x = x2, x (1 - x) = o, involves (p. 367) one of the " verwunderlichsten Irrungen der mathematischen Logik," and "needs no criticism." There are a number of references of the same general character scattered through this volume. Nor is the reason of Erdmann's antipathy far to seek. He is, namely, a pronounced opponent of the "Subsumtionstheorie" of the judgment. And the theory of the judgment is, as he tells us already in his preface, the "Brennpunkt der Logik." The geometrical method of symbolizing judgments is the natural expression (p. 247, p. 446 sq.) of this false subsumption theory, and, "roh" as it is, "may be of some use to the beginner." But Erdmann loses no opportunity to warn us against any extension or elaboration of it. In his dislike of the "mathematisirende Logik," and of its "formalism," Erdmann reminds us in fact of Hegel's attitude towards so much of the mathematical tendency as existed in the logic of his own time, and one is rather surprised to find Erdmann himself putting Hegel (pp. 247, 248) in the wrong company, in consequence of the latter's account of "das abstrakte Urtheil." In many respects, as a fact, Erdmann's notion of the nature of the thinking process brings him fairly near to Hegel, although in other respects the two are very far apart.
Our author's personal theory of the judgment allies him, meanwhile, to the teachers of the " Logic of Intension " in general. Intension determines extension (p. 151). The extension is the "totality of the species in a genus" (p. 134), but has nothing to do with the "Anzahl der einzelnen Exemplare" of the genus in question. The extension of the class match, for example, is not decreased when you burn this individual match, or when you manufacture new matches of an old sort (loc. cit.). Not only is intension thus prior to extension, and of far deeper significance than the latter, but, in view of the rejection of all forms of the "subsumption theory," we are driven (p. 261) to define the judgment as a "Gleichheitsbeziehung der Einordnung" — a technical expression which needs some elucidation, but which is at all events the embodiment of an interpretation of the process of judgment in terms of intension. The predicate of a judgment points out elements or groups of elements which, intensively regarded, were already immanent in the idea of the subject. Such is Erdmann's view.
Our elucidation of the foregoing expression must needs be inadequate, since our author's intricate argument defies successful condensation. But it is upon this "focal" point that all the rays of this treatise are indeed brought to bear; and a hint of the nature of this doctrine involves of necessity a characterization of the whole book. And such a characterization, inadequate as it must needs be, we have here to undertake.
