April 22, 1922] 



NATURE 



507 



the inconsistencies of general theory. The logician 

 is therefore of necessity a very serious person, and to 



■suspect a twinkle in his eye when he is propounding 

 ■s problem is to undermine his authority. But there 

 K another reason why he must be serious. If he 

 vould make formal logic a distinctive science he must 

 walk warily between the devil and the deep sea, for 



a the one hand he has to beware of falling into pure 

 matters of grammar, the use and misuse of the parts 

 of speech, and on the other hand he has to avoid the 

 abyss of metaphysics. Indeed if one were to take a 

 pencil and score through everything in a treatise on 

 logic which really depends on an intelligent under- 

 standing and use of grammar and everything also 

 which depends on a disputable metaphysical theory, 

 it would be difficult to be sure that anything would 

 remain. There used to be a subject, taught at uni- 

 versities, called rhetoric, and many chair's of it still 

 survive, but it would puzzle any one now to say 

 definitely what a professor of rhetoric is expected to 

 teach. It looks as though logic may some day and 

 very soon be in a similar case. 



Two parts of Mr. Johnson's logic are yet to come. 

 The two parts before us are exceedingly well written. 

 Every sentence is a model of clearness and lucidity. 

 However puzzled the reader may be when he discovers 

 the sort of problems he is invited to discuss, if he 

 yields to the spell and plays the game, he will find a 

 certain philosophical interest which will engage his 

 attention throughout. 



The influence of ^- Principia Mathematica " is very 

 much in evidence ; probably without that work few of 

 the problems here dealt with would have had any raison 

 d'etre, even if they had been discovered to exist. 

 Thus Mr. Johnson makes a very important point of a 

 division he proposes between propositions, verbally 

 identical, into primary and secondary. Truth and 

 falsity, he tells us, can be predicated of propositions 

 in quite different senses according as they are one or 

 the other. " Some fairies are malevolent " if it is a 

 primary proposition is necessarily false because fairies 

 do not exist. But if it applies to " descriptions " of 

 fairies then, as descriptions exist, it is true, and it is 

 a secondary proposition. Similarly, in the chapter on 

 negation we are asked to consider propositions such 

 as these opposites. " An integer between 3 and 4 is 

 prime " and " An integer between 3 and 4 is composite." 

 Here we are told that though one is contradictory 

 of the other, neither is true because both have a non- 

 existent subject. This is in keeping with the endless 

 interest Mr. Russell discovered in the question of the 

 truth or falsity of the proposition " The present King 



• France is bald." All one can say is that if any 



nsensical content becomes a proposition once it is 

 NO. 2738, VOL. 109] 



invested with the propositional form, then logic had 

 better be abandoned to those for whom games are the 

 serious business of life. 



The author's main purpose, however, seems to be a 

 more exact classification and an improved terminology. 

 He thinks the serious objection urged against the 

 correspondence theory of truth can be got rid of 

 by substituting the terms " accordance " and " dis- 

 cordance " for correspondence and non-correspondence. 

 We may admit that the new terms are in a sense non- 

 committal, but is that a gain ? Another proposal is 

 concerned with the subject of Modality. It is to 

 substitute " certified and uncertified," for the term 

 problematic, and to distinguish the certified into 

 formally certified and experientially certified, appar- 

 ently in order to have technical terms in logic for the old 

 philosophical distinction between truths of reason and 

 matters of fact. Also for " necessary " he would substi- 

 tute two pairs of terms, nomic and contingent, and, epis- 

 temic and constitutive. The peculiat character of proper 

 names he proposes to designate by the term "ostensive." 

 In all this we seem to be hearing the echo of Mr. Russell's 

 complaint that we shall never make progress in science 

 ^ntil we construct and use a scientific language. 



Perhaps the most novel thing in the logical theory 

 expounded in Part i is the Paradoxes of Implication. 

 The " typical paradox " is certainly not what we 

 ordinarily designate by that term, and the author is 

 aware that his use requires justification. A paradox 

 in the ordinary meaning is the affirmation of a proposi- 

 tion the actual terms of which include its negation, as for 

 example, " Whoso loses his life shall save it." The 

 essence of the paradox is that despite its apparent 

 contradiction in form it contains defensible philosophic 

 truth. The logical paradox here discussed is very 

 different. You may be led by implication (/> implies q) 

 technically correct, to the form " if /> then q " where 

 p may stand for the proposition 2+3 = 7 and q for the 

 proposition " it will rain to-morrow," then you have 

 the paradox. At this point no doubt the ordinary 

 person would lose interest, but if you are a logician 

 it is here the problem becomes engrossing. 



One very interesting discussion, also in Part i, is 

 the famous Leibnizian principle of " the identity of 

 indiscernibles." No one can fail to see that meta- 

 physically the principle is an essential part of the 

 concept of substance, yet logically there seems no 

 way of keeping this in view, and the author reaches 

 the conclusion — which is quite correct on his prin- 

 ciples — that it seems to him in any case to have no 

 logical justification whatever. 



In Part 2 there is a distinct increase in the philo- 

 sophical interest. The difference between the aspect 

 of a probleni to the philosopher and to the logician 



