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 VON JUL. BEEGMANN, Die Grundprobleme der Logik. 257 everything has) is, as it were, the pivot on which Inference turns ; and this comes out perhaps even more strongly in the case of syllogistic inference it is because of this that the presence of a true Middle Term is the only condition necessary in order that some conclusion may be drawn from any pair of premisses. Bergmann allows that as regards syllogistic Inference there is, All M is P) , Alia - -D inference in passing from A n a AT *> All S is P. All M is P) But what is the Sachverhalt in (1) All M is P, (2) A 11 a -v/r f respectively? In as far as the matter of fact is concerned it would seem that what is before the speaker's mind in (1) is some- thing which is both M and P, and what is before him in (2) is something which is at the same time M and P and S. And there would seem to be as much a difference of Auffassung between (1) and Some (or This, etc.) M is P, as between (2) and All (or Some) S is P. If difference of aspect or emphasis is all that is needed for Inference, Sub-alternation seems as much inference as Conver- sion ; if not, are not the conclusions of syllogisms in Figs. 1 and 2 not inferences, while the conclusion in the third and fourth Figures are so ? Dr. Bergmann's view of Analytic Judgments is a part of his doctrine to which he draws special attention in the Preface, and it is connected in an interesting way with other parts of his theory. According to him, we can have ' Analytic ' Judgments which " enlarge knowledge " ; that is to say, Judgments in which the Pre- dicate, though in some sense ' contained ' in the Subject, yet adds to the information conveyed by the Subject. He distinguishes ( 20) between Analytic and Synthetic Judgments as follows : "For the recognition of a Judgment as true or untrue, the object [of the Judgment] need be brought up for comparison (1) only in as far as it is set before the thinker by the Subject-notion ( = the notion which is the ground of the Judgment and is restricted to its constitutive content) ; so that the predicated determination though no part of the constitutive content of the Subject-notion yet is, after a fashion, contained in it ; or (2) something more of the object must be taken in than is included in the notion that is the ground of the judgment in other words, there is needed an intuition of the object which goes beyond the apprehension of the bare Subject-notion. E.g., in order to recognise the truth of the sentence 2 + 3 = 4 + 1 by mere comparison with its object, this object need only be taken into account in so far as it possesses the determination by which the Subject-notion of the sentence marks it out as distinct from all other objects. Assuming that the sum of 2 and 3 had other properties besides those which are somehow contained in being this sum, these might be entirely left out of account. And we might convince ourselves in the same way of the untruth of the sentence : The sum of 2 and 3 is not equal to the sum of 4 and 1. 17