MILOŠ ADŽIĆ i SENKA MILOŠEVIĆ Uni ver zi tet u Be o gra du, Fi lo zof ski fa kul tet Ode lje nje za fi lo zofiju, Be o grad, Srp ska aka de mi ja na u ka i umet no sti, Ma te ma tič ki in sti tut, Be o grad DOI 10.5937/kultura1234237A UDK 371.3::16(497.11) 16 Недић Љ. originalan naučni rad IZ STA RI JE SRP SKE LO GI KE Sa-že-tak: U ovom ra du uka za će mo na ne ke od sta ni ca raz vo ja lo gi- ke u Sr bi ji, od osni va nja Li ce ja 1836. pa sve do kra ja XIX ve ka. Cilj nam je da pot cr ta mo ulo gu ko ju je Lju bo mir Ne dić, fi lo zof i knji žev ni kri ti čar, od i grao u ovom po gle du. Iako se srp ska lo gi ka ovog pe ri o- da ne mo že po hva li ti ori gi nal no šću, Ne dić je od i grao zna čaj nu ulo gu u iz la ga nju sa vre me nih re zul ta ta en gle ske sim bo lič ke lo gi ke, ko ji će kra jem ve ka, pr ven stve no kroz Fre ge o ve ra do ve, do ve sti do stva ra nja mo der ne lo gi ke. Ključ-ne-re-či: Lju bo mir Ne dić, tra di ci o nal na lo gi ka, sim bo lič ka lo gi ka, mo der na lo gi ka. Pe-riod- s- kra-ja-XIX- ve-ka- sma-tra- se- do-bom- na-stan-ka-mo-der-ne- lo-gi-ke.-Pre-ci-zni-je,-1879.-go-di-na,-u-ko-joj-je-Fre-ge-(Got-tlob-Fre- ge)-ob-ja-vio-svoj-Be griffsschrift,1-pred-sta-vlja-pre-kret-ni-cu-u-ovom- po-gle-du.-Kao- i- sva-ko- ve-li-ko- ot-kri-će,- i- ovo-Fre-ge-o-vo- ni-je- bez- pret-hod-ni-ka,- ali- je- iz-ne-na-đu-ju-će- ko-li-ko- no-vi-na- ono- sa- so-bom- no-si.- Šta-vi-še,- Fre-ge-o-vom- de-lu- ni-je- po-treb-na- ni-ka-kva- de-talj-na- eg-ze-ge-za;- sva-ko- ko- je- upo-znat- sa- pre-di-kat-skom- lo-gi-kom,- ka- ko-se-ona-da-nas-pre-da-je-đa-ci-ma,-ve-o-ma-la-ko-će-je-pre-po-zna-ti-i- kod-Fre-gea.2 1- Fre-ge- G.,- Be griffsschrift: eine der arit hme tischen nac hge bil de te For mel- sprac he des re i nen Den kens,-Hal-le,-1879. 2- De-ta-ljan-pre-gled-isto-ri-je-lo-gi-ke,-ko-ji-ob-ra-đu-je-i-te-me-ko-jih-će-mo-se-do-ta-ći-u- na-stav-ku-ra-da,-za-in-te-re-so-va-ni-či-ta-lac-mo-že-pro-na-ći-u-vi-še-tom-nom,-en-ci-klo-pe- dij-skom-pri-ruč-ni-ku:--Hand bo ok of the Hi story of Lo gic, eds.-Gab-bay-D.-M.-i- Wo-ods-J.,-Vols. I-XI,-Am-ster-dam,-2004-2012.-Stu-di-ja-ma-njeg-obi-ma,-ko-ja-ne- za-o-sta-je-po-kva-li-te-tu-je-ste-i:-Kne-a-le-W.-i-Kne-a-le-M.,-The De ve lop ment of Lo- gic,-Ox-ford,-1962.-Od-ne-dav-no,-po-sled-nja-knji-ga-po-sto-ji-i-u-pre-vo-du-na-srp-ski- je-zik:-Nil-V.-i-Nil-M.,-Raz voj lo gi ke,-Be-o-grad,-2011.-Na-po-me-ni-mo-još-i-to-da- je- je-di-ni-ca- „Isto-ri-ja- lo-gi-ke",- pi-sana- za-Ro-u-tli-džo-vu-osmo-tom-nu-Fi lo zof sku en ci klo pe di ju,-pre-ve-dena-na-naš-je-zik-i-ob-ja-vljena-kao:-Pri-or-A.-N.,-Hi sto ri ja lo gi ke,-Za-greb,-1970. 238 MILOŠ ADŽIĆ i SENKA MILOŠEVIĆ U-Sr-bi-ji- ovog- do-ba,- sve-ga- če-ti-ri- de-ce-ni-je- od- na-stan-ka-Li-ce-ja,- lo-gi-ka- i- da-lje-ne- zna- za-Fre-ge-o-va-do-stig-nu-ća.-Ovo-ni-je-ni-ma- lo- iz-ne-na-đu-ju-će,-bu-du-ći-da- je- svo-ju-ka-no-ni-za-ci-ju-mo-der-na- lo- gi-ka-do-ži-ve-la-tek-s-po-čet-kom-XX-ve-ka.-U-ovom-pe-ri-o-du-ra-đa- nja,- ni-mno-ge- sta-ri-je,- i- ugled-ni-je,- evrop-ske- ško-le- ni-su- se-mo- gle- po-hva-li-ti- ne-go-va-njem- ove-mla-de- na-u-ke.