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SCIENCE 



[N. S. Vol. XXV. No. 631 



somewhat gratuitous, at least Mr. Shearman 

 cites no authority for his statement. Be that 

 as it may, it is true that Leibniz first sug- 

 gested the problem of the symbolic logic, al- 

 though he did not attain the solution of it. 

 How often, however, the pioneers in a new 

 field of thought have merely started inquiry 

 without achieving the reward of discovery. 

 In reference to the problem of the symbolic 

 logic which has been mentioned above, it 

 might be a matter of general interest to the 

 lay reader to learn somewhat more explicitly 

 as to the characteristic features which it pre- 

 sents. The problem in the main is this: to 

 devise a method by which any given relations 

 expressible by symbols may be made to exhibit 

 the full range of possibilities which these rela- 

 tions imply both afiirmatively and negatively 

 — that is what they render necessarily true or 

 necessarily false. Moreover, there has been 

 a constant endeavor through the whole devel- 

 opment of symbolic logic to make such a 

 method as general as possible. The general- 

 izing of method, indeed, has been one of the 

 chief characteristics of this development. For 

 instance, the earlier symbolists dealt almost 

 exclusively with logical classes; the later, as 

 Frege, Peano, MacColl and others, extended 

 their method so as to include propositions, 

 and to represent every other relation as well 

 as the ordinary relation of logical subsump- 

 tion ; the later symbolists also endeavor to em- 

 brace in their method the quantitative as well 

 as the qualitative relations. In this connec- 

 tion I am constrained to refer to what may be 

 called a fetich of symbolic logic and which 

 has proved a snare to many. It is the notion 

 that by representing certain ideas by symbols 

 — the ideas themselves for a time being thus 

 placed in the background — the merely formal 

 processes of the accepted logical operations 

 will disclose some entirely new relation of the 

 symbols employed, which being reinterpreted 

 in terms of the original ideas will reveal a 

 new significance never before conceived. This 

 is a vain delusion, for it labors under the 

 misapprehension that there is something mys- 

 terious about certain formal processes by vir- 

 tue of which new material content will be 

 revealed. It has been urged that scientific 



discoveries of some moment may be stumbled 

 upon merely by following out the subtle work- 

 ings of formal processes whose significance 

 can be appreciated only when such processes 

 have been finally completed. It is as though 

 the stream of reason was able to cut out cer- 

 tain subterranean channels to emerge again 

 into the light of day. Leibniz had this idea 

 as a kind of a will-o'-the-wisp, in his ' Charac- 

 teristica Universalis ' by which he thought 

 that formal rules might take the place of 

 brains and the conscious processes of thought. 

 " If we had it," he says, " we should be able 

 to reason in metaphysics and morals in much 

 the same way as in geometry and analysis " 

 (G. vii. 21). "If controversies were to arise, 

 there would be no more need of disputation 

 between two philosophers than between two 

 accountants. For it would sufiice to take their 

 pencils in their hands, to sit down to their 

 slates, and to say to each other (with a friend 

 as witness, if they liked) : Let us calculate " 

 (G. vii. 200). The practical utility of the 

 symbolic logic is not, however, in the direction 

 of the discovery of new possibilities never 

 before conceived, but rather in the line of 

 providing a method by which every possibility 

 is embraced in one comprehensive survey. 

 In a field of complex relations it is very easy 

 to overlook one and another of the many pos- 

 sibilities, and a method is valuable both theo- 

 retically and practically which provides that 

 no single possibility can escape the attention, 

 and which thus shows that logical implications 

 are both manifold and complex. It is a ques- 

 tion largely of whether every possibility has 

 been brought to the attention of the observing 

 mind, and not whether a possibility can be 

 discovered by certain logical processes as an 

 entirely new result never before imagined. 

 Mr. Shearman cites as an example of a new 

 truth discovered by calculation that of the 

 existence of the planet Neptune by Adams and 

 Leverrier. It must be remembered, however, 

 that each one of these men in his calculation 

 had clearly before him from the beginning 

 the desired end which he expected his calcula- 

 tions to prove. In other words, these men 

 were not working in the dark, simply trusting 



