It is generally held that Peano and his school played an important role at the end of the last century in the development of logic and foundations of mathematics. This paper surveys the results achieved by Peano and his school and examines the motivation behind their work, thus demonstrating the validity of their reputation.

We deal with the heuristic influence of C.S. Peirce's logical ideas on the creation of imaginary, non-Aristotelian logic (logic free of the laws of contradiction and excluded middle) by Nikolai Aleksandrovich Vasil'ev (Vasiliev) in 1910-13 and with the circumstances that attended and made easier the creation of imaginary logic.

In February 1992, T. Ivanovic, working with the author in the archives at Kazan University discovered new material relating to the life and work of the logician P.S. Poretskij (1846-1907). These include: various documents related to Poretskij's lectures on mathematical logic for mathematics department students at Kazan University which were intended to be given for three semesters in autumn of 1887 and all of 1888 but delivered only during the Spring 1888 semester; a complete mathematical logic program compiled by Poretskij; materials related to Poretskij's father and family; Poretskij's Magister's (master's) dissertation and the decision of the Physics-mathematics faculty council to award him the doctorate in astronomy rather than the Magister; a complete list of the sources he use (including Boole, Jevons, Schröder, and Peano); biographical data and materials regarding his illness and subsequent dismissal from Kazan University.

Kazan was an active center for the development of logic in the 19th and early 20th centuries. Logic courses were included in the philosophy and psychology curricula of Kazan University and the Theological Academy. Issues of logic were dealt with by Lubkin in his critical consideration of Kant and Kant's successor Kisewetter, and Lobachevskij reviewed the logic textbooks of Kant and Kisewetter.

Some of the university logic courses were taught by Theological Academy members, including Archimandrate Gavriil, A. M. Bukharev, and V. A. Snegirev. The emphasis here was on Aristotelianism. The syncretic unity of philosophy and psychology present at that time led to the psychologistic interpretation of logic of N. A. Vasil'ev and I. I. Yagodinskij and hampered formalization, although Vasil'ev effectively contributed to its heuristic aspects. Meanwhile, M. M. Troitskij and Yagodinskij worked on inductive logic. E. A. Bobrov, A. D. Gulyaev, and A. O. Makovel'skij worked on traditional and "gnoseological" logic, and Vasil'ev created a non-traditional (non-aristotelian) "imaginary" logic based upon elimination of the law of contradiction and the law of excluded middle, and he developed the idea of metalogic. His ideas also contributed towards the development intuitionistic and modal logic, although indirectly. P. S. Poretskij worked on mathematical logic. These developments of logic were broken off in 1922 by the reorganization of the university.