-Me-đu-tim,- da-le-ko- od- to-ga- da- lo-gi-ka- u- Sr-bi-ji- ni-je- bi-la- pred-met- pro-u-ča-va-nja.-Od- osni-va-nja-Li-ce-ja-1838.-go-di-ne,- lo-gi-ka- je,-pr-ven-stve-no-u- svom- tra-di-ci-o-nal-nom- ob-li-ku,- za-u-zi-ma-la- va-žno- me-sto- u- na-stav-nom- pro-gra-mu-fi-lo-zo-fi-je.- Pr-vi-na-stav-ni-ci-fi-lo-zo-fi-je-i-lo-gi-ke-na-Li-ce-ju-bi-li-su-Ata-na-si-je-Te- o-do-ro-vić- i- Pe-tar- Ra-do-va-no-vić.3- Već- kra-jem- 1839-te,- na-sta-vu- fi-lo-zo-fi-je- pre-u-zi-ma- Kon-stan-tin- Bran-ko-vić,- ro-dom- No-vo-sa-đa- nin,- ko-ji- je- na-kon- ne-do-vr-še-nih- stu-di-ja- pra-va- u- Pe-šti- i- za-vr-še- nih-stu-di-ja-bo-go-slo-vi-je-u-Kar-lov-ci-ma,-imao-pri-li-ku-da-ne-ko-li-ko- go-di-na-pro-ve-de-u-Laj-pci-gu.-Ovo-mu-je-omo-gu-ći-lo-da-po-se-ću-je- pre-da-va-nja-Vil-hel-ma-Kru-ga-(Wil-helm-Tra-u-gott-Krug),-fi-lo-zo-fa- kan-tov-ske-tra-di-ci-je,-ko-ji-je,-na-kon-Kan-to-ve-smr-ti-1804.-go-di-ne,- na-sle-dio-ka-te-dru-za-lo-gi-ku-i-me-ta-fi-zi-ku-na-Uni-ver-zi-te-tu-u-Ke-nig- sber-gu.-Pod-nje-go-vim-uti-ca-jem,-Bran-ko-vić- je- lo-gi-ku-pre-da-vao- pu-nih-26-go-di-na,-is-pr-va-na-Li-ce-ju,-a-ka-sni-je-i-na-Ve-li-koj-ško-li,- či-ji-je-je-dan-od-osni-va-ča-1863.-go-di-ne-i-sam-bio.-Kru-gov-uti-caj- na-Bran-ko-vi-ća- ja-sno- se-ogle-da- i-u-udž-be-ni-ci-ma-ko-je- je-pi-sao.- Ta-ko-„Mi-slo-slo-vlje-ili-lo-gi-ka-za-mla-dež",-ob-ja-vlje-no-1849-te,-i- „Mi-slo-slo-vlje-ili-lo-gi-ka-za-pr-vo-go-di-šnje-slu-ša-te-lje-Mu-dro-slo-vlja- u-Li-ce-u-mu",-ob-ja-vlje-no-dve-go-di-ne-ka-sni-je,-po-ka-zu-ju-ja-san-uti- caj-Kru-go-ve-Den kle hre oder Lo gik.-U-nji-ma,-Bran-ko-vić-iz-la-že- na-če-la- lo-gi-ke-kao-na-u-ke-o-„do-brom-[...]-upo-tre-blja-va-nju- ra-zu- ma",-sle-de-ći-tra-di-ci-o-nal-nu-kla-si-fi-ka-ci-ju-lo-gič-kih-uče-nja-o-poj-mu,- su-du-i-za-ključ-ku.-- Bran-ko-vi-ćev-na-sled-nik-na-Ve-li-koj-ško-li-od-1869-te,-bio-je-Alim- pi-je-Va-si-lje-vić.-Na-kon-za-vr-še-ne-be-o-grad-ske-bo-go-slo-vi-je,-Va-si- lje-vić-stu-di-ra-fi-lo-zo-fi-ju-i-bo-go-slo-vi-ju-na-Ki-jev-skoj-du-hov-noj-aka- de-mi-ji.-Po-po-vrat-ku-u-Sr-bi-ju,-ne-ko-li-ko-go-di-na-ra-di-kao-pre-da-vač- na-bo-go-slov-skoj-ško-li,-da-bi-se-po-čet-kom-še-zde-se-tih-go-di-na-ob- reo-na-usa-vr-ša-va-nju-u-Pa-ri-zu,-gde-do-la-zi-u-do-dir-sa-sa-vre-me-nim- to-ko-vi-ma-evrop-ske-fi-lo-zo-fi-je.-Vra-tiv-ši-se-u-Be-o-grad,-Va-si-lje-vić- do-bi-ja-pro-fe-su-ru-fi-lo-zo-fi-je-na-Ve-li-koj-ško-li-gde,-iz-me-đu-osta-lih- pred-me-ta,-pre-da-je-i-lo-gi-ku.-Svo-ju-lo-gič-ku-stu-di-ju--O lo gič kim za- blu da ma ili pri vid nim do ka zi ma,-kao-i-udž-be-nik-za-đa-ke-Ve-li-ke- ško-le,-na-slo-vljen-jed-no-stav-no-Lo gi ka,-ob-ja-vio-je-1871.-go-di-ne.- Na-su-prot-svom-pret-hod-ni-ku,-Kon-stan-ti-nu-Bran-ko-vi-ću,-či-ja-je-lo- gi-ka-u-ve-li-koj-me-ri-in-spi-ri-sa-na-Kru-go-vom,-Va-si-lje-vić-fa-vo-ri-zu-je- 3- Za-is-crp-ni-ji-pre-gled-isto-ri-je-fi-lo-zo-fi-je-na-Li-ce-ju-i-Ve-li-koj-ško-li-u-XIX-ve-ku,-za- in-te-re-so-va-nog-či-ta-o-ca-upu-ću-je-mo-na:-Stoj-ko-vić-A.,-Raz vi tak fi lo so fi je u Sr ba: 1804-1944,-Be-o-grad,-1972. 