Logique de Proposition Catégorique PDF

¢el−fr hQe Hhw …Z J f¢lj¡Z Ae¤p¡−l ¢el−fr hQ−el −nËZ£¢hi¡N £¢hi¡N :- ¢el−fr hQ−e L¡−l¡ pð−å ¢exnaÑi¡−h −L¡e ¢LR¥ hm¡ quz HC −r−œ "k¡l' pð−å hm¡ qu Hhw "k¡' hm¡ qu, c¤¢VC qm ¢houz AbÑ¡v ¢el−fr hQ−e c¤¢V j¡œ ¢hou b¡−Lz HC ¢hou c¤¢Vl fË−aÉL¢VC në(R¡œ) q−a f¡−l, B...

¢el−fr hQe Hhw …Z J f¢lj¡Z Ae¤p¡−l ¢el−fr hQ−el −nËZ£¢hi¡N £¢hi¡N :- ¢el−fr hQ−e L¡−l¡ pð−å ¢exnaÑi¡−h −L¡e ¢LR¥ hm¡ quz HC −r−œ "k¡l' pð−å hm¡ qu Hhw "k¡' hm¡ qu, c¤¢VC qm ¢houz AbÑ¡v ¢el−fr hQ−e c¤¢V j¡œ ¢hou b¡−Lz HC ¢hou c¤¢Vl fË−aÉL¢VC në(R¡œ) q−a f¡−l, Bh¡l në-pj¢ø (j¡dÉ¢jL fl£r¡u Eš£ZÑ R¡œ) q−a f¡−lz HC në h¡ në-pj¢ø−L fc h−mz AbÑ¡v ¢el−fr hQ−el ¢hou ¢q−p−h hÉhq©a q−a f¡−l Hje në h¡ në-pj¢ø−L fc h−mz ¢el−fr hQ−el HC fc c¤¢Vl HL¢Vl p−‰ AeÉ¢Vl pðå −O¡oZ¡ Ll¡ quz HC pðå ü£L«¢al q−a f¡−lz −kje g¥m qu m¡mz HM¡−e g¥m−L m¡m h−m ü£L¡l Ll¡ q−µRz Bh¡l Aü£L«¢alJ q−a f¡−lz −kje g¥m eu m¡mz HM¡−e g¥m−L m¡m h−m ü£L¡l Ll¡ q−µR e¡z HCi¡−h ü£L«¢al pðå−L ül©f pðå J Aü£L«¢al pðå−L ¢hl©f pðå h−mz a¡q−m HL Lb¡u hm¡ k¡u, −k- −k-h¡−LÉl h¡−LÉl j¡dÉ−j c¤¢V f−cl j−dÉ ül©f h¡ ¢hl©f pðå −O¡oZ¡ O¡oZ¡ Ll¡ Ll¡ qu, qu, AbÑ¡v HL¢ HL¢V fc pð−å AeÉ fc¢fc¢V−L ü£L¡l h¡ Aü£ Aü£L¡l Ll¡ Ll¡ qu, qu, Hhw HC −O¡oZ¡ O¡oZ¡ h¡ ü£L¢« a h¡ Aü£ Aü£L¢« a −L¡e lLj n−aÑl Jfl ¢eiÑl L−l e¡, a¡−L ¢el−fr hQe (Categorical proposition)z h−mz "−kje p−œ²¢Vp qe HLSe c¡nÑ¢eLzz' −k hQ−e ¢h−du fc−L E−ŸnÉ fc pð−å ü£L¡l h¡ Aü£L¡l Ll¡ qu −L¡e n−aÑl Jfl ¢eiÑl L−l, a¡−L hm¡ qu p¡−fr hQe (Non-categorical proposition)z −kje k¢c hª¢ø qu, a¡q−m gpm i¡−m¡ qu h¡ B¢j k¡−h¡ Abh¡ a¥¢j Bp−hz c¤¢V hQ−el ü£L«¢a n−aÑl Jfl ¢eiÑln£mz * ¢el−fr hQ−el