Qeyri-s\u0259lis m\u0259ntiq riyaziyyat\u0131n, az\u0259rbaycanl\u0131 riyaziyyat\u00e7\u0131 L\u00fctfi Zad\u0259nin t\u0259klif etdiyi klassik m\u0259ntiq v\u0259 qeyri-s\u0259lis \u00e7oxluqlar n\u0259z\u0259riyy\u0259sinin \u00fcmumil\u0259\u015fdirilm\u0259sin\u0259 \u0259saslanan bir qoludur. Klassik m\u0259ntiqi m\u0259s\u0259l\u0259l\u0259rd\u0259 qiym\u0259tl\u0259r 1 v\u0259 ya 0 olmal\u0131d\u0131rsa, 1965-ci ild\u0259 L\u00fctfi Zad\u0259 t\u0259r\u0259find\u0259n ir\u0259li s\u00fcr\u00fclm\u00fc\u015f qeyri-s\u0259lis m\u0259ntiq\u0259 g\u00f6r\u0259 m\u0259s\u0259l\u0259l\u0259rd\u0259 qiym\u0259tl\u0259r [0;1] interval\u0131nda olur. \u0130lk d\u0259f\u0259 1930-cu ild\u0259 \u00e7oxqiym\u0259tli m\u0259ntiq sisteminin klassik m\u0259ntiqd\u0259n f\u0259rql\u0259n\u0259n variant\u0131n\u0131 t\u0259klif ed\u0259n m\u0259ntiq\u00e7il\u0259rd\u0259n biri Pol\u015fa riyaziyyat\u00e7\u0131s\u0131 Yan Lukasievi\u00e7 olub. Bu m\u0259ntiq \u00fc\u00e7 qiym\u0259tli \u2013 \u201cyanl\u0131\u015f\u201d, \u201cdo\u011fru\u201d v\u0259 \u201cimkan\u201d olmaqla Aristotel m\u0259ntiqind\u0259n f\u0259rql\u0259nirdi. Daha sonra \u201cqeyri-s\u0259lis m\u0259ntiq\u201d termini \u201c\u0130nformatika v\u0259 idar\u0259etm\u0259\u201d jurnal\u0131nda \u00e7ap olunmu\u015f \u201cQeyri-s\u0259lis \u00e7oxluqlar\u201d \u0259s\u0259rind\u0259 professor L\u00fctfi Zad\u0259 t\u0259r\u0259find\u0259n t\u0259qdim edilib. Buna g\u00f6r\u0259 d\u0259 L\u00fctfi Zad\u0259 haql\u0131 olaraq qeyri-s\u0259lis m\u0259ntiqin atas\u0131 hesab olunur.<\/p>\n
Bu fikirl\u0259r Birl\u0259\u015fmi\u015f N\u00fcv\u0259 T\u0259dqiqatlar\u0131 \u0130nstitutunun (Rusiya Federasiyas\u0131, Dubna \u015f\u0259h\u0259ri) b\u00f6y\u00fck elmi i\u015f\u00e7isi fizika \u00fczr\u0259 f\u0259ls\u0259f\u0259 doktoru Elmar \u018fsg\u0259rov v\u0259 Az\u0259rbaycan Milli Elml\u0259r Akademiyas\u0131n\u0131n vitse-prezidentinin xidm\u0259tinin ba\u015f m\u00fct\u0259x\u0259ssisi G\u00fcnel M\u0259mm\u0259dovan\u0131n h\u0259mm\u00fc\u0259llifi olduqlar\u0131 \u201cL\u00fctfi Zad\u0259nin qeyri-s\u0259lis m\u0259ntiqi v\u0259 fizikada qeyri-m\u00fc\u0259yy\u0259nlikl\u0259r\u201d adl\u0131 m\u0259qal\u0259d\u0259 yer al\u0131b.<\/p>\n