239 MILOŠ ADŽIĆ i SENKA MILOŠEVIĆ Mi-lov-(John-Stu-art-Mill)-pri-stup- lo-gi-ci-kroz-nje-na- tri-osnov-na- aspek-ta:- de-duk-ci-ja,- in-duk-ci-ja,- po-sma-tra-nje- i- eks-pe-ri-ment.- Po- red-ovih,-Va-si-lje-vić- is-ti-če- i- iz-ve-sne-spo-red-ne-pro-ble-me-lo-gi-ke,- i- to:- ana-li-zu- je-zi-ka,- op-šte- oso-bi-ne- lo-gič-kog- is-pi-ti-va-nja,- kao- i- lo-gič-ke-za-blu-de. U-ovo-vre-me,-po-red-Va-si-lje-vi-ća,-na-Ve-li-koj-ško-li-pre-da-je-i-Mi- lan-Ku-jun-džić-Aber-dar.-Svo-je- ško-lo-va-nje- u-Be-o-gra-du,-Ku-jun- džić-je-na-sta-vio-u-Be-ču,-Min-he-nu-i-Pa-ri-zu.-Fi-lo-zo-fi-ju-je-stu-di-rao- na-Oks-for-du,-oda-kle- se,- na-kon- svr-še-nih- stu-di-ja,- vra-tio-u-Be-o- grad-1865-te.-Na-Ve-li-koj-ško-li-pre-da-je-u-dva-na-vra-ta,-od-1866.- do-1867.-go-di-ne,-kao-i-od-1873.-do-1882.-go-di-ne.-Ku-jun-dži-će- vo-raz-u-me-va-nje-lo-gi-ke-kao-„na-u-ke-o-sve-sti",-u-ve-li-koj-me-ri-je- psi-ho-lo-gi-stič-ko.-Kao-i-Va-si-lje-vić,- i-on-na-vo-di-Mi-la-kao-uzor-u- po-gle-du-lo-gi-ke,-iako-u-ve-ćoj-me-ri-in-si-sti-ra-na-psi-ho-lo-gi-stič-kom- tu-ma-če-nju-lo-gič-kih-ka-te-go-ri-ja. Na-kon- Ku-jun-dži-ća,- na-sta-vu- lo-gi-ke- na-Ve-li-koj- ško-li- pre-u-zi-ma- Lju-bo-mir-Ne-dić.--Ro-đen-je-1858.-go-di-ne-u-Be-o-gra-du,-gde-je-za- vr-šio-osnov-nu-ško-lu-i-gim-na-zi-ju.-Svo-je-ško-lo-va-nje-na-sta-vio-je-na- uni-ver-zi-te-ti-ma-u-Laj-pci-gu-i-Je-ni.-To-kom-de-se-to-go-di-šnjih-stu-di-ja- u-ino-stran-stvu,-bio-je-u-pri-li-ci-da-go-di-nu-da-na-stu-di-ra-lo-gi-ku-u- Lon-do-nu.-Za-ni-mlji-vo-je-pri-me-ti-ti-da-se-Ne-dić-ob-reo-u-Je-ni-već- 1878.-go-di-ne,- sve-ga-go-di-nu-da-na-pre-ob-ja-vlji-va-nja-Fre-ge-o-vog- Be griffsschrift-a.-U-ovo-vre-me,-Fre-ge-u- Je-ni-pre-da-je-u- zva-nju- pri vat do zent-a,-da-bi-na-red-ne-1879.-go-di-ne-do-bio-pu-nu-pro-fe-su- ru.-Ni-je-za-be-le-že-no-da-li-je,-i-ka-da,-Ne-dić-bio-u-pri-li-ci-da-slu-ša- Fre-ge-o-va-pre-da-va-nja. Na-Ve-li-koj- ško-li- Ne-dić- pre-da-je- od- 1884.- do- 1895.- go-di-ne.-U- po-sled-njoj- de-ce-ni-ji- ži-vo-ta,- u-pot-pu-no-sti- se,- i- sa-ve-li-kim-uspe- hom,-po-sve-ću-je-knji-žev-noj-kri-ti-ci.-Nje-gov-ot-klon-od-isto-ri-o-graf- skog- pri-stu-pa- ovoj- di-sci-pli-ni,- i- in-si-sti-ra-nje- na- estet-skim- od-li- ka-ma-knji-žev-nog-de-la,-či-ne-ga-za-čet-ni-kom-mo-der-ne-knji-žev-ne- kri-ti-ke-kod-Sr-ba.-- Svo-ju-dok-tor-sku-di-ser-ta-ci-ju-pod-na-slo-vom-Uče nje o kvan ti fi ka- ci ji pre di ka ta u no vi joj en gle skoj lo gi ci,-Ne-dić-je-od-bra-nio-1884.- go-di-ne-u-Laj-pci-gu.-Men-tor-mu- je-bio-Vil-helm-Vunt- (Wil-helm- Wundt),- da-nas- po-znat- kao- za-čet-nik- eks-pe-ri-men-tal-ne- psi-ho-lo- gi-je.- Ide-ju- svo-je-dok-tor-ske-di-ser-ta-ci-je-Ne-dić- je,- po- sve-mu- su- de-ći,- for-mi-rao-to-kom-jed-no-go-di-šnjeg-bo-rav-ka-u-Lon-do-nu,-gde- je-bio-u-pri-li-ci-da-se-upo-zna-sa-ra-do-vi-ma-sa-vre-me-nih-en-gle-skih- lo-gi-ča-ra.