ül©fNa °hh¢nøÉ :- 1z ¢el−fr hQe qm k¤¢š²l Awn h¡ A‰z 2z ¢el−fr hQe qm ¢hhª¢aj§mL h¡LÉ h¡ −O¡oL h¡LÉz HM¡−e L) c¤¢V fc h¡ ¢ho−ul j−dÉ pðå −O¡oZ¡ Ll¡ quz (M) HC pðå ül©f h¡ ü£L«¢al pðå q−a f¡−l, Bh¡l ¢hl©f h¡ Aü£L«¢alJ q−a f¡−lz (N) HC pðå −L¡el©f n−aÑl Jfl ¢eiÑl L−l e¡z 3z hQ−e −O¡¢oa hš²−hÉl p−‰ h¡Ù¹−hl p‰¢a-Ap‰¢a Ae¤p¡−l hQe paÉ h¡ ¢jbÉ¡ q−a f¡−lz ¢el−fr hQ−el Awn h¡ Ef¡c¡e :- HL¢V ¢el−fr hQ−e p¡d¡lZa c¤¢V fc J a¡−cl jdÉhaÑ£ HL¢V pðå b¡−Lz L−SC HL¢V ¢el−fr hQe−L ¢h−nÔoZ Ll−m ¢ae¢V Awn h¡ Ef¡c¡e f¡Ju¡ k¡u - 1z F−ŸnÉ fc : −L¡e hQ−e −k fc pð−å −L¡e ¢LR¥ −O¡oZ¡ Ll¡ qu, a¡−L E−ŸnÉ fc h−mz −kje g¥m qu m¡m - HC hQe¢V−a g¥m pð−å −L¡e¢LR¥ −O¡oZ¡ Ll¡ q−µRz a¡C "g¥m' qm E−ŸnÉ fcz 2z ¢h−du fc : −L¡e hQ−e E−ŸnÉ fc pð−å k¡ ¢LR¥ −O¡oZ¡ Ll¡ qu, a¡−L ¢h−du fc h−mz −kje g¥m qu m¡m - HC hQ−e g¥m AbÑ¡v E−ŸnÉ−L m¡m hm¡ q−u−Rz a¡C HM¡−e "m¡m' në¢V qm ¢h−du fcz 3z pw−k¡SL : −L¡e hQ−e −k ¢Q−q²l à¡l¡ E−ŸnÉ J ¢h−du f−cl jdÉhaÑ£ ü£L«¢a h¡ Aü£L«¢al pðå−L fËL¡n Ll¡ qu, a¡−L pw−k¡SL h−mz pw−k¡SL phÑc¡C "qJu¡' d¡a¥l haÑj¡e L¡−ml BL¡−l b¡−Lz −kje "−N¡m¡f qu p¤¤N¢å' - HC hQ−e pw−k¡SL ¢qp¡−h "qu' Lb¡¢V l−u−Rz H¢V ü£L«¢al pðå−L fËL¡n Ll−Rz Bh¡l "Sh¡ eu p¤¤N¢å' - HC hQ−e pw−k¡SL ¢qp¡−h "eu' Lb¡¢V l−u−Rz H¢V Aü£L«¢al pðå−L fËL¡n Ll−Rz a¡q−m hm¡ k¡u ü£L«¢ap§QL pw−k¡SL qm qu, qJ h¡ qCz Bh¡l Aü£L«¢ap§QL pw−k¡SL qm eu, eJ h¡ eCz pw−k¡S−Ll ül©fNa °hh¢nøÉ : 1z pw−k¡SL E−ŸnÉ fc J ¢h−du f−cl j¡TM¡−e b¡−Lz 2z pw−k¡SL ü£L«¢al −r−œ "qu' BL¡−l Hhw Aü£L«¢al −r−œ "eu' BL¡−l b¡−Lz 3z E−ŸnÉ J ¢h−du qm fcz ¢L¿¹¥ pw−k¡SL fc euz H¢V c¤¢V f−cl jdÉhaÑ£ pðå p§QL ¢Qq²z 4z −k-ph h¡−LÉ ¢œ²u¡fc pw−k¡S−Ll BL¡−l, AbÑ¡v "qJu¡' d¡a¥l