According to American philosopher W. W. Bartley, the transition from tradi- tional Aristotelian to Boolean logic is a revolutionary milestone in the history of logic. The work of George Boole which was followed by a developement of a mathematicaly oriented logic brings a shift of paradigm. In my thesis I follow the period in which the shift is said to have happened. I explicate the elements of syllogistic and its main conceptions as expounded in a textbook The Rudiments of Logic written by Henry Aldrich. Furthermore I demon- strate logical systems of three authors: Archbishop Richard Whately, George Boole and Lewis Carroll. I accent the connection of those systems and the practical aspect of logic. With this in mind I consider Bartley's statement and estimate the role of the rules in the systems and its possible use in three domains circumscribed in Aldriches book: simple apprehension, judgement and discourse. 1