-U-ovom-po-gle-du-iz-dva-ja-ju-se-ra-do-vi-Vi-li-ja-ma-Ha-mil- to-na-(Wil-li-am-Ha-mil-ton),-is-pi-ti-va-nje-ko-jih-pred-sta-vlja-oko-sni-cu- Ne-di-će-ve-di-ser-ta-ci-je:- „U- ovoj- ras-pra-vi- na-či-njen- je- po-ku-šaj- da- se- uče-nje- o- kvan-ti-fi- ka-ci-ji,-ona-ko-ka-ko-ga-je-ob-li-ko-vao-Ha-mil-ton,-pred-sta-vi-u-svo- jim-glav-nim-mo-men-ti-ma.-Ve-li-ki-zna-čaj-ko-ji- je-nje-go-vo-učenje- 240 MILOŠ ADŽIĆ i SENKA MILOŠEVIĆ ka-sni-je-za-do-bi-lo,-kao-i-okol-no-sti-da-je-u-Ne-mač-koj-osta-lo-ma- lo- po-zna-to,- uči-ni-li- su- da- se- ovaj- po-ku-šaj- ja-vi- kao- mo-žda- ne- sa-svim-neo-prav-dan"4. Ne-ko-li-ko-re-či-o-Ha-mil-to-no-voj-kvan-ti-fi-ka-ci-ji-pre-di-ka-ta-je-na-me- stu.- Ova- te-o-ri-ja,- kao- i- mno-ge- nje-ne- sa-vre-me-ni-ce,- pred-sta-vlja- raz-ra-du-Ari-sto-te-lo-ve-si-lo-gi-stič-ke-lo-gi-ke.-Ari-sto-te-lo-va-ide-ja,-ko- ja-se-odr-ža-la-sve-do-kra-ja-XIX-ve-ka- i-na-stan-ka-mo-der-ne- lo-gi- ke,- je-ste-da- je- is-prav-na-ana-li-za- lo-gič-ke- for-me- is-ka-za- tro-del-na:- (S)ubjekt-ko pu la-(P)re di kat.- Ari-sto-tel- raz-li-ku-je- če-ti-ri- osnov-na- ob-li-ka-is-ka-za-i-to:- (SaP)-Svi-S-su-P,- (SeP)-Ni-je-dan-S-ni-je-P,- (SiP)-Ne-ki-S-su-P,- (SoP)-Ne-ki-S-ni-su-P.- Ha-mil-to-no-va-pri-med-ba-na-ova-kvu-kla-si-fi-ka-ci-ju-osnov-nih-is-ka-za- je-ste-da-je-ona-neo-d-re-đe-na-u-po-gle-du-to-ga-da-li-se-ovi-is-ka-zi-od- no-se-na-či-ta-vu-eks-ten-zi-ju-pre-di-ka-ta-P-ili-pak-na-njen-pra-vi-deo.-U- sve-tlu-ove-pri-med-be,-Ari-sto-te-lo-vu-po-de-lu-mo-že-mo-uči-ni-ti-pre-ci- zni-jom-ta-ko-što-će-mo-eks-pli-cit-no-kvan-ti-fi-ko-va-ti-ne-sa-mo-su-bjekt- is-ka-za-S,-već-i-pre-di-kat-P.-Ovo-nam,-ume-sto-Ari-sto-te-lo-va-če-ti-ri- osnov-na-ob-li-ka-is-ka-za,-da-je-osam: Svi-S-su-svi-P, Svi-S-su-ne-ki-P, Ni-je-dan-S-ni-je-ni-je-dan-P, Ni-je-dan-S-ni-je-ne-ki-P, Ne-ki-S-su-svi-P, Ne-ki-S-su-ne-ki-P, Ne-ki-S-ni-su-ni-je-dan-P, Ne-ki-S-ni-su-ne-ki-P. Da-bi-smo-ilu-stro-va-li-pred-no-sti-ova-kve-ana-li-ze,-raz-mo-tri-mo-pri- mer-dva-is-ka-za:-(a)-„Svi-lju-di-su-smrt-ni",-i-(b)-„Svi-lju-di-su-ra-ci- o-nal-ne-ži-vo-ti-nje".-Pre-ma-Ari-sto-te-lo-voj-ana-li-zi,-oba-is-ka-za-ima-ju- istu-lo-gič-ku-for-mu,-na-i-me-SaP.-Me-đu-tim,-sle-de-ći-Ha-mil-to-na,-vi- di-mo-da-je-is-kaz-(a)-in-stan-ca-od-„Svi-S-su-ne-ki-P",-dok-je-is-kaz- (b)-in-stan-ca-od-„Svi-S-su-svi-P".- Ha-mil-to-no-vo-uče-nje-ima-lo-je-i-iz-ve-sne-ne-do-stat-ke.-Na-i-me,-bi-lo- je- ja-ko- te-ško- for-mu-li-sa-ti- kvan-ti-fi-ka-ci-ju- pre-di-ka-ta- u- pri-rod-nom- 4- Ne-dić-Lj.,-Fi lo zof ski spi si,-Be-o-grad,-2000,-str.-7. 241 MILOŠ ADŽIĆ i SENKA MILOŠEVIĆ je-zi-ku-na-na-čin-ko-ji-je-ne-či-ni-ro-go-bat-nom.-Jed-no-od-mo-gu-ćih- re-še-nja- ovog- pro-ble-ma,- ko-jem- je- pri-be-gao- i- Ha-mil-ton,- je-ste- osmi-šlja-va-nje-ade-kvat-ne-no-ta-ci-je,-uz-po-moć-ko-je-bi-se,-na-ja-san- i- pre-ci-zan- na-čin,- ova-kva- kvan-ti-fi-ka-ci-ja-mo-gla- za-be-le-ži-ti.- Ovo- ima-za-po-sle-di-cu- tran-sfor-mi-sa-nje-ka-te-go-rič-kih- is-ka-za-u- jed-na- ko-sti-iz-me-đu-to-tal-nih-ili-par-ci-jal-nih-eks-ten-zi-ja-te-ra-ma-ko-ji-se-u- nji-ma-ja-vlja-ju,-što-nam-pru-ža-mo-guć-nost- is-pi-ti-va-nja- lo-gi-ke-al- ge-bar-skim- sred-stvi-ma.