\u00dcmumiyy\u0259tl\u0259, idrak elmi olan m\u0259ntiq onun yarad\u0131c\u0131s\u0131 Aristotelin \u201cBir adam\u0131n dediyi ya do\u011frudur, ya yalan\u201d f\u0259ls\u0259fi deyimi \u00fcz\u0259rind\u0259 qurulub. Aristotel \u201cyalan\u201d v\u0259 \u201cdo\u011fru\u201d kimi kateqoriyalar aras\u0131nda qalan aral\u0131q d\u0259r\u0259c\u0259l\u0259ri n\u0259z\u0259r\u0259 almay\u0131b. \u0130lk d\u0259f\u0259 d\u00fcnyada L\u00fctfi Zad\u0259 h\u0259r \u015feyin d\u0259r\u0259c\u0259sinin oldu\u011funu s\u00fcbut ed\u0259r\u0259k g\u00f6st\u0259rib ki, real d\u00fcnyada q\u0259ti olaraq tam a\u011f v\u0259 q\u0259ti olaraq tam qara deyil\u0259n bir \u015fey yoxdur. Bu iki m\u0259fhum (s\u0259rh\u0259d) aras\u0131nda real olaraq sonsuz sayda \u00e7alar d\u0259yi\u015fikliyi \u2013 aral\u0131q fazalar vard\u0131r. Probleml\u0259rin h\u0259ll olunmas\u0131nda, h\u0259qiq\u0259tin a\u015fkarlanmas\u0131nda hesablamalar n\u0259tic\u0259l\u0259rin etibarl\u0131l\u0131\u011f\u0131 \u00fc\u00e7\u00fcn aral\u0131q fazalara \u0259h\u0259miyy\u0259t verilm\u0259d\u0259n apar\u0131la bilm\u0259z. Apar\u0131lm\u0131\u015f olsa bel\u0259 onlarda kifay\u0259t q\u0259d\u0259r q\u00fcsurlar v\u0259 x\u0259talar m\u00f6vcud olacaq.<\/p>\n
Qeyri-s\u0259lis m\u0259ntiq m\u00fcr\u0259kk\u0259b texnoloji prosesl\u0259r \u00fc\u00e7\u00fcn idar\u0259etm\u0259 sisteml\u0259rinin qurulmas\u0131n\u0131n \u0259n \u0259lveri\u015fli \u00fcsulu kimi meydana \u00e7\u0131x\u0131b, h\u0259m\u00e7inin m\u0259i\u015f\u0259t elektronikas\u0131nda, diaqnostika v\u0259 dig\u0259r ekspert sisteml\u0259rind\u0259 t\u0259tbiqini tap\u0131b. N\u0259z\u0259riyy\u0259nin t\u0259tbiqin\u0259 ehtiyac elektron cihazlar\u0131n, ma\u015f\u0131nlar\u0131n robotla\u015fd\u0131r\u0131lmas\u0131na \u2013 \u201cintellektualla\u015fmas\u0131\u201dna artan ehtiyacdan qaynaqlan\u0131b. Texnologiyan\u0131n m\u00fcasir inki\u015faf\u0131 \u00fc\u00e7\u00fcn insanla adekvat \u015f\u0259kild\u0259 qar\u015f\u0131l\u0131ql\u0131 \u0259laq\u0259 qura bil\u0259n h\u0259qiqi \u201ca\u011f\u0131ll\u0131\u201d sisteml\u0259r yaratmaq, qeyri-m\u00fc\u0259yy\u0259n h\u0259yat ifad\u0259l\u0259rini ayd\u0131n v\u0259 formal riyazi d\u00fcsturlar\u0131n dilin\u0259 \u00e7evir\u0259 bil\u0259n yeni riyazi aparata ehtiyac var idi. Qeyri-s\u0259lis m\u0259ntiqin, hava sisteml\u0259ri qur\u011fular\u0131n\u0131n idar\u0259etm\u0259 sisteml\u0259rind\u0259n tutmu\u015f statistik proqnozla\u015fd\u0131r\u0131lmalara, h\u0259tta siyas\u0259ti m\u00fcnasib\u0259tl\u0259r\u0259 q\u0259d\u0259r bir s\u0131ra perspektivli t\u0259tbiql\u0259ri m\u00fcmk\u00fcn olub.<\/p>\n
