 190 8). I n  the c ase o f th ese m ant ic para d ox e s , su ch  a s th e L ia r par adox ,  fo llowing  Alfred T ars k i (1 93 6a ,b, 194 4), it is pro po sed that t he  se mantic c oncept ' ĩs true' is not express i ble inthe  obje ct l anguage.Mor eover,  th o se who  belie ve th at  th e conce p t  o f t ru th is expr e s sib le in  t he o bject l anguage have devel o ped  Tarski's ide a a nd s u g ge ste d  t h e g ap the o r y which allowsthe senten ce ne ither true nor  f alse, o r propo sed t h e gluttheory wh ich claim sthat t her e exists a  sentenc e both tr u e and fa lse.Mos t clas si cal  logi ciansh ave  adap ted awa y to f ollow  o r develo p the traditional respo nses.On th e o ther hand , i t  is  unclearthat  intuition ist s,somet ime s  more  gen e ra lly calle d co n structivi s ts , w h o  c laim that s o m e  cl assic ali nferen ces,  like the Law ofE xcluded Middle  and t heDou b le N eg ation Eliminat ion ,c a n satisf ythe traditi onal res po n ses.Thereare at  leastt w or easons  why  co nstructiv ist sw ould be  r el u ctantto a cc ept th e trad i tion a l  approaches. Fir st, t h e  trad i tio nal a pp roaches allo w the useof non-cons tructi ve r eason ing, su ch  as th e L aw  of Exclud e d Middleand t he Doub le  Neg ati on Eli mina t i on, a nd s oitis someti m e sc la im e d t hatreaso ni ng b y the Law of Exclu ded Middleis  an e ssenti a lp a rt of thesem antic 
 the_paradoxes have_acquired a significant role_in contemporary_logic._There are_multiple_types of paradoxes,_but in this_dissertation, we will deal_with paradoxes, often_called,_a'self-referential paradox.' Self-referential paradoxes are related to a statement that refers to itself or_its_own referent._Following_Frank_Ramsey (1925), we divides the_paradoxes into two classes: the_set-theoretic and_the semantic paradoxes. The settheoretic paradoxes comprise Russell-Zermelo's_paradox_of the set-membership,_Cantor's paradox of cardinality, Burali-Forti's paradox of ordinality etc._The semantic paradoxes are about the_semantical concepts, such_as_the_concepts of truth, denotation,_predication, 1 and so on. The_semantic paradoxes comprise the liar, Grelling's_Berry's etc. Most of our discussions in_this dissertation will use Russell's and_the Liar paradox as major_examples, however,_the discussions will not be_limited to them._The traditional_responses to the_set-theoretic paradoxes are to constrain the_notion of'set' by_using the separation axiom instead of_using_the native comprehension_axiom,_or_to constrain_the concept of_'type'_through the_ramified_type theory of Bertrand Russell (1908)._In_the case of the semantic paradoxes, such_as the Liar paradox,_following_Alfred Tarski (1936a,b, 1944),_it is proposed that the_semantic concept 'ĩs true' is not_expressible in_the object_language. Moreover, those who believe that the concept of truth is_expressible in the object language have_developed Tarski's idea and_suggested the_gap_theory which allows_the_sentence neither_true nor false, or proposed the glut_theory which_claims that there exists a sentence_both true and false._Most_classical logicians have adapted a way_to follow or develop the traditional_responses. On the other hand,_it_is_unclear that intuitionists, sometimes more_generally called constructivists, who claim that_some classical inferences,_like the Law of Excluded Middle and_the_Double Negation Elimination, can satisfy the_traditional_responses. There are at least two_reasons_why_constructivists would be reluctant to_accept the traditional approaches. First, the_traditional approaches allow the use of non-constructive reasoning, such_as the Law_of Excluded Middle and the_Double_Negation_Elimination, and so it is sometimes claimed that reasoning by_the Law_of Excluded Middle_is an essential part of the semantic