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taeniae propositions) from our rules would only be a slightly greater 

 encroachment upon the full freedom of popular speech than has 

 already been brought about by the exclusion of such terms as ' many/ 

 4 most,' and others of a somewhat quantitative character." Mr. Venn 

 consequently restricts himself generally to what may be called uni- 

 versal propositions. But suppose that we have the data xy=20 

 and ,^=20; from these numerical propositions, though each is despi- 

 cable in itself, we obtain, when combined, the important universal 

 proposition x — ccy. To exclude number is to draw a very arbitrary 

 line. Connected with this is the standpoint involved in the title 

 ' Symbolic Logic,' a standpoint with which as it is explained in the 

 work we are not wholly satisfied. It appears to us that Boole's 

 work, properly understood, leads rather to the conception of an 

 Algebra of Logic; not an Algebra of and 1, as Boole understood 

 it, but an Algebra in which an elementary symbol may have any 

 value between and 1. In every properly expressed equation the 

 quantitative value of the one member is equal to the quantitative 

 value of the other member. The identity of two groups of the same 

 kind of logical unit surely involves equality in the numbers of those 

 groups. Thus viewed, the science is every whit as quantitative as 

 ordinary Algebra. 



Chapter XII. contains a series of original problems which are 

 used to illustrate the subject. The various neat methods employed 

 there and throughout the work lead us to the conception, not of a 

 limited system (a word which is a fallacy in itself), but to the con- 

 ception of a science which is limited only in the sense that the 

 portion which has been made actual knowledge is limited. 



A. Mactaklane. 



An Introduction to Logic. By "W. H. S. Moxck, M.A., Professor of 

 Moral Philosophy in the University of Dublin. Dublin : Hodges, 

 Foster, and Figgis, Grafton Street. 1880. 

 Professor Monck's work consists of two parts — the one devoted 

 to an elementary exposition of the subject, the other to the discus- 

 sion of questions more suitable to the advanced student, — the two 

 together forming an excellent manual on the Aristotelian Logic. 

 But while Prof. Monck describes with exactness and precision the 

 whole province he has traversed, we cannot but consider that pro- 

 vince artificially limited. " The fact is that Logic does not draw 

 inferences at all, but only lays down rules for drawing them " 

 (p. x). In accordance with this, Logic cannot help us to conclude 

 from " John is the father of Thomas " that " Thomas is the son of 

 John;" but suppose we know that "If John is the father of 

 Thomas, Thomas is the son of John," and that " John is the father 

 of Thomas," then Logic can assure us that Thomas is the son of 

 John. In accordance with this theory of the function of Logic, we 

 have (at p. 70), " An argument of this form — three-fourths of the 

 army were killed ; three-fourths of the army were Prussians ; 

 therefore some of the Prussians were killed — is logically incom- 

 plete ; and to complete it we must state in terms that any two frac- 



