[Sidenote: _Identity of nature of Logistic with formalist Logic._] Thus it is seen that if the words and the formulæ be somewhat different, the nature of mathematical Logic in no respect differs from that of formalist Logic. Where the new Logic contradicts the old, it is not possible to say which of the two is right; as of two people walking side by side over insecure ground, it is impossible to say which of the two walks securely. The very doctrine of the _quantification of the predicate_ (which has been the leaven of the reform) in no wise alters the traditional manner of conceiving the judgment, with the corresponding arbitrary manner of distinguishing subject and predicate. It simply establishes a convention with the object of being able to symbolize, with the sign of equality, the subject and the predicate:--the subject being included in the predicate, is part of it: "men are mortal" equals: "men are some mortals"; and so, "men" being indicated with _a_ and "some mortals" with _b,_ the judgment can be symbolized: _a = b._ For us, it is indifferent whether the modes of the syllogism be the 64 and the 19 recognized as valid by traditional Logic, or the 12 affirmative and the 24 negative of Hamilton's Logic, which distinguishes four classes of affirmative and four of negative propositions. It is indifferent whether the methods of conversion be three or two or one. It is indifferent whether logical laws or principles be enumerated as two, three, five or ten. Since we do not accept the point of departure, it is impossible for us, far from admitting the development, even to discuss it; save to demonstrate that from capricious choice comes capricious choice, as we have made sufficiently clear in our treatment of formalist Logic. Mathematical Logic is a new manifestation of this formalist Logic, involving a great change in traditional formulæ, but none in the intimate substance of that pretended science of thought. [Sidenote: _Practical aspect of Logistic._]