This is not the occasion to go on expounding in its other particulars this construction, of which we have given an example, for it is very well known: nor to attach importance to criticizing it, since' its foundations themselves have already been shown to be false and its hybrid genesis explained. Verbal Logic, which vaunts itself as rational, carries its own caricature in itself, namely the creation of _Sophisms_; because, since it seeks the force of thought in words, it cannot prevent sophistical ability from making use, in its turn, of words, in order capriciously to create thoughts and forms of thought. Thus verbal Logic, in order to combat sophisms, is constrained hastily and eagerly to abandon simple verbal connections, and to take refuge in concepts and connections of concepts thought in words; that is to say, neither more nor less than to negate the formalist point of view. And with analogous self-irony it renounces that point of view and dissolves itself, when it tries to refute the fourth figure of the syllogism, or to reduce the second, third and fourth to the first, as the only real figure, and then the first to a connection of three concepts; not to mention the permanent self-irony and patent demonstration of falsity involved in the logical deduction of the figures of the syllogism which it makes from a series of moods, recognized as _not conclusive._ [Sidenote: _Mathematical Logic or Logistic._] Formalist Logic has been the object of many violent attacks from the Renaissance onwards; but it cannot be said that it has been struck in its essential part, because up to the present, the principle itself, or the incoherence from which it springs, has not been attacked. Several attempts at reform have followed and still follow; they have all of them the same defect, which is the wish to reform formal Logic without issuing from its circle, and without refuting its tacit presumption-- the pretension of obtaining thought in words, concepts in propositions. The most considerable attempt of the kind that has been made, which has many zealous followers in our day, is _mathematical Logic,_ also called _calculatory, algebraical, algorhythmic, symbolic, a new analytic,_ or a _Logical calculus or Logistic._ [Sidenote: _Its non-mathematical character._]