It is admitted by those who profess it and is for the rest evident from the definitions of Logistic that have been given, that it has nothing in common with mathematics, for although the majority of its cultivators are mathematicians and use is made of the phraseology usual in Mathematics, and it is directed toward Mathematics, in certain of its practical intentions, there is nothing intrinsically mathematical in it. Logistic is a science which deals, not with quantity alone, but with _quantity and quality together_; it is a science of _things in general_; it is _universal mathematics,_ containing also, subordinated to itself, the mathematical sciences properly so-called, but not coinciding with these. It means to be, not mathematics, but _a general science of thought._ [Sidenote: _Example of its mode of treatment._] But the "thought" of Logistic is nothing but the "verbal proposition," which, in fact, supplies its starting-point. What the proposition is; whether it be possible truly to distinguish the proposition we call "verbal" from all the others, poetical, musical, pictorial; whether the verbal proposition does not bear indistinctly in itself, a series of very diverse spiritual formations, from poetry to mathematics, from history and philosophy to the natural sciences; what language is and what the concept is--these and all other questions concerning the forms of the spirit and the nature of thought, remain altogether extraneous to Logistic and do not disturb it in its work. The propositions (the concept of the proposition remaining an unexplained presupposition) can be indicated by _p, q,_ etc.; the relation of implication of one proposition in another can be indicated by the sign _⊃,_ hence an isolated proposition is "that which implies itself" _(p.⊃.q.)._ By following a method such as this, many distinctions of the traditional formalist Logic are eliminated, and in compensation for this, new ones are added and old and new are dressed in a new phraseology. The logical _sum a + b_ is the smallest concept, which contains the other two _a_ and _b_ and is what was previously called the "sphere of the concept"; the logical _product a x b_ indicates the greater concept contained in _a_ and in _b,_ and answers to that which was previously called "comprehension." There are also new or renovated laws, like the law of _identity,_ by force of which, in Logic (differently from Algebra), _a + a + a ... = a;_ by which it is desired to signify this profound truth, that the repetition of one and the same concept as many times as one wishes, always gives the same concept;--the law of _commutation,_ by which _ab = ba_;--or that of absorption, by which _a(a + b) = a;_ or--(the convention being that the negation of a concept is indicated by placing against it a vertical line) the other beautiful laws and formulæ: _a + a | = a| (a | )a = a; aa | = o._ This is a charming amusement for those who have a taste for it.