May^, 1887] 



NATURE 



problem is complicated by the strong winds, the copious 

 precipitation, and the ascending currents, which afifect the 

 results in ways which no physicist has yet been able to 

 explain. 



The problem of the weather would be immensely simpli- 

 fied if it could be explained, first, how it is that air highly 

 heated and approximately saturated with aqueous vapour 

 comes to overspread a definite well-marked region, usually 

 a very extensive one, while the atmosphere over con- 

 tiguous regions remains relatively cold and dry ; and, 

 secondly, how the low temperature which is so character- 

 istic a feature of anticyclones and of the rear of cyclones 

 has its origin. The complete changes which weather- 

 maps show us to take place in these respects over 

 enormous tracts of the earth's surface within even such 

 brief spaces of time as twenty-four hours, point to volumes 

 and velocities of translation of masses of air through the 

 upper currents which meteorologists have yet scarcely 

 taken cognisance of. Prof. Loomis's paper is a well- 

 worked-out and valuable contribution towards the solution 

 of this all-important practical problem. 



THE GAME OF LOGIC. 

 The Game of Logic. By Lewis Carroll. (London: Mac- 

 millan and Co., 1887.) 



MR. " LEWIS CARROLL'S" new book has both the 

 merit and the sterilitywhich might be expected from 

 a fresh and rather independent system of diagrammatic 

 or visual logic. That is to say, it is ingenious and closely 

 worked out, but cannot be said to advance either our 

 theoretic knowledge of reasoning processes or the more 

 practical craft of dealing with assertions and arguments 

 as found in ordinary life. Perhaps so trying a standard 

 ought not in fairness to be applied to the work before us, 

 which is intended — so the preface and the title hint — to 

 amuse those who would otherwise play with some less 

 instructive puzzle. But it is because it seems unlikely 

 that " The Game of Logic " will be patiently studied as a 

 game, or would reward such patience by providing " an 

 endless source of amusement," that one is inclined to 

 consider it rather as a contribution to visual logic than to 

 any other form of literature. 



Technically speaking, the propositions contemplated 

 are "extensive" and "existential." That is to say, all 

 assertions are supposed to be concerned with things as 

 members of classes, and to be translatable into the form 

 " Of the class u x there are none (or ' some ') which are 

 u y" ; so that, for example, " I feel much better" becomes 

 (pp. 50, 70, and 9) " Of the class of persons who are I, 

 there are none who do not feel much better, and there are 

 some who do " ; and " There is no one in the house but 

 John" becomes "Of the class of persons who are not 

 John, none are in the house." Of course these are here 

 chosen as examples of difficulty in translation : a great 

 many propositions can be much more naturally treated as 

 expressing class-relations. 



Every assertion is thus supposed to perform two 

 inctions : it provides a certain number of labelled com- 

 partments, and it tells us that one or more of these is 

 Either empty or " occupied." If, for example, we regard 

 fa given proposition as containing only two terms, ;irand jj^, 

 the compartments provided are four^ in number : x y, 



X non-y, non-x y, and non-x non-y. (Mr. Lewis Carroll 

 however adopts Mr. MaccoH's neater notation for the 

 negative terms.) And if two such propositions have 

 one term in common— say, if the first speaks of ;r and m, 

 and the second oi y and w— the two can be taken together 

 as one complex assertion providing eight compartments, 

 and giving, under certain conditions, more information 

 about X and y than is to be found in either proposition 

 when taken singly. 



As regards the division of the universe into compart- 

 ments, there is little to distinguish Mr. Lewis Carroll's 

 system from others which, like Boole's or Jevons', make 

 use of a similar framework ; and nothing to distinguish 

 it from Mr. Venn's, except the form of picture employed. 

 But the special features consist in (i) making all affirma- 

 tive propositions assume the real existence of the subject, 

 and (2) providing for the expression of certain forms of 

 proposition which are usually found difficult to put into 

 diagrams. For example, by means of the restricted sense 

 given to the assertion that a compartment is occupied, the 

 " particular " proposition, which often causes trouble, be- 

 comes easily expressed. In Mr. Venn's scheme, proposi- 

 tions either tell us that a compartment is empty or else 

 tell us nothing about it, whereas here the information 

 that a compartment is occupied (meaning merely " not 

 empty ") can also be distinctly given ; so that to mark the 

 compartment x y as " occupied " expresses " some x a.rey " 

 and " some y are x " together. Again, " some x exist," " no 

 X exist," and " only some x are y " are readily and neatly 

 represented ; and a distinction, due to the assumption of 

 real existence, is drawn between " all x are y " and " no x 

 are non-y" and similarly between "no x are y" and 

 " all X are non-y." 



The author is in one or two instances not quite fair to 

 the more old-fashioned logicians. It is not the case, as 

 stated on p. 30, that those who regard the universal nega- 

 tive as asserting incompatibility of attributes would there- 

 fore regard the assertion " No policemen are eight feet 

 high " a.s false. They might rather be inclined to consider 

 any such a priori treatment of it as a case of petitia 

 principii, since, if the assertion be supposed to intend 

 giving information at all, the question whether or no the 

 attributes are compatible is supposed to be at issue. 

 Again, there are probably few logicians in existence who 

 would simply turn away with scorn from the premises 

 given on p. 35. Even the more 'pedantic would rather 

 suggest that a very slight verbal alteration performed on 

 the minor premise by recognised processes (conversion 

 and obversion) would give a legitimate syllogism in 

 celarent. But no doubt Mr. Lewis Carroll's method deals 

 with such premises more directly. 



It is held by some who ought to know, that logic might 

 be taught at a much earlier age than is now the fashion ; 

 and possibly the book should be regarded as an attempt 

 to make a beginning in this direction. If so, the advant- 

 ages and disadvantages of the scheme seem about evenly 

 balanced. Certainly the diagram is simple to draw, full 

 in its information, and easily read ; but these good 

 qualities are gained at some expense. The difficulty of 

 forcing all assertions into the forms of class-inclusion is 

 not indeed peculiar to Mr. Lewis Carroll's system ; but 

 the assumption of the real existence of the subject leads, 

 in certain cases, to additional troubles of interpretation. 