BL¡−l b¡−L e¡, −pM¡−e hQe-BL¡l −cM¡h¡l pju pw−k¡SL−L fªbLi¡−h ¢e−cÑn Ll−a quz −kje h¡LÉ = p§kÑ f§hÑ¢c−L J−Wz hQe = p§kÑ qu hÙ¹¥ k¡ f§hÑ¢c−L J−Wz 5z pw−k¡SL phÑc¡C haÑj¡e L¡−m b¡−Lz −L¡e h¡−LÉ Aa£a h¡ i¢hoÉ−al −L¡e fËp‰ b¡L−m hQe-BL¡l −cM¡h¡l pju HC fËp‰−L ¢h−du f−cl j−dÉ E−õM Ll−a quz −kje h¡LÉ : cnlb A−k¡dÉ¡l l¡S¡ ¢R−mez hQe : cnlb qe hÉ¢š² ¢k¢e A−k¡dÉ¡l l¡S¡ ¢R−mez h¡LÉ : l¡j HC hRl fl£r¡ −c−hz hQe : l¡j qu hÉ¢š² −k HC hRl fl£r¡ −c−hz pw−k¡S−Ll L¡S : 1z hQ−el E−ŸnÉ J ¢h−du fc−L k¤š² Ll¡z 2z E−ŸnÉ J ¢h−du f−cl jdÉhaÑ£ ü£L«¢aj§mL h¡ Aü£L«¢aj§mL pðå−L fËL¡n Ll¡z 3z h¡LÉ J hQ−el j−dÉ f¡bÑLÉ ¢e−cÑn Ll¡z E−ŸnÉ J ¢h−du f−cl ¢h−noaÆ : HL¢V hQ−el E−ŸnÉ fc S¡¢a h¡QL −kje j¡e¤o, g¥m CaÉ¡¢c −h¡T¡−a f¡−l, Bh¡l hÉ¢š² h¡QL h¡ HLh¡QLJ q−a f¡−lz −kje l¡j, −p, I N¡R¢V CaÉ¡¢cz ¢h−du f−c JC S¡¢a h¡ hÉ¢š² (HL)-Hl …Z h¡ mrZ−L −O¡oZ¡ Ll¡ quz …Z h¡ mrZ qm ¢h−noZz ¢L¿¹¥ ¢h−no−Zl fc qJu¡l −k¡NÉa¡ e¡Cz a¡C −L¡e hQ−e k¢c −L¡e ¢h−noZ ¢h−du ¢qp¡−h b¡−L, a¡q−m a¡−L ¢h−n−oÉl BL¡−l ¢e−u Bp−a q−hz −kje pv (¢h−noZ), pvhÉ¢š² qm ¢h−noÉ, i¡l£ ¢h−noZ , i¡l£ hÙ¹¥ qm ¢h−noÉz HLCi¡−h jlZn£m Hl k¡uN¡u jlZn£m S£h CaÉ¡¢c CaÉ¡¢cz ¢el−fr hQ−el f¢lj¡Z : HL¢V hQ−el ¢h−du f−c E−ŸnÉ pð−å ¢LR¥ hm¡ quz fc ¢qp¡−h E−ŸnÉ fc −L¡e ¢hou−L ¢e−cÑn L−lz HC ¢hou¢V HL¢V S¡¢a h¡ −nËZ£l pjNË q−a f¡−l, Bh¡l AwnJ q−a f¡−lz E−ŸnÉ f−cl HC pjNË h¡ Awn−L hQ−el f¢lj¡Z ¢qp¡−h −cM¡ quz f¢lj¡Z Ae¤p¡−l hQ−el −nËZ£¢hi¡N : f¢lj¡Z Ae¤p¡−l ¢el−fr hQe c¤lL−jl q−a f¡−l - p¡¢hÑL Hhw ¢h−noz p¡¢ p¡¢hÑL hQe : −k-¢el−fr hQe ¢h−du fc−L E−ŸnÉ f−cl à¡l¡ ¢edÑ¡¢la S¡¢a h¡ −nËZ£l "pjNË' h¡ Awn pÇf−LÑ ü£L¡l h¡ Aü£L¡l Ll¡ qu a¡−L p¡¢hÑL hQe h−mz −kje : 1z pLm j¡e¤o qu