Banisi Aristotel hesab olunan klassik m\u0259ntiqin bir \u0259h\u0259miyy\u0259tli \u00e7at\u0131\u015fmazl\u0131\u011f\u0131 vard\u0131 ki, onun k\u00f6m\u0259yi il\u0259 insan\u0131n assosiativ d\u00fc\u015f\u00fcnc\u0259sini t\u0259svir etm\u0259k m\u00fcmk\u00fcn deyil. Klassik m\u0259ntiq h\u0259r hans\u0131 aral\u0131q d\u0259y\u0259rl\u0259r istisna olmaqla, yaln\u0131z iki anlay\u0131\u015fla i\u015fl\u0259yir: do\u011fru v\u0259 yalan. Bu, sad\u0259 h\u0259yat t\u0259rzi \u00fc\u00e7\u00fcn \u201cb\u0259li\u201d v\u0259 \u201cyox\u201ddan ba\u015fqa suallar\u0131 cavabland\u0131rm\u0131rd\u0131, \u0259traf\u0131m\u0131zdak\u0131 b\u00fct\u00fcn d\u00fcnyan\u0131 yaln\u0131z a\u011f-qara r\u0259ngd\u0259 t\u0259s\u0259vv\u00fcr edirdik. Aristotelin davam\u00e7\u0131lar\u0131 olan filosoflar, riyaziyyat\u00e7\u0131lar v\u0259 fizikl\u0259r hesab edirdil\u0259r ki, h\u0259r bir arqument ya do\u011frudur, ya da yanl\u0131\u015fd\u0131r.<\/p>\n
XX \u0259sr riyaziyyat\u0131n\u0131n \u0259n b\u00f6y\u00fck nailiyy\u0259tl\u0259rind\u0259n biri olan qeyri-s\u0259lis m\u0259ntiqd\u0259n sonra insan t\u0259f\u0259kk\u00fcr\u00fcn\u0259 v\u0259 bizi \u0259hat\u0259 ed\u0259n d\u00fcnyaya, kvant d\u0259rinlikl\u0259rind\u0259 v\u0259 meqa al\u0259md\u0259 h\u0259l\u0259 d\u0259 tam d\u0259rk ed\u0259 bilm\u0259diyimiz d\u00fcnyag\u00f6r\u00fc\u015f\u00fc prizmas\u0131ndan bax\u0131l\u0131r. Y\u0259ni riyaziyyat d\u00fcnyas\u0131ndan \u0259traf\u0131m\u0131zdak\u0131 real d\u00fcnyaya qay\u0131danda qeyri-s\u0259lisliyin h\u00f6km s\u00fcrd\u00fcy\u00fc al\u0259md\u0259, elm\u0259 m\u0259lum olmayan, riyazi dild\u0259 ver\u0259 bilm\u0259diyimiz bir \u00e7ox m\u0259s\u0259l\u0259l\u0259r h\u0259l\u0259 d\u0259 h\u0259llin tapmam\u0131\u015f qal\u0131r. Qeyri-s\u0259lis m\u0259ntiqin \u0259n maraql\u0131 t\u0259r\u0259fi \u00e7oxlu m\u00fcxt\u0259lif \u0259laq\u0259 yaratmaq qabiliyy\u0259tidir, daha konkret des\u0259k, qeyri-s\u0259lis m\u0259ntiq biz\u0259 d\u0259rk etdirib ki, kainat\u0131n s\u0259rh\u0259dl\u0259ri d\u00fc\u015f\u00fcnd\u00fcy\u00fcm\u00fcz kimi yox, daha geni\u015f v\u0259 r\u0259ngar\u0259ngdir. Bu is\u0259 o dem\u0259kdir ki, d\u00fcnyan\u0131 t\u0259svir etm\u0259k \u00fc\u00e7\u00fcn yaln\u0131z iki \u2013 qara v\u0259 a\u011f \u0259v\u0259zin\u0259 \u201cbozun b\u00fct\u00fcn \u00e7alarlar\u0131\u201dn\u0131 n\u0259z\u0259r\u0259 almaq m\u00fctl\u0259qdir. Qeyri-s\u0259lis