P. K. EAT'S DEDUCTIVE LOVIC. 559 view of most logicians and regards adjectives as sometimes abstract, namely, when they qualify abstract nouns (p. 38). This is a case that has perhaps been generally overlooked, and it re- quires some consideration. I should, however, prefer to adopt the other alternative and say that when the name of an attribute is qualified by an adjective the attribute itself then passes into the category of things that possess attributes and its name there- fore becomes concrete. This view, of course, involves the admis- sion that the distinction between concretes and abstracts is not an absolute one. On another question connected with abstract names Dr. Kay follows Mill in a view that I have always found very puzzling, namely, that some abstracts possess both connota- tion and denotation ; I cannot add that he has made it clear to me why virtue and beauty should be regarded as counotative (p. 41), while colour, weight and humanity (pp. 42, 47) are non- connotative. Professor Kay's discussion of Immediate Inferences is more complete than that of most text-books with which I am. ac- quainted, and his views of Obversion, Contraposition, &c., are clear and consistent. The value not indeed of this part of the book only but of the whole of it is enhanced by the large number of useful examples with which most of the chapters conclude. It is only in his treatment of Hypotheticals that I think the author not quite successful. " Whenever A is, nothing other than B is," should hardly be given as the obverse of "If A is B is," since "other than" is not equivalent to "inconsistent with," and the existence of something other than B is compatible with B's own existence. The obverse of the given proposition should rather be stated, " If A is, it is not true that B is not ". One distinctive feature of Dr. Ray's book is the extensive use that he makes of what are commonly known as Euler's diagrams ; and, although he mentions Hamilton's use of these circles with apparent approval and at any rate without criticism (p. vi.), he does not fall into Hamilton's error of attempting to represent by a single pair of circles A, O, and I propositions, which cannot be adequately represented by less than two, three and four such pairs respectively. Dr. Ray is very successful in his application of the diagrams to immediate inferences and the different syllo- gistic moods. If I have a criticism to offer here, it is that he goes too far in his attempt not merely to illustrate the syllogism by this means but to distinguish by its aid the valid from the invalid moods. The attempt meets with success, but the working it out is exceedingly laborious. In applying the diagrams to some of the syllogistic rules (pp. 173-179), I am doubtful whether the author shows the method to be equally adequate. I may add that the interpretation of the circles, when the terms contained in a proposition are read in connotation (pp. 124, 125), is not very satisfactory. It is inevitable that in using diagrams of this kind we should fall back on the denotative reading. "With regard 40