- Iako- je-Ha-mil-to-no-va- no-ta-ci-ja- za- kvan- ti-fi-ka-ci-ju-pre-di-ka-ta-pro-šla-go-to-vo-bez-od-je-ka,-mo-že- se- re-ći-da- je-ona,-ma-kar-po-sred-no,-pru-ži-la-do-dat-ni-pod-sti-caj-al-ge-bri-za-ci-ji- lo-gi-ke-u-XIX-ve-ku.5 Još-je-dan-en-gle-ski-lo-gi-čar-tog-do-ba,-u-či-jim-se-ra-do-vi-ma-ja-vlja- ide-ja- o- kvan-ti-fi-ka-ci-ji- pre-di-ka-ta,- bio- je- De-Mor-gan- (Augu-stus- De-Mor-gan).-Za-raz-li-ku-od-Ha-mil-to-na,-De-Mor-gan-je-bio-ma- te-ma-ti-čar-po-obra-zo-va-nju- i,-po-red- lo-gi-ke,-ba-vio-se-al-ge-brom-i- ma-te-ma-tič-kom-ana-li-zom.-Kao-i-Ha-mil-ton,-De-Mor-gan-se-ba-vio- is-pi-ti-va-njem-raz-li-či-tih-ob-li-ka-si-lo-gi-zma,-ali-je-nje-gov-si-stem-bio- da-le-ko--na-pred-ni-ji.-Sma-tra-ju-ći-da-je-ve-ći-nu-svo-jih-re-zul-ta-ta,-da- se-po-slu-ži-mo-eufe-mi-zmom,-„pre-u-zeo"-iz-nje-go-vih-ra-ni-jih-de-la,- Ha-mil-ton-op-tu-žu-je-De-Mor-ga-na-za-pla-gi-ja-tor-stvo,-i-sa-njim-ot- po-či-nje-du-go-go-di-šnju-štam-pa-nu-po-le-mi-ku.-Ka-ko-je-vre-me-od-mi- ca-lo,-po-sta-lo-je-ja-sno-da-Ha-mil-to-no-ve-op-tu-žbe-ne-sto-je,-i-dok-je- Ha-mil-ton-sve-vi-še-gu-bio-na-ugle-du,-do-tle-je-De-Mor-ga-no-vo-ime- bi-va-lo- sve- pri-zna-ti-je.- Po-Gard-ne-ro-vim- (Mar-tin-Gard-ner)- re-či- ma,-na-de-lu-je-bi-la-„naj-o-gor-če-ni-ja-i-naj-ko-mič-ni-ja-ras-pra-va-o-for- mal-noj-lo-gi-ci-od-do-ba-uče-nih-lju-di,-iako-su-go-to-vo-sav-hu-mor-i- pro-nic-lji-vost-bi-li-na-stra-ni-De-Mor-ga-na"6. Po-me-nu-ta-ras-pra-va-ima-la- je- i-ne-ke-bla-go-rod-ne-po-sle-di-ce.-Na-i- me,-ona-je-ob-no-vi-la-in-te-re-so-va-nje-Džor-dža-Bu-la-(Ge-or-ge-Bo-o-le)- za-lo-gi-ku,-što-je-kul-mi-ni-ra-lo-nje-go-vom-stu-di-jom-Mat he ma ti cal Analysis of Lo gic,-ob-ja-vlje-nom-1847.-go-di-ne.-Ovo-va-žno-de-lo- za-isto-ri-ju-lo-gi-ke-po-ro-di-lo-je-mno-go-na-pred-nih-ide-ja.-Osim-što- se-slu-žio-sim-bo-li-ma-da-bi-pred-sta-vio-is-ka-ze-kao-jed-na-ko-sti-me-đu- te-rmima,-Bul-je-uveo-i-ope-ra-ci-je-pro-iz-vo-da-i-su-me-na-ter-mi-ma,- za-jed-no-sa-al-ge-bar-skim-za-ko-ni-ma-ko-ji-ove-ope-ra-ci-je-od-re-đu-ju.- S-jed-ne-stra-ne,-Bu-lo-va-za-mi-sao-bi-la-je-da-raz-ma-tra-al-ge-bru-en- ti-te-ta- ko-ji- ni-su- bro-je-vi,- ne- in-si-sti-ra-ju-ći,- s- dru-ge- stra-ne,- da- svi- al-ge-bar-ski-za-ko-ni-ko-ji-va-že-za-bro-je-ve-mo-ra-ju-va-ži-ti-i-u-slu-ča-ju- ove-no-ve-al-ge-bre.-Ovo-mu-je-omo-gu-ći-lo-da-ana-li-zu-lo-gič-ke-for- me-is-ka-za-pro-ši-ri-na-mno-go-ve-ću-kla-su-od-one-ko-ju-je-do-pu-šta-la- tra-di-ci-o-nal-na-Ari-sto-te-lo-va-lo-gi-ka.- 5- O-isto-rij-skim-iz-vo-ri-ma-ide-je-o-kvan-ti-fi-ka-ci-ji-pre-di-ka-ta,-za-in-te-re-so-va-nog-či-ta- o-ca-upu-ću-je-mo-na-Ne-di-će-vu-di-ser-ta-ci-ju:-Ne-dić-Lj.,-op.-cit.,-str.-10. 6- Gard-ner-M.,-Lo gic, Mac hi nes and Di a grams,-New-York-1958,-str-37. 242 MILOŠ ADŽIĆ i SENKA MILOŠEVIĆ De-Mor-ga-no-vi- i-Bu-lo-vi- ra-do-vi-bi-li- su-po-zna-ti-Ne-di-ću,- i-on- ih- eks-pli-cit-no- spo-mi-nje- u- svo-joj- di-ser-ta-ci-ji.