jlZn£m S£hz H¢V HL¢V p¡¢hÑL hQez L¡lZ HM¡−e "jlZn£m S£h' fc¢V−L pjNË j¡e¤o S¡¢a pÇf−LÑ ü£L¡l Ll¡ q−u−Rz AbÑ¡v l¡j, l¢qj fËi«¢a fË−aÉL−LC jlZn£m S£h hm¡ q−u−Rz 2z −L¡e j¡e¤o eu Ajl S£hz H¢VJ HL¢V p¡¢hÑL hQez L¡lZ HM¡−e "Ajl S£h' fc¢V−L pjNË j¡e¤o S¡¢a pÇf−LÑ Aü£L¡l Ll¡ q−u−Rz AbÑ¡v l¡j, l¢qj fËi«¢a j¡e¤−ol L¡E−LC Ajl hm¡ qu ¢ez ¢h−no hQe : −k-¢el−fr hQ−e ¢h−du fc−L E−ŸnÉ f−cl à¡l¡ ¢edÑ¡¢la S¡¢a h¡ −nËZ£l "HL¢V Awn' pÇf−LÑ ü£L¡l h¡ Aü£L¡l Ll¡ qu, a¡−L ¢h−no hQe h−mz −kje : 1z −L¡e −L¡e j¡e¤o qu pv hÉ¢š²z H¢V HL¢V ¢h−no hQez L¡lZ, HM¡−e "pv hÉ¢š²' fc¢V−L j¡e¤o S¡¢al A¿¹iÑš § ² L−uLSe pÇf−LÑ ü£L¡l Ll¡ q−u−Rz 2z −L¡e −L¡e g¥m eu m¡m hÙ¹¥z H¢V HL¢V ¢h−no hQez L¡lZ, HM¡−e "m¡m hÙ¹¥' fc¢V−L g¥m S¡¢al A¿¹iÑš § ² L−uL¢V pÇf−LÑ Aü£L¡l Ll¡ q−u−Rz A−eL−r−œ ¢e¢cÑø HLh¡QL fc ¢el−fr hQ−el E−ŸnÉ ¢qp¡−h b¡−Lz H−r−œ hQ−el f¢lj¡Z ¢L q−h ? ¢e¢cÑø HLh¡QL fc "HL¢V' h¡ "HLSe'-−L ¢e−cÑn L−lz HC H−Ll −L¡e Awn b¡L−a f¡−l e¡z HC HL p¡j¢NËLi¡−hC "HL'z a¡C e¡jfc (l¡j), phÑe¡j (−p), ¢e¢cÑø ¢h¢nø fc(JC N¡R¢V) fËi«¢a HL h¡QL fc −L¡e hQ−el E−ŸnÉ ¢qp¡−h b¡L−m hQe¢V−L p¡¢hÑL hQe ¢qp¡−h ü£L¡l Ll−a q−hz −kje : 1z JC N¡R¢V qu hVN¡Rz 2z l¡j qu pv hÉ¢š²z 3z −p eu −jd¡h£z ¢el−fr hQ−el …Z: HL¢V ¢el−fr hQ−e E−ŸnÉ J ¢h−du - HC c¤¢V f−cl j−dÉ pðå −O¡oZ¡ Ll¡ quz HC pðå ü£L«¢aj§mL q−a f¡−l, Bh¡l Aü£L«¢aj§mLJ q−a f¡−lz …Z Ae¤p¡−l hQ−el −nËZ£ ¢hi¡N : …Z Ae¤p¡−l ¢el−fr hQe c¤-fËL¡l q−a f¡−l - qyÉ¡-h¡QL Hhw e¡-h¡QLz qyÉ¡-h¡QL hQe : E−ŸnÉ J ¢h−du f−cl j−dÉ ül©f h¡ ü£L«¢al pðå fËL¡¢na qu, a¡−L qyÉ¡-h¡QL hQe h−mz "qu', "qJ' Hhw "qC' HC ¢ae¢V qm ü£L«¢al ¢Qq²z pw−k¡SL ¢qp¡−h E−ŸnÉ J ¢h−du f−cl j¡TM¡−e H−cl −L¡e HL¢V b¡L−mC ¢el−fr