m\u0259ntiq bu problemi h\u0259ll ed\u0259r\u0259k h\u0259yat\u0131m\u0131z\u0131 r\u0259ngar\u0259ngl\u0259\u015fdirdi v\u0259 yeni ideyalar\u0131n yaranmas\u0131na t\u0259kan verdi. Qeyri-s\u0259lis m\u0259ntiqin dili klassik m\u0259ntiqd\u0259n f\u0259rqli olaraq a\u011f-qara, uzaq-yax\u0131n, soyuq-isti v\u0259 s. m\u0259i\u015f\u0259td\u0259 tez-tez qar\u015f\u0131la\u015fd\u0131\u011f\u0131m\u0131z sif\u0259tl\u0259rin n\u00f6vb\u0259li d\u0259r\u0259c\u0259l\u0259rinin (a\u011fappaq – a\u011f -…boz…- qara – qapqara kimi) istifad\u0259sin\u0259 \u0259saslan\u0131r, y\u0259ni bu m\u0259ntiqin \u0259sas prinsipi deyir ki, h\u0259r \u015fey d\u0259r\u0259c\u0259d\u0259n as\u0131l\u0131d\u0131r v\u0259 m\u00fcqayis\u0259 yolu il\u0259 \u00f6yr\u0259nilir.<\/p>\n
N\u0259z\u0259riyy\u0259ni komp\u00fcterl\u0259rd\u0259 istifad\u0259 etm\u0259k \u00fc\u00e7\u00fcn linqvistik d\u0259yi\u015f\u0259nl\u0259rd\u0259n elektron cihazlarda onlar\u0131n \u0259d\u0259di analoqlar\u0131na ke\u00e7m\u0259k \u00fc\u00e7\u00fcn riyazi \u00e7evrilm\u0259l\u0259rd\u0259n istifad\u0259 olunur. T\u0259\u0259cc\u00fcbl\u00fc deyil ki, t\u0259f\u0259kk\u00fcr\u00fcm\u00fcz z\u0259rr\u0259cikl\u0259rd\u0259 ba\u015f ver\u0259n, y\u0259ni mikro al\u0259md\u0259ki prosesl\u0259ri tam t\u0259svir etm\u0259k iqtidar\u0131nda deyil, \u00e7\u00fcnki Heyzenberq s\u00fcbut edib ki, kvant mexanikas\u0131nda bizim he\u00e7 vaxt bilm\u0259y\u0259c\u0259yimiz b\u0259zi \u015feyl\u0259r var ki, tan\u0131nmazd\u0131r. 1923-c\u00fc ild\u0259 frans\u0131z fiziki Lui de Broyl fotonun dal\u011fa-z\u0259rr\u0259cik ikili xass\u0259sinin materiyan\u0131n b\u00fct\u00fcn z\u0259rr\u0259cikl\u0259rin\u0259 \u2013 elektrona, protona, neytrona, atomlara v\u0259 s. xas ola bil\u0259c\u0259yi hipotezini ir\u0259li s\u00fcr\u00fcb. Onun ideyas\u0131na g\u00f6r\u0259, ixtiyari z\u0259rr\u0259cik enerji v\u0259 impulsa malik olarsa, bu halda h\u0259min z\u0259rr\u0259cik h\u0259r\u0259k\u0259t tezliyi enerji il\u0259 d\u00fcz, Plank sabiti il\u0259 t\u0259rs m\u00fct\u0259nasib olan dal\u011faya uy\u011fun g\u0259lir. Hipotez ingilis fiziki C.Tomson, Amerika fiziki K.Devisson v\u0259 komandalar\u0131 t\u0259r\u0259find\u0259n elektronlar\u0131n kristal q\u0259f\u0259sd\u0259n difraksiyas\u0131 t\u0259cr\u00fcb\u0259l\u0259ri n\u0259tic\u0259sind\u0259 t\u0259sdiql\u0259nib. Bu hadis\u0259d\u0259n sonra 1927-ci ild\u0259 Verner Heyzenberq