REVIEWS 561 



reference to scientific principles. The statement (p. 244) that the scientific 

 status of the indestructibility of matter has been impaired by the discovery of 

 radioactivity is highly disputable. It depends on definition and point of 

 view. The sentence on the conservation and the dissipation of energy is liable to 

 give the impression that the author does not understand the meaning of the latter 

 principle. Moreover, any one speaking of "gravitation " as axiomatic is using the 

 term in a sense very different from that commonly understood. The importance 

 of the treatment of axioms in all discussions on the foundations of logic can 

 hardly be over-estimated, and the critic approaching Dr. Schiller's volume with 

 the desire to find a clear and coherent view will be left with the impression 

 that an adequate discussion of this point would exhibit inconsistencies with the 

 main trend of the argument. 



The second fundamental is that ancient problem, the nature of formally valid 

 inference. The old logical query whether syllogistic reasoning ever elucidates new 

 truth is a particular case of the larger general question. Those who maintained 

 that the syllogism was a.petitio principii were confronted with the inference that 

 any one acquainted with the axioms and postulates of Euclid, therefore, knew and 

 understood every truth of geometry. It was evident, in this case, that something 

 new was elucidated. Dr. Schiller's solution is interesting and plausible. He says 

 that, in all real reasoning, we reason with regard to a doubt. Every syllogism 

 applied to a particular case is an experiment to discover whether an individual who 

 belongs to a class for most purposes can have attributed to him some specific 

 character possessed by other members of the class. This is true enough in its 

 way. But it hardly elucidates the relation between the properties of a parallelo- 

 gram and the axioms and postulates of Euclid. The meaning of the iron rigidity 

 of logical inference is a problem which none who seeks to penetrate to the 

 foundations of logic can ignore. Dr. Schiller, unfortunately, talks round the 

 problem. I am, no doubt, free to infer that the angles of a triangle are together 

 equal to two right angles, or that the diagonals of a rhombus bisect each other 

 at right angles, or neither. But this does not explain why both are absolutely 

 certain formally valid truths implicit in Euclidean geometry. What is the meaning 

 of this certainty? Why does each step of the reasoning follow from the last? 

 The problem is very similar to the one concerning the nature of axioms. 



Considerations of this kind will show a sphere for formal logic much greater 

 than Dr. Schiller is willing to admit. Dr. Schiller wishes to displace logic by 

 some as yet unformulated science of "psychologic." In a later chapter he, semi- 

 humorously, commends formal logic as a good game. The passage is worth 

 quoting : 



" Friends, your judgment is too harsh. You must not judge logic by your own 

 feelings nor condemn it because you have no use for it. You should live and let 

 logic live. Moreover, it really has a use. Its use is to keep logicians employed 

 and amused. The study of Formal Logic makes a highly intellectual game. . . . 

 You think it a silly game ; well, in a sense, all games are silly. ..." and so on 

 (p. 388). 



This is interesting and amusing. But Dr. Schiller does not appear to 

 realise that every time we make any inference whatever, practical or theoretical, 

 a part of the process, the conceptual part, the formation of the conceptual systems 

 which we apply to reality, whether in mathematics, in science, or elsewhere, comes 

 within the sphere of influence of this game. Granted that it is not the whole 

 process. It is sufficiently important if it is only a part. Also, with regard to the 

 extension of logic which all philosophers contemplate, it is very doubtful whether 



