Vii.—critical Notices

Abstract

Die Urtheilsfunction. Eine psychologische und erkenntniskritische Untersuchung. Von WILHELM JERUSALEM. Wien und Leipzig: W. Braumiiller, 1895. Pp. 269. THE author starts with a consideration of the meaning and importance, from the psychological, logical, grammatical and philosophical points of view, of the question, What is Judgment ? With regard to the grammatical reference, that bears chiefly on the relation between thought and language-from the logical point of view as expressly explained by Mr Jerusalem, living flexible judgments have to be reduced to a rigid connexion of concepts. The author's view of the philosophical place of the doctrine of judgment is discussed at the beginning and end of the book, and its importance strongly emphasized. But the bulk of the work is devoted to what the writer regards as the psychological view of judgment-his expressed intention is to furnish "a thorough psychological analysis of the cognitive function." In part of this investigation-the part which is distinguished as analytic rather than genetic or biological*, the exceedingly close connexion between Logic and Psychology, and the difficulty of everywhere drawing a sharp line between them comes out very strikingly; for we are given what purports to be an absolutely general account of Judgment-an account, i.e., which will and does apply to every judgment without exception, when rigidly analysed. This analysis is of course psychological, and it appears to me that it is judgments as thus understood that are the subject and centre of Logic. If there is an absolutely general account of judgments, on that, it would seem, Logic must rest, and with that it must begin. Although the author, to judge from some of his statements, is not in harmony with this view,-it is apparently involved in his opinion that on a complete and satisfactory answer to the (psychological) question What do we do when we judge? depends our whole theoretical view of the world, and that whatever is essential to judgment must hold of every content of judgment. Part of this view seems to me true and important-and it is involved in Mill's account of the Import of Propositions, according to which, for a due analysis, there are two questions which have to be answered (1) What do the Terms stand for? (2) What is the relation

Type-I quantum superalgebras, q-supertrace, and two-variable link polynomials

“…Following the celebrated discovery by Jones [1] of the so-called Jones' link polynomial, there has been considerable interest in recent years in modern knot theory, which has been found to be closely related, through the quantum Yang-Baxter equation (QYBE), to various areas of physics such as solvable models and quantum field theories [2,3]. With the equally important discovery of quantum algebras during the same period by Drinfeld [4] and Jimbo [5] following the initiatives of the St. Petersberg group, it was soon realized by Reshetikhin [6] and Turaev [7] that quantum algebras provided a useful tool in constructing link polynomials.…”