hrvatski

Zastupljenost matematičke logike u spisu Samouka. Pokus pèrvi Vatroslava Bertića

Vatroslav (Ignatius) Bertić bio je matematičar i logičar porijeklom iz Hrvatskog zagorja: rođen je 1818. godine u Orehovici, naselju u današnjoj općini Bedekovčina, a umro je 1901. godine u Humu, naselju pored grada Zaboka. Potkraj 1846. napisao je, a tijekom 1847. godine objavio spis Samouka. Pokus pèrvi, koji je, kako 1977. godine tvrdi Žarko Dadić, »prva matematička knjiga na hrvatskom jeziku nakon hrvatskoga narodnog preporoda«. U spisu Samouka. Pokus pèrvi Bertić je izložio brojna promišljanja o pojmu, istini, svojstvu (vlastitosti), tautologiji (očevidnoj istini), jednakosti (svejednosti) i skupovima (množinama). Pojmove i brojeve pritom je zapisao simbolima (znakovima), dok je stvari istovjetnih svojstava objedinio u skupove (množine), pri čemu je na simbole i skupove primijenio algebarsku operaciju množenja. Na oblikovanje Bertićeve misli nedvojbeno su utjecala djela filozofa Gottfrieda Wilhelma Leibniza (1646–1716) i matematičara te astronoma Josepha Johanna von Littrowa (1781– 1840). Naime, Bertić se, kao i Leibniz, koristio simbolima, te je, kao i von Littrow, koristio algebarske operacije. Premda nije, poput matematičara i logičara Georgea Boolea (1815–1864), uspostavio sustav matematičke logike, i premda nije, poput matematičara i jezikoslovca Hermanna Günthera Grassmanna (1809–1877), razradio odnose između simbolā i algebarskih operacija, Bertić je u Samouki. Pokusu pèrvom ipak iznio promišljanja iz kojih proizlazi da se u tom spisu nalaze i, kako izvještava Dadić, »neki elementi matematičke logike«. Vatroslav (Ignatius) Bertić was a mathematician and logician from Hrvatsko Zagorje: he was born in 1818 in Orehovica, a settlement in the present-day municipality of Bedekovčina, and he died in 1901 in Hum, a settlement near the city of Zabok. By the end of 1846 he had written and during 1847 had published his writings First Attempt of the Self-educated Person (Samouka. Pokus pèrvi) which is, as Žarko Dadić claims in 1977, “the first mathematical book in Croatian after the Croatian National Revival”. In his writings First Attempt of the Self- educated Person Bertić exposed numerous considerations on concept, truth, quality (propriety), tautology (self-evident truth), equivalence (equalness) and sets (pluralities). In so doing, he wrote down concepts and numbers by using symbols (signs), while he united concepts of identical qualities in sets (pluralities), whereat he applied the algebraic operation of multiplication on symbols and sets. Works of both the philosopher Gottfried Wilhelm Leibniz (1646–1716) and of the mathematician and astronomer Joseph Johann von Littrow (1781– 1840) undoubtedly affected the formation of Bertić’s thought. Namely, Bertić, as well as Leibniz, used symbols, and he, as well as Littrow, applied algebraic operations. Although he did not, as the mathematician and logician George Boole (1815–1864) did, establish the system of mathematical logic, and although he did not, as the mathematician and linguist Hermann Günther Grassmann (1809–1877) did, elaborate upon relations between symbols and algebraic operations, Bertić, however, did express his considerations which may lead to the conclusion that the First Attempt of the Self-educated Person contains, as Dadić reports, “some elements of mathematical logic”.

Vatroslav Bertić, matematička logika

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