- Po-red- to-ga,- u- svo- jim- pre-da-va-nji-ma- iz- lo-gi-ke,- ko-ja- su- sa-ču-va-na- u- vi-du- be-le-ža- ka-nje-go-vih- stu-de-na-ta- i- ne-dav-no-u-ovom-ob-li-ku- i-ob-ja-vlje-na,7 Ne-dić-ka-že: „Sva-ki-akt-na-šeg-mi-šlje-nja-pred-sta-vlja-lo-gič-ku-jed-na-či-nu-iz-me-đu- ono-ga-o-če-mu-se-su-di-i-ono-ga-šta-se-su-di-(su-bjek-ta-i-objek-ta),-i- na-taj-na-čin-kad-mo-že-mo-poj-mo-ve-sma-tra-ti-kao-ko-li-či-ne-i-su-do-ve- kao-lo-gič-ke-jed-na-či-ne,-on-da-oče-vid-no-iz-la-zi-da-se-mo-že-u-Lo-gi-ci- ona-ko-isto-ope-ri-sa-ti-sa-poj-mo-vi-ma-kao-u-ma-te-ma-ti-ci-sa-ko-li-či-na- ma,-i-na-taj-na-čin-je-otvo-ren-put-ma-te-ma-tič-koj-lo-gi-ci,-ko-ju-smo- ra-ni-je-ima-li-pri-li-ku-da-vi-di-mo;-iako-ta-lo-gi-ka-ni-je-ob-ja-vlje-na-u- si-ste-mat-skom-ob-li-ku-ipak-je-svo-je- ide-je- iz-neo-u-svo-jim-pre-da- va-nji-ma-u-lo-gi-ci-[Ha-mil-ton]-oko-če-tvr-tog-de-ce-ni-ja-na-šeg-sto-le- ća,-ali-što-on-ni-je-uči-nio,-to-je-ura-dio-Džordž-Bul-oko-po-lo-vi-ne- na-šeg-sto-le-ća;-te-ta-ko-je-da-kle-si-stem-Bu-lo-ve-lo-gi-ke-raz-vio-se-iz- Ha-mil-to-no-ve-te-o-ri-je-o-„kvan-ti-fi-ka-ci-ji-pre-di-ka-ta".-Da-nas-je-uve-li- ko-po-čeo-osva-ja-ti-ze-mlji-šte-me-đu-lo-gi-ča-ri-ma-en-gle-skim,-i-mo-že- se-go-to-vo-re-ći-da-i-ova-no-va-lo-gi-ka-u-to-me-po-gle-du-ni-ma-lo-ne- za-o-sta-je-iza-in-duk-tiv-ne-lo-gi-ke-Mi-lo-ve.-I-ta-ko-mi-ima-mo-lo-gi-ča- ra-s-jed-ne-stra-ne-in-duk-tiv-ne-ško-le,-i-s-dru-ge-stra-ne-sim-bo-lič-ke-=- ma-te-ma-tič-ke-ško-le.-[...]-To-je-bi-lo-u-En-gle-skoj"8. Vi-di-mo-da-Ne-dić-ja-sno-uoča-va-zna-čaj-Bu-lo-vih-re-zul-ta-ta-na-po- lju- sim-bo-lič-ke- lo-gi-ke.- Iako- je- pre-na-gla-sio-Bu-lov- in-te-lek-tu-al-ni- dug- Ha-mil-to-nu,- Ne-dić- s- pra-vom- is-ti-če- nje-gov- uti-caj- na- Bu- la.9-U-pri-log-či-nje-ni-ci-da- je-Ne-dić-raz-u-meo-zna-čaj-ko-ji-pri-me- na-ma-te-ma-tič-kih-sred-sta-va-na-po-lju- lo-gi-ke-mo-že- ima-ti,-go-vo-ri- i- to- da- je- svo-jim- đa-ci-ma- pre-po-ru-či-vao,- iz-me-đu- osta-lih,- Dro- bi-še-ve- (Mo-ritz- Wil-helm- Dro-bisch)- i- Li-ja-ro-ve- (Lo-u-is- Li-ard)- udž-be-ni-ke-iz-lo-gi-ke.10 Dro-bi-še-va-stu-di-ja,-Ne ue Dar stel lung der Lo gik,-či-je-je-pr-vo-iz- da-nje-ob-ja-vlje-no-1836-te,- a-ko-ja- je-do-svog-pe-tog- iz-da-nja-po- sta-la-stan-dar-dan-udž-be-nik-lo-gi-ke-u-Ne-mač-koj,-pi-sa-na-je-u-du-hu- Her-bar-to-vog-for-ma-li-zma.-Po-Dro-bi-še-vom-mi-šlje-nju,- lo-gi-ku-ne- sme-mo-po-i-sto-ve-ti-ti-sa-fak-tič-kim-opi-som-ljud-skog-mi-šlje-nja;-lo- gi-ka-ni-je-de-skrip-tiv-na-na-u-ka,-na-pro-tiv,-ona-je-nor-ma-tiv-na-na-u-ka- ko-ja- pro pi su je- op-šte- za-ko-ne-mi-šlje-nja.- Lo-gi-ku- tre-ba- raz-u-me-ti- kao-„[...]-pu-ki-for-ma-li-zam.-Ona-ne-mo-že-i-ne-sme-bi-ti-ni-šta-osim- 7- Ne-dić-LJ.,-op.-cit.,-str.141-280. 8- Ibid.,-str.-162-163. 9- Za-vi-še-o-ovoj-te-mi,-za-in-te-re-so-va-nog-či-ta-o-ca-upu-ću-je-mo-na:-Hand bo ok of the Hi story of Lo gic, eds. Gab-bay-D.-M.-i-Wo-ods-J.,-Vol. IV: Bri tish Lo gic in the Ni ne te enth Cen tury,-Am-ster-dam-2008. 10-Ne-dić-Lj.,-op.-cit.,-str.-164. 243 MILOŠ ADŽIĆ i SENKA MILOŠEVIĆ ovo-ga"11.- Sa- da-na-šnjeg- sta-no-vi-šta,- naj-za-ni-mlji-vi-ji- deo- Dro-bi- še-vog- udž-be-ni-ka- pred-sta-vlja- „Lo-gič-ko-ma-te-ma-tič-ki- do-da-tak",- ko-ji,- na-ža-lost,- ni-je- uklju-čen-u- iz-da-nja-na-kon-pr-vog.