hQe¢V qyÉ¡-h¡QL hQe q−hz −kje : 1z pLm j¡e¤o qu jlZn£ S£hz H¢V HL¢V qyÉ¡-h¡QL hQez L¡lZ HM¡−e "qu' pw−k¡SL¢Vl à¡l¡ "jlZn£m S£h' fc¢V−L j¡e¤o S¡¢a pÇf−LÑ ü£L¡l Ll¡ q−u−Rz 2z −L¡e −L¡e j¡e¤o qu pv hÉ¢š²z H¢V HL¢V qyÉ¡-h¡QL hQez L¡lZ HM¡−e "qu' pw−k¡SL¢Vl à¡l¡ "pv hÉ¢š²' fc¢V−L L−uLSe j¡e¤o pÇf−LÑ ü£L¡l Ll¡ q−u−Rz e¡- e¡-h¡QL hQe : −k-¢el−fr hQ−e E−ŸnÉ J ¢h−du f−cl j−dÉ ¢hl©f h¡ Aü£L«¢al pðå fËL¡¢na qu, a¡−L e¡-h¡QL hQe h−mz "eu', "eJ' Hhw "eC' - HC ¢ae¢V qm Aü£L«¢al ¢Qq²z pw−k¡SL ¢qp¡−h E−ŸnÉ J ¢h−du f−cl j¡TM¡−e H−cl −L¡e HL¢V b¡L−mC ¢el−fr hQe¢V e¡-h¡QL hQe q−hz −kje 1z −L¡e j¡e¤o eu Ajl hÉ¢š²z H¢V HL¢V e¡-h¡QL hQez L¡lZ, HM¡−e "eu' pw−k¡SL¢V à¡l¡ "Ajl hÉ¢š²' fc¢V−L j¡e¤o S¡¢a pÇf−LÑ Aü£L¡l Ll¡ q−u−Rz 2z −L¡e −L¡e j¡e¤o eu f¢lnËj£ hÉ¢š² - H¢V HL¢V e¡-h¡QL hQez L¡lZ, HM¡−e "eu' pw−k¡SL¢Vl à¡l¡ f¢lnËj£ hÉ¢š² fc¢V−L L−uLSe j¡e¤o pÇf−LÑ Aü£L¡l Ll¡ q−u−Rz ¢el−fr hQ−el …Z J f¢lj¡Z ¢eZÑ−ul fÜ¢ fÜ¢a : hQ−el f¢lj¡Z p§QL ¢Qq² ¢qp¡−h E−ŸnÉ f−cl p−‰ "pLm', "−L¡e −L¡e' fËi«¢a në…¢m b¡−Lz H−cl j¡eL h−mz HC j¡eL −c−MC hQ−el f¢lj¡Z ¢edÑ¡lZ Ll¡ quz −kje (1) pLm j¡eL b¡L−m p¡¢hÑL hQe−L ¢e−cÑn L−lz (2) −aj¢e −L¡e −L¡e j¡eL ¢h−no hQe−L ¢e−cÑn L−lz (3) HLh¡QL hQ−e −L¡e j¡eL b¡−L e¡ - a¡C HC dl−Zl hQe p¡¢hÑL hQe h−m NZÉ quz −nËZ£ : −nËZ£ : k¤¢š²¢h‘¡−e −nËZ£ hm−a Hje −L¡e ¢h−no …Z p¡d¡lZi¡−h haÑj¡e Hje −L¡e hÙ¹¥ h¡ hÉ¢š²pj¢ø−L −nËZ£ hm¡ quz −kje "¢hQ¡lh¤¢ÜaÆ' - HC ¢h−no …Z¢V j¡e¤o −nËZ£l A¿¹iÑš § ² qJu¡u j¡e¤o HL¢V −nËZ£z ¢WL HLCi¡−h q¡¢a, −O¡s¡, EV, ¢pwq, c¡nÑ¢eL, ¢h‘¡e£ fËi«¢a HL HL¢V −nËZ£z k¤¢š²¢h‘¡−e ¢el−fr hQ−e E−ŸnÉ J ¢h−du hm−a E−ŸnÉ −nËZ£ J ¢h−du −nËZ£−L −h¡T¡uz f¢lf§ lflLlL −nËZ£ : −L¡e −nËZ£l f−l¡f§lL −nËZ£ qm −pC hÉ¢š² h¡ hÙ¹p¥ j¢ø k¡ j§m −nËZ£l A¿¹NÑa euz −L¡e HL¢V −nËZ£l A¿¹NÑa −k pcpÉ b¡−L, −pC pLm pcpÉ ¢iæ Bl fË−aÉL¢V pcpÉ HL−œ JC −nËZ£l f¢lf§lL −nËZ£ (Complementary Class)z −kje "j¡e¤o' HL¢V −nËZ£z Hl f¢lf§lL −nËZ£ qm "j¡e¤o eu' Hje pLm −nËZ£l pj¢øz a¡q−m −cM¡ −Nm −L¡e HL¢V −nËZ£l f¢lf§lL h¡ ¢hl¦Ü −nËZ£ qm A−eL…¢m −nËZ£l pj¢øz HL¢V −nËZ£l −kje HL¢V f¢lf§lL −nËZ£ b¡−L, −aj¢e HL¢V f−clJ HL¢V f¢lf§lL fc b¡−Lz HL¢V f−cl f¢lf§lL fc qm −pC f−cl pjÙ¹ ¢hfl£a f−cl pj¢øz −kje "p¡c¡' HL¢V fcz Hl ¢hfl£a fc qm L¡−m¡, m¡m, ph¤S CaÉ¡¢c pLm lP h¡QL fc AbÑ¡v p¡c¡ ¢iæ pLm fcz HC p¡c¡ ¢iæ pLm fc HL−œ p¡c¡ f−cl ¢hl¦Ü fc h¡ f¢lf§lL fc k¡ fËL¡n Ll¡ qu A-p¡c¡ e¡j ¢c−uz "p¡c¡'l ¢hfl£a fc "L¡−m¡' ¢L¿¹¥ ¢hl¦Ü h¡ f¢lf§lLfc qm "A-p¡c¡'z neÉNiÑ §eÉNiÑ −nËZ£ : n§eÉNiÑ −nËZ£ hm−a Hje HL¢V −nËZ£−L −h¡T¡u k¡l j−dÉ −L¡e hÉ¢š² h¡ hÙ¹¥ pcpÉ ¢qp¡−h Ef¢ÙÛa e¡Cz H¢V HL¢V pcpÉq£e −nËZ£z −kje jvpÉLeÉ¡l −nËZ£, −p¡e¡l f¡q¡−sl −nËZ£, hªš¡L¡l Qa¥iѧ−Sl −nËZ£ CaÉ¡¢cz Eš² h¡LÉ¡w−nl fË−aÉL¢V Hje HL¢V −nËZ£−L ¢e−cÑn Ll−R k¡ pcpÉq£ez Bd¤¢eL k¤¢š²¢h‘¡−e HC dl−el −nËZ£−L −h¡T¡−e¡l SeÉ "0' fËa£L ¢Qq²¢V hÉhq¡l Ll¡ q−u b¡−Lz dl¡k¡LÚ S HL¢V n§eÉNiÑ −nËZ£ h¡ pcpÉq£e −nËZ£z HC −nËZ£−L −h¡T¡−e¡l SeÉ " 0' fËa£L ¢Qq²¢V hÉhq¡l Ll¡ quz S k¢c HL¢V n§eÉNiÑ −nËZ£ qu a−h S J 0-Hl j¡TM¡−e HL¢V pj£LlZ ¢Qq² (=) hÉhq¡l L−l −pC Lb¡ hÉš² Ll−a quz Bh¡l k¢c S −nËZ£ pcpÉq£e e¡ qu, AbÑ¡v S −nËZ£l HLSe q−mJ pcpÉ b¡−L, aMe S J n§−eÉl j¡TM¡−e (≠ ) Apja¡l ¢Qq² hÉhq¡l L−l Eiu−L k¤š² Ll−a quz a¡q−m S n§eÉNiÑ −nËZ£l p¡w−L¢aLlZ qm S = 0 Hhw S n§eÉNiÑ −nËZ£ eu, Hl p¡w−L¢aLlZ qm S ≠ 0z AdÉ¡fL ¢h−hL¡e¾c p¡E cnÑe ¢hi¡N ¢hcÉ¡eNl L−mS