Notices respecting New Boohs. 63 



nected with the view taken of the Universe of Discourse, to the dis- 

 cussion of which our author devotes a chapter. Mr. Venn does 

 not give an exact definition of the meaning he assigns to this term ; 

 but from pp. 128 and 185 I gather that he considers it formed by 

 setting limits to the sum-total of logical existence. The conception 

 of a universe is held to be, strictly speaking, extra -logical, — a 

 question of the application of our formulae, not of their symbolic 

 statement ; and on the symbolic system it is said to be universally 

 admitted that the distinction between subject and predicate is lost. 

 " We may extend our universe so as to embrace the sum-total of 

 logical existence, in which case European includes things other than 

 men, and not-European includes the unlimited myriads of entities 

 which people that heterogeneous domain." "What I object to is, 

 having any thing to do with the sum-total of logical existence or 

 any limited portion of it : I object to considering any such hetero- 

 geneous subject. The term universe may be used to denote a more 

 exact and more useful idea, which is really the idea required to make 

 Boole's processes intelligible. It may be used to denote a collec- 

 tion of things all of the same type, such as is denoted by a sub- 

 stantive. We hold that the logical function of an adjective is dif- 

 ferent from that of a substantive, and so different that the distinc- 

 tive cannot be lost sight of in any exact symbolic system. The 

 logical function of an adjective is to express an attribute — in the 

 language of the grammarians, to qualify a substantive. " Black " has 

 a certain meaning in itself ; but it can no more denote a class of 

 things before being applied to a particular type than can a number 

 such as 2 denote a quantity before being applied to some unit. But 

 Mr. Yenn says (p. 181) that " we all know what is in most cases to 

 be included under the name ' black.' " I reply that we know only, 

 provided we are given the logical type to which the attribute 

 refers. Otherwise the supposed class must include black men, 

 black berries, black birds, black coats, blacking, &c, — and not only 

 the black men, but the black hairs on the heads of the black 

 men, their black skins, but, in general, not their teeth — and not 

 only the black hairs, but the black particles of each black hair — 

 and so on ad infinitum. Here, at all events, there is danger of 

 counting twice, and of having some impossible subtractions to 

 perform. Man, berry, bird, coat, particle of blacking, hair, skin, 

 tooth, each denotes a kind of logical unit, to any one of which black 

 may be applied as a qualification. This conception of a universe, 

 instead of being extra-logical, seems to me to be one of the funda- 

 mental ideas of the science. 



' Symbolic Logic ' possesses a feature which could scarcely be an- 

 ticipated in a work coming from so great an authority on the Theory 

 of Probability, namely an aversion to all quantitative considera- 

 tions. " So far from being fairly open to the charge of being too 

 numerical, we are really more open to that of being almost pru- 

 dishly averse to being seen or thought to enumerate, as will be 

 found when we discuss the treatment of particular propositions 

 (p. xxii). Turning to p. 169, we find: — " To exclude them t^pau- 