-U-nje-mu,- Dro-biš- is-pi-tu-je-od-nos-ma-te-ma-ti-ke- i- lo-gi-ke,-nu-di-ori-gi-nal-ne-al- ge-bar-ske-kon-struk-ci-je-naj-jed-no-stav-ni-jih-ob-li-ka-is-ka-za,-kao-i-de- duk-ci-je-ko-je-na-nji-ma-po-či-va-ju.-Osim-to-ga,-on-for-mu-li-še-je-dan- al-ge-bar-ski- ra-čun-kla-sa-ko-ji-pra-ti- tra-di-ci-o-nal-no-uče-nje-o-si-lo-gi- zmu.-Iako-ne-raz-vi-je-na,-Dro-bi-še-va-ide-ja-da-se-lo-gi-ka-mo-že-is-pi- ti-va-ti-ma-te-ma-tič-kim-sred-stvi-ma,-do-ve-šće-po-la-ve-ka-ka-sni-je-do- ve-li-kih-pro-me-na-u-ovoj-na-u-ci.- Li-ja-ro-vu- knji-gu,- Les lo gi ci ens an gla is con tem po ra ins,- či-je- je- prvo-iz-da-nje-ob-ja-vlje-no-1878.,-a-ko-ja-je-1907.-godine-osva-nu-la-u- pe-tom-iz-da-nju,-Ne-dić-pre-po-ru-ču-je-kao-naj-bo-lju-za-upo-zna-va-nje- sa-ma-te-ma-tič-kom-lo-gi-kom.-U-njoj-se,-po-red-Mi-lo-ve-in-duk-tiv-ne- lo-gi-ke,-ob-ra-đu-ju-i-ra-do-vi-Ha-mil-to-na,-De-Mor-ga-na,-Bu-la-i-Dže- von-sa- (Wil-li-am-Stan-ley- Je-vons),- iz-me-đu-osta-lih.-Go-di-nu-da-na- ra-ni-je,-Li-jar,-ta-da-pro-fe-sor-fi-lo-zo-fi-je-u-Bor-dou,-ob-ja-vio-je-dva-ra- da-o-lo-gič-kim-si-ste-mi-ma-Dže-von-sa-i-Bu-la.-Iako-ni-je-dao-ori-gi-na- lan-do-pri-nos-sim-bo-lič-koj-lo-gi-ci-svog-vre-me-na,-Li-ja-ro-vi-ra-do-vi,- od-ko-jih-su-ne-ki-pre-ve-de-ni-i-na-ne-mač-ki-je-zik,-uči-ni-li-su-pu-no-da- ova-gra-na-lo-gi-ke-za-ži-vi-i-van-Ve-li-ke-Bri-ta-ni-je.-Još-jed-na-stu-di-ja,- ovog-pu-ta-sa-ne-mač-kog-go-vor-nog-pod-ruč-ja,-Die en glische Lo gik der Ge gen wart-iz-1877.-go-di-ne,-Aloj-sa-Ri-la-(Alo-is-Ri-ehl),-pro- fe-so-ra-Uni-ver-zi-te-ta-u-Gra-cu,-ima-la-je-sli-čan-cilj-kao-i-Li-ja-ro-va:- pro-mo-vi-sa-nje-no-ve,-sim-bo-lič-ke-lo-gi-ke.---- Ne-di-će-vo-mi-šlje-nje-pak-o-udž-be-ni-ci-ma-lo-gi-ke-srp-skih-auto-ra,-ne- mo-že-se-na-zva-ti-po-hval-nim:- „Mi-ima-mo-vi-še-de-la-u-na-šoj-li-te-ra-tu-ri-od-no-sno-Lo-gi-ke.-Naj-sta- ri-je-je-de-lo-od-Ši-mi-ća-iz-ra-đe-no-sa-onom-na-iv-no-šću,-ko-ja-je-ka- rak-te-ri-sa-la,-ili-ako-ho-će-te-i-od-li-ku-je-sta-ra-pi-sca,-de-lo,-ko-je-ne-ma- ve-li-ke-na-uč-ne-vred-no-sti-po- -to-me-što-su-stra-na-de-la-ovog-do-ba- ova-ko-sa-sta-vlje-na,-te-sto-ga-ne-ma-ju-ve-li-ku-ni-isto-rij-sku-vred-nost.- [...]-To-što-vre-di-o-Ši-mi-će-voj-lo-gi-ci,-vre-di-i-o-dru-gim-lo-gi-ka-ma- u-nas.-Mi-ne-ma-mo-nijed-nog-sa-mo-stal-nog-de-la-u-na-šoj-li-te-ra-tu-ri,- ne-go-ima-mo-de-la-ra-đe-nih-po-stra-nim-auto-ri-ma,-pa-i-u-nji-ma-ni-je- se-po-sti-glo,-da-se-ver-no-iz-ne-se,-pra-vil-ni-po-gled-stra-ni-pi-sa-ca;-i- da-ne-bi-ov-de-ula-zi-li-u-pre-tres-po-je-di-nih-pi-sa-ca-i-nji-ho-vih-de-la-o- lo-gi-ci,-do-volj-no-će-bi-ti-da-ka-že-mo-da-nijed-no-ne-za-slu-žu-je-na-ro- či-te-pre-po-ru-ke,-i-ako-ni-je-od-šte-te-pro-či-ta-ti-ova-kve-spi-se,-jer-se-u- nji-ma-mo-že-na-ći-po-ne-čeg-i-do-brog."12 11-Dro-bisch- M.,- Ne ue Dar stel lung der Lo gik nach ihren ein fac hsten Verhältnissen. Nebst einem lo gisch-mat he ma tischen An han ge, Lip-zig-1836.,- S.-VI. 12-Ne-dić-Lj.,-op.-cit.,-str.-163-164. 244 MILOŠ ADŽIĆ i SENKA MILOŠEVIĆ Iako-strog,-Ne-di-ćev-sud-ni-je-po-gre-šan.-Srp-ska-lo-gi-ka-u-XIX-ve-ku- na-pro-sto-se-ne-mo-že-po-hva-li-ti-ori-gi-nal-nim-de-li-ma.