t\u0259r\u0259find\u0259n ir\u0259li s\u00fcr\u00fcl\u0259n, klassik mexanikaya v\u0259 deterministik d\u00fc\u015f\u00fcnc\u0259l\u0259r\u0259 qar\u015f\u0131 yeni elmi istiqam\u0259tin \u2013 kvant fizikas\u0131n\u0131n yaranmas\u0131na he\u00e7 bir \u015f\u00fcbh\u0259 yaratmad\u0131. Kvant fizikas\u0131n\u0131n \u0259sas\u0131n\u0131 t\u0259\u015fkil ed\u0259n Heyzenberqin qeyri-m\u00fc\u0259yy\u0259nlik prinsipin\u0259 g\u00f6r\u0259, bir z\u0259rr\u0259ciyin momenti v\u0259 koordinat\u0131, o c\u00fcml\u0259d\u0259n enerjisi v\u0259 zaman\u0131 eyni anda tam d\u0259qiqlikl\u0259 \u00f6l\u00e7\u00fcl\u0259 bilm\u0259z. Qeyri-m\u00fc\u0259yy\u0259nlik prinsipini \u00fcmumil\u0259\u015fmi\u015f \u015f\u0259kild\u0259 anlamaq \u00fc\u00e7\u00fcn klassik fizikadan f\u0259rqli olaraq, kvant fizikas\u0131nda h\u0259r bir fiziki k\u0259miyy\u0259t\u0259 uy\u011fun g\u0259l\u0259n real, d\u0259qiq \u00f6l\u00e7\u00fcl\u0259 bil\u0259n parametr deyil, birehtimall\u0131, d\u0259qiq t\u0259yin ed\u0259 bilm\u0259y\u0259c\u0259yimiz k\u0259miyy\u0259tl\u0259rin uy\u011fun olmas\u0131n\u0131 d\u0259rk etm\u0259k laz\u0131md\u0131r. Bu k\u0259miyy\u0259tl\u0259r klassik mexanikadan f\u0259rqli olaraq say qiym\u0259tl\u0259ri il\u0259 yox, matrisalar vasit\u0259sil\u0259 t\u0259msil olunur. Bu, onunla \u0259laq\u0259dard\u0131r ki, mikro al\u0259md\u0259 materiyaya d\u00fc\u015f\u00fcnd\u00fcy\u00fcm\u00fcz kimi zaman\u0131n h\u0259r hans\u0131 an\u0131nda enerjisi v\u0259 impulsu olan z\u0259rr\u0259cik kimi deyil, h\u0259m d\u0259 tezliyi v\u0259 dal\u011fa \u0259d\u0259di olan dal\u011fa kimi bax\u0131lmal\u0131d\u0131r. Bu prinsip elm d\u00fcnyas\u0131n\u0131 heyr\u0259t\u0259 g\u0259tirib. Bel\u0259 ki, bir cism\u0259 daha yax\u0131ndan baxmaq daha az g\u00f6r\u0259 bilm\u0259yimizi d\u0259rk etdirib. \u015e\u00fcurumuzdak\u0131 materiya haqq\u0131nda m\u0259ntiqin qeyri-m\u00fc\u0259yy\u0259n oldu\u011funu g\u00f6st\u0259rib ki, bir \u015fey haqq\u0131nda tam m\u0259lumat\u0131m\u0131z olsa bel\u0259, 100 faiz \u0259minlikl\u0259 bu bar\u0259d\u0259 a\u00e7\u0131qlama ver\u0259 bilm\u0259rik. Y\u0259ni bir hiss\u0259ciyin bir x\u00fcsusiyy\u0259ti n\u0259 q\u0259d\u0259r d\u0259qiq \u00f6l\u00e7\u00fcl\u00fcrs\u0259, dig\u0259r x\u00fcsusiyy\u0259ti haqq\u0131nda daha az m\u0259lumatl\u0131 olaca\u011f\u0131q. Heyzenberq g\u00f6st\u0259rdi ki, materiyan\u0131n h\u0259qiqiliyi d\u0259r\u0259c\u0259 