On Сlarifying the List of Aristotelian Syllogisms
It is substantiated the fallacy of the thesis that it is impossible to get a negative statement from affirmative simple categorical proposition at least in that part where it is a question of acceptability of syllogistic formulas on the basis of their X-matriх. The article presents the two Aristotle syllogisms ApmAmsOsp and AmsApmOsp in which the truth of the premises guarantees the truth of the conclusions if that it is forbidden to substitute the identic general names instead of s, p, m. These syllogisms are erroneously referred to the set of “incorrect” and therefore to the not accepted formulas of the Aristotelian syllogistic. The results obtained allow us to detect the “lost” laws of Aristotelian syllogistic: the Asp Osp formula that has the same X-matrix as the laws of inversion or subordination for expressions of the form Asp, Isp, Esp, Osp was found. It is appropriate to call this formula the second law of applying universal affirmative proposition. Formulas ApmAmsOsp, AmsApmOsp, Asp Ops are difficult to be found, but they are easily proved with the help of Euler circles. The discovery of these syllogistic formulas as “canonical” essentially changes the existing theories of Aristotelian syllogistic.