Plato Sergejewitsch Porezki

PS Porezki

Plato Sergeyevich Porezki ( Russian Платон Сергеевич Порецкий , scientific. Transliteration Plato Sergeevič Poreckij * 3 ^{. Jul} / 15. October  1846 ^greg. In Jelisawetgrad , Russian Empire ; † 9 ^jul. / 22. August  1907 ^greg. In Schowid , Oblast Chernigov ) was a Russian mathematician, astronomer, logician, and philosopher.

Porezki studied at the Faculty of Physics and Mathematics in Kharkov . From 1876 he worked as an astronomer at the University of Kazan . He defended his dissertation in 1886 in the field of astronomy. He taught mathematics and astronomy and was the first mathematician in Russia to give lectures on mathematical logic, thus helping to popularize this discipline in Russia.

His research is based on the field of algebra of logic by George Boole , William Stanley Jevons and Ernst Schröder . He has the merit of developing an independent theory of logical identities, which is a generalization of Boolean algebra . The main features of his logical investigations are his theory of the consequences and causes of logical identities in connection with the treatment of the canonical forms of logical expressions.

He set himself the task of solving the problem of decidability in class calculus by finding the simplest and most effective decision algorithm possible. A central problem of his theory of logic is the solution of the question of the derivation of conclusions from a given system of premises and the finding of those premises from which the respective logical identity can be derived as a consequence. The theory also included the establishment of hypotheses regarding the rationale for given inferences. Among them were also methods that make it possible to obtain the sharpest inferences.

In his theory of logical equations, he developed original and simple methods to derive all possible conclusions from the given assumptions or to specify the assumptions for a given logical equation. Porezki made an important contribution to the theory of normal forms.

Porezki saw the difference between logic and algebra in the fact that in logic qualitative forms and in algebra quantitative forms are examined. He also warned that this difference should not obscure what is common to both of these disciplines. In his view, the methodology of mathematical logic is analogous to the mathematical methodology of algebra. In his last work, Porezki also examined the logical inequalities. He generalized the syllogistic theory of traditional logic and examined and analyzed many forms of non-syllogistic indirect inference.

Porezki was of the opinion that the laws of logic are not independent of the properties of the objects in the area that is being studied by a particular discipline. According to Porezki, the laws of logic are truths "which contain some specific indication of the nature of the material to be examined" (1). Even an algebraic treatment of logic cannot ignore the question of its content.

Porezki asserted that every axiomatically constructed system has a right to exist in science only if all statements that can be proven in it are true in terms of content when interpreted in some area of ​​objective reality. When examining the formal logic of the final procedure, he did not consider the form in isolation from the content. He was of the opinion that the analytical apparatus of a logical calculus is only in order if it expresses a certain real content and that, even if an axiomatic is already available, content-related considerations by no means lose their meaning.

The investigation of the interrelationships between form and content in science led Porezki to the dialectical thesis that the more abstract character of a theory - provided that the abstractions used in it are really scientific - does not weaken its practical effect, but on the contrary even increases it .

Fonts

• Isloschennije osnownych naschal matematischeskoi logiki w vosmoschno boleje nagljadnoi i obschedostypnoi forme , 1881
• (1) O sposobach reschenija lopgischeskich rawenstw i ob obrathom spocobe matematischeskoi logiki (About methods for solving logical equations and about an inverse method of mathematical logic), 1884
• La loi de racines en logique , 1896
• Reschenije obschei sadaschi teori werojatnostei pri pomoschi matematischeskoi logiki , 1887
• Sept lois fondamentales de la théorie des égalités logiques à deux termes (The seven basic laws of the theory of logical equations for two terms), 1898–1899
• Exposé élémentaire de la théorie des égalités logiques à deux termes , 1900
• Quelques lois ultérieures de la théorie des égalités loqiques , 1900–1901
• From the field of mathematical logic (Russian), 1902
• Théorie des non-égalités logiques , 1903–1904
• Théorie conjointe des égalités et des non-égalités logiques , 1908–1910

Web links

• John J. O'Connor, Edmund F. Robertson :  Plato Sergejewitsch Porezki. In: MacTutor History of Mathematics archive .