m\u0259s\u0259l\u0259sidir v\u0259 d\u00fcnya \u00e7oxqiym\u0259tli m\u0259ntiql\u0259, a\u011f, qara v\u0259 biz\u0259 m\u0259lum olmayan qeyri-m\u00fc\u0259yy\u0259n, \u201cbozun \u00e7alarlar\u0131\u201d il\u0259 r\u0259ngar\u0259ngdir. Bu yeni fikirl\u0259r elm adamlar\u0131n\u0131 \u015f\u00fcbh\u0259 alt\u0131na sald\u0131 v\u0259 h\u0259l\u0259 d\u0259 elmin inki\u015faf\u0131na t\u0259sir ed\u0259n bu k\u0259\u015ffin tam d\u0259rk olunmamas\u0131na s\u0259b\u0259b, o d\u00f6vrd\u0259 \u0259limizd\u0259 yegan\u0259 riyazi aparat olan ehtimal n\u0259z\u0259riyy\u0259si vasit\u0259sil\u0259 \u015f\u00fcbh\u0259l\u0259ri qism\u0259n riyazi formaya salmaq idi. Bel\u0259 ki, a\u011f-qara reall\u0131\u011f\u0131ndan boz h\u0259qiq\u0259t\u0259 ke\u00e7m\u0259k \u0259v\u0259zin\u0259 qeyri-m\u00fc\u0259yy\u0259nlik prinsipi ehtimal\u0131 ya var ya yox \u201ch\u0259qiq\u0259tind\u0259\u201d q\u0259rarla\u015fd\u0131: ham\u0131s\u0131 v\u0259 ya he\u00e7 biri. \u018fslind\u0259 is\u0259 h\u0259yatda he\u00e7 n\u0259 he\u00e7 vaxt qeyri-s\u0259lis olmayacaq, \u0259sas\u0259n d\u0259 riyazi dild\u0259 yaz\u0131la bil\u0259n h\u0259r \u015fey. Ona g\u00f6r\u0259 ki, bu d\u00fcnyada Allah h\u0259r \u015feyi elmi il\u0259 \u0259hat\u0259 edib v\u0259 qeyri-s\u0259lisliy\u0259 he\u00e7 bir yer qoymay\u0131b. Sad\u0259c\u0259 olaraq, bizim anlamad\u0131\u011f\u0131m\u0131z, t\u0259f\u0259kk\u00fcr\u00fcm\u00fcz\u00fcn d\u0259rk ed\u0259 bilm\u0259diyi \u015feyl\u0259r\u0259 qeyri-m\u00fc\u0259yy\u0259n ad\u0131 veririk. M\u0259s\u0259l\u0259n, klassik m\u0259ntiq\u0259 g\u00f6r\u0259 istiy\u0259 1, soyu\u011fa 0 des\u0259k temperaturun 30 d\u0259r\u0259c\u0259 Selsid\u0259 olmas\u0131, Aristotel m\u0259ntiqi n\u0259tic\u0259si etibar\u0131 il\u0259 \u201cbirdirmi?\u201d ya \u201cs\u0131f\u0131rd\u0131rm\u0131?\u201d sual\u0131 qeyri-m\u00fc\u0259yy\u0259n olacaq, cismin hans\u0131 temperaturdan sonra isti v\u0259 ya hans\u0131 temperaturda soyuq oldu\u011fu bizim \u00fc\u00e7\u00fcn qeyri-s\u0259lisdir. Temperatur \u015fkalas\u0131 konkret olaraq cismin hans\u0131 v\u0259ziyy\u0259td\u0259 olmas\u0131 haqq\u0131nda d\u0259qiq m\u0259lumat verir v\u0259 qeyri m\u00fc\u0259yy\u0259nliyi aradan qald\u0131r\u0131r.<\/p>\n
