A categorical syllogism is a rule of inference, consisting of two premisses and one conclusion. Every premiss and conclusion consists of dual relationships between the objects M, P, S. Logicians usually use only true syllogisms for deductive reasoning. After predicate logic had superseded syllogisms in the 19th century, interest on the syllogistic system vanished. We have analysed the syllogistic system, which consists of 256 syllogistic moods in total, algorithmically. We have discovered that the symmetric structure of syllogistic figure formation is inherited to the moods and their truth values, making the syllogistic system an inherently symmetric reasoning mechanism, consisting of 25 true, 100 unlikely, 6 uncertain, 100 likely and 25 false moods. In this contribution, we discuss the most significant statistical properties of the syllogistic system and define on top of that the fuzzy syllogistic system. The fuzzy syllogistic system allows for syllogistic approximate reasoning inductively learned M, P, S relationships.