There are one or two other brief tracts in which Leibnitz anticipates the modern views of logic. Thus in the eighteenth tract in Erdmann’s edition (p. 92), called “Fundamenta Calculi Ratiocinatoris”, he says: “Inter ea quorum unum alteri substitui potest, salvis calculi legibus, dicetur esse æquipollentiam.” There is evidence, also, that he had arrived at the quantification of the predicate, and that he fully understood the reduction of the universal affirmative proposition to the form of an equation, which is the key to an improved view of logic. Thus, in the tract entitled “Difficultates Quædam Logicæ,”[3] he says: “Omne *A* est *B*; id est æquivalent *AB* et *A*, seu *A* non *B* est non-ens.” [3] Erdmann, p. 102. It is curious to find, too, that Leibnitz was fully acquainted with the Laws of Commutativeness and “Simplicity” (as I have called the second law) attaching to logical symbols. In the “Addenda ad Specimen Calculi Universalis” we read as follows.[4] “Transpositio literarum in eodem termino nihil mutat, ut *ab* coincidet cum *ba*, seu animal rationale et rationale animal.” “Repetitio ejusdem literæ in eodem termino est inutilis, ut *b* est *aa*; vel *bb* est *a*; homo est animal animal, vel homo homo est animal. Sufficit enim dici *a* est *b*, seu homo est animal.” [4] Ibid. p. 98. Comparing this with what is stated in Boole’s *Mathematical Analysis of Logic*, pp. 17–18, in his *Laws of Thought*, p. 29, or in this work, pp. 32–35, we find that Leibnitz had arrived two centuries ago at a clear perception of the bases of logical notation. When Boole pointed out that, in logic, *xx* = *x*, this seemed to mathematicians to be a paradox, or in any case a wholly new discovery; but here we have it plainly stated by Leibnitz. The reader must not assume, however, that because Leibnitz correctly apprehended the fundamental principles of logic, he left nothing for modern logicians to do. On the contrary, Leibnitz obtained no useful results from his definition of substitution. When he proceeds to explain the syllogism, as in the paper on “Definitiones Logicæ,”[5] he gives up substitution altogether, and falls back upon the notion of inclusion of class in class, saying, “Includens includentis est includens inclusi, seu si *A* includit *B* et *B* includit *C*, etiam *A* includet *C*.” He proceeds to make out certain rules of the syllogism involving the distinction of subject and predicate, and in no important respect better than the old rules of the syllogism. Leibnitz’ logical tracts are, in fact, little more than brief memoranda of investigations which seem never to have been followed out. They remain as evidence of his wonderful sagacity, but it would be difficult to show that they have had any influence on the progress of logical science in recent times. [5] Erdmann, p. 100.