-U-ovom-po- gle-du,-za-ža-lje-nje-je-či-nje-ni-ca-da-sam-Ne-dić,-ko-ji-je-bio-upo-znat- sa-re-zul-ta-ti-ma-En-gle-ske-sim-bo-lič-ke-lo-gi-ke,-a-ko-ji-pri-pre-ma-ju-te- ren-stva-ra-nju-mo-der-ne-lo-gi-ke,-ni-je-iza-se-be-osta-vio-stu-di-ju-ko-ja- bi-ove- re-zul-ta-te-pri-bli-ži-la- ši-roj-aka-dem-skoj- jav-no-sti.-Ne-di-će-va- pre-da-va-nja-na-Ve-li-koj-ško-li,-iako-ne-ori-gi-nal-na,-do-sled-no-iz-la-žu- ne-ke-od-ovih-re-zul-ta-ta.-Iako-po-for-mi-sle-de-tra-di-ci-o-nal-ne-udž-be- ni-ke-lo-gi-ke,-iz-la-žu-ći,-re-dom,-uče-nja-o-poj-mu,-su-du-i-za-ključ-ku,- u-nji-ma-se-i-da-lje-mo-že-na-ći-do-sta-to-ga-za-ni-mlji-vog-i-no-vog.-Ne- di-ćev-do-pri-nos-ogle-da-se-u-to-me-što-ni-je-pro-pu-stio-da-uka-že-na- zna-čaj-on-da-šnjih-stre-mlje-nja-u-lo-gi-ci,-ko-ja-će-na-kra-ju-re-zul-ti-ra-ti- ra-đa-njem-mo-der-ne- lo-gi-ke,-mla-de-na-u-ke-ko-ja-će-svo-je-me-sto-u- srp-skim-ško-la-ma-pro-na-ći-tek-na-kon-Dru-gog-svet-skog-ra-ta.--- LI-TE-RA-TU-RA: Dro-bisch-M.,-Ne ue Dar stel lung der Lo gik nach ihren ein fac hsten Verhältnissen. Nebst einem lo gisch-mat he ma tischen An han ge,-Voss, Lip-zig-1836. Fre-ge-G.,-Be griffsschrift: eine der arit hme tischen nac hge bil de te For- mel sprac he des re i nen Den kens,-Lo-u-is-Ne-bert-Ver-lag,-Hal-le-1879. Hand bo ok of the Hi story of Lo gic,-eds.-Gab-bay-D.-M.-i-Wo-ods-J.,-Vol. IV: Bri tish Lo gic in the Ni ne te enth Cen tury,-North-Hol-land,-Am-ster- dam-2008. Gard-ner-M.,-Lo gic, Mac hi nes and Di a grams,-McGraw-Hill,-New-York- 1958. Kne-a-le-W.-i-Kne-a-le-M,-The De ve lop ment of Lo gic,-Cla-re-don-Press,- Ox-ford-1962.-[U-pre-vo-du-na-srp-ski-je-zik:-Nil-V.-i-Nil-M.,-Raz voj lo gi- ke,-Ja-sen,-Be-o-grad-2011.] Li-ard-L.,-Les lo gi ci ens an gla is con tem po ra ins,-Ger-mer-Ba-il-liè-re,-Pa-ris- 1878. Ne-dić-Lj.,-Fi lo zof ski spi si,-Pla-to,-Be-o-grad-2000.- Pri-or-A.-N.,-Hi sto ri ja lo gi ke,-Na-pri-jed,-Za-greb-1970. Stoj-ko-vić-A.,-Raz vi tak fi lo so fi je u Sr ba: 1804-1944,-Slo-vo-ljub-ve,-Be- o-grad-1972. 245 MILOŠ ADŽIĆ i SENKA MILOŠEVIĆ Mi-loš-Adžić-and-Sen-ka-Mi-lo-še-vić Uni-ver-sity-of--Bel-gra-de,-Fa-culty-of-Phi-lo-sophy----Phi-lo-sophy-De-part-ment,- Bel-gra-de-Ser-bian-Aca-demy-of-Sci-en-ces-and-Arts,-In-sti-tu-te-of-Mat-he-ma-tics,- Bel gra de OF-OL-DER-SER-BIAN-LO-GIC Ab-stract In-this-pa-per-we-aim-to-pin-po-int-so-me-of-the-key-mar-kers-of-the-de-ve- lop-ment-of-lo-gic-in-Ser-bia,-star-ting-from-the-fo-un-ding-of-the-Lyce-um--in- 1836-un-til-the-end-of-the-19th-cen-tury.-Our-main-goal--is-to-un-der-li-ne-the- ro-le-that-Lju-bo-mir-Ne-dić,-a-phi-lo-sop-her-and-li-te-rary-cri-tic,-had-in-this- con-text.-Alt-ho-ugh-he-did-not-le-a-ve-any-ori-gi-nal-con-tri-bu-ti-ons-in-lo-gic,- Ne-dić- played- a- sig-ni-fi-cant- part- by- ex-po-sing- con-tem-po-rary- re-sults- in- symbo-lic-lo-gic,-which-we-re-to-lead,-thro-ugh-Fre-ge's-la-ter-work,-to-the- cre-a-tion-of-mo-dern-lo-gic. Key- words: Lju bo mir Ne dić, tra di ti o nal lo gic, symbo lic lo gic, mo dern lo gic Scott-William-Christensen,-Beogradski grafit, 2011.