Real d\u00fcnya qeyri-m\u00fc\u0259yy\u0259nlikl\u0259rl\u0259 doludur, bu bax\u0131mdan m\u00fclahiz\u0259l\u0259r ad\u0259t\u0259n n\u0259 ayd\u0131n \u015f\u0259kild\u0259 1, n\u0259 d\u0259 ayd\u0131n \u015f\u0259kild\u0259 0 qiym\u0259ti al\u0131r. Elmd\u0259 dem\u0259k olar ki, b\u00fct\u00fcn hadis\u0259l\u0259r, n\u0259z\u0259riyy\u0259l\u0259r klassik m\u0259ntiql\u0259 \u2013 ikiqiym\u0259tli m\u0259ntiql\u0259, y\u0259ni rasional t\u0259f\u0259kk\u00fcrl\u0259 izah olunub v\u0259 h\u0259l\u0259 d\u0259 bu d\u00fc\u015f\u00fcnc\u0259d\u0259 qalma\u011f\u0131m\u0131z, elmd\u0259 ya\u015fad\u0131\u011f\u0131m\u0131z dur\u011funlu\u011fun n\u0259tic\u0259sidir ki, mikro d\u00fcnyan\u0131n v\u0259 meqa al\u0259min \u00f6yr\u0259nilm\u0259sind\u0259 qeyri-m\u00fc\u0259yy\u0259n hadis\u0259l\u0259rl\u0259 \u2013 kvant fizikas\u0131nda qeyri-m\u00fc\u0259yy\u0259nlik prinsipi, relativistik fizikada nisbilik prinsipi (Lorens \u0259msal\u0131n\u0131n sonsuzlu\u011fa yax\u0131nla\u015fmas\u0131 qeyri-m\u00fc\u0259yy\u0259nliyi), kosmologiyada qaranl\u0131q materiya v\u0259 s. il\u0259 rastla\u015f\u0131r\u0131q. H\u0259qiq\u0259t\u0259n d\u0259, bu qeyri-s\u0259lislik m\u0259ntiqimiz \u00fc\u00e7\u00fcn qeyri-adidir, \u00e7\u00fcnki a\u011f\u0131l bax\u0131m\u0131ndan d\u0259rkolunmazd\u0131r \u2013 a\u011flabatan olan reald\u0131r, y\u0259ni t\u0259cr\u00fcb\u0259d\u0259 m\u00f6vcud olan el\u0259 bir \u015fey yoxdur ki, a\u011f\u0131lda olmas\u0131n. Cismin temperatur xarakteristikas\u0131 olan, soyuq – … – m\u00fclayim -…- isti – qaynar sif\u0259tl\u0259ri q\u0259bul etdiyimiz faza ke\u00e7idi n\u00f6qt\u0259si il\u0259 temperatur \u015fkalas\u0131nda qeyri-m\u00fc\u0259yy\u0259nlik problemini h\u0259ll etdiyimiz kimi, dal\u011fa -…- yar\u0131mdal\u011fa v\u0259 ya yar\u0131mz\u0259rr\u0259 -…- z\u0259rr\u0259cik, enerji -…- yar\u0131menerji v\u0259 ya yar\u0131mmateriya -…- materiya yax\u0131nla\u015fmalar\u0131 il\u0259 hans\u0131sa parametr daxil etm\u0259kl\u0259 qeyri-m\u00fc\u0259yy\u0259nlikl\u0259ri, sonsuzluqlar\u0131 \u2013 d\u00fcnyan\u0131 real d\u0259rk etm\u0259yimiz \u00fc\u00e7\u00fcn biz\u0259 ehtimal n\u0259z\u0259riyy\u0259sinin iki d\u0259y\u0259rli m\u0259ntiqi yox, qeyri-s\u0259lis m\u0259ntiq\u0259 \u0259saslanan m\u00fcasir t\u0259f\u0259kk\u00fcr\u00fcn m\u0259hsulu \u2013 yeni ideyalar v\u0259 n\u0259z\u0259riyy\u0259 laz\u0131md\u0131r. \u0130nan\u0131r\u0131q ki, qeyri-s\u0259lis riyaziyyat v\u0259 qeyri-s\u0259lis kvant fizikas\u0131 bu probleml\u0259ri tezlikl\u0259 h\u0259ll ed\u0259 bil\u0259c\u0259k v\u0259 elmin inki\u015fafina yeni qap\u0131 a\u00e7acaq.<\/p>\n