NATURE 



233 



THURSDAY, JULY 14, 1881 



SYMBOLIC LOGIC 

 Symbolic Logic. By John Venn, M.A., Fellow and Lec- 

 turer in the Moral Sciences, Gonville and Caius College, 

 Cambridge. Pp. xxxix. 446. (London: Macmillan, 

 1881.) 



MANY who are interested in the progress of logics 1 

 science have looked forward to the appearance of 

 this long-expected work as one likely to give them a 

 logical treat. They will not be disappointed. It may be 

 impossible to accept Mr. Venn's opinions as decisive of 

 some points which he discusses, and it would not be diffi- 

 cult to indicate deficiencies ; but we have no book which 

 approaches the one before us in the thoroughness with 

 which it opens up the logical questions of the day. With 

 equal industry and ability Mr. Venn has gone over almost 

 the whole literature of logic so far as it contains any 

 germs of the scientific system associated with the name 

 of Boole. Mr. \'enn writes professedly as an admirer of 

 Boole, and his work consists to a great extent of the 

 matter of lectures upon Boole's logic, delivered under the 

 inter-collegiate scheme of lecturing, which has now been 

 in operation for about twelve years at Cambridge. Thus 

 the book is substantially an exposition of Boole's Logic, 

 and practically the only one which we have. Boole's own 

 great work, "The Laws of Thought," appeared more than 

 a quarter of a century ago (1854), and has never reached 

 a second edition. It has been much more talked about 

 than read. 



If Mr. Venn then had done nothing more than publish 

 a comparatively easy and readable exposition of Boole's 

 profound but difficult treatise, he would have done a good 

 work. But he has done a good deal more, because he has 

 worked out the relation of Boole's sjstem to all discover- 

 able previous attempts at a symbolic or quasi-algebraic 

 treatment of the syllogism, as also to all who have since 

 Boole's time endeavoured to improve upon his system. 

 The writings of almost one hundred logicians have been 

 investigated by Mr. Venn, and not a few of these writers 

 are practically unknown to English readers. If I mention 

 the names, for instance, of Bolzano, Bardili, Dalgarno, 

 Darjes, Lipschitz, Maass, Maimon, Segner, Semler, 

 Servois, Weise, it is unlikely that the reader, unless he 

 has made a very special study of logic, will ever have 

 heard of most of these names before. A great change 

 has taken place in the standard of scholarship expected 

 of authors nowadays. During the last century philo- 

 sophers calmly wrote down whatever came uppermost in 

 their minds, in complete indifference to their ignorant 

 predecessors. David Hume discovered and expounded 

 the laws of the association of ideas, unconscious that it 

 was all in Aristotle's works. Jeremy Bentham wrote 

 upon logic with sublime confidence, although his reading 

 had been confined to the compendiums of Sanderson and 

 Isaac Watts. Now a man is expected to read everything 

 about his subject before he writes anything. The late 

 Sir William Hamilton of Edinburgh was the ideal of the 

 new method, towards the introduction of which he much 

 contributed. He had all the doctrines of logicians of 

 various schools classified in his common-place books ; 

 Vol. XXIV. — No. 611 



but when he came to work out his own system of the 

 syllogism, fell disease arrested him before the work was 

 half done. It must require much judgment to use the 

 bibliographic method, as one may call it, to an adequate, 

 and yet not to an excessive extent. 



Perhaps the most interesting chapter in the whole book 

 is the last one, containing "Historic Notes," which are 

 however merely supplementary to a great quantity of 

 historical information given incidentally in the preceding 

 chapters. The table on p. 407 is one of extreme interest. 

 It shows and classifies in the clearest way no less than 

 twenty-five apparently different modes in which logicians 

 from the time of Leibnitz had attempted to represent 

 symbolically the ordinary universal negative proposition, 

 say, no S is P. Boole and Dr. Macfarlane, for instance, 

 express it as denying the existence of the class of things 

 S which is P. Hamilton introduced a clumsy wedge- 

 shaped copula with a stroke across it to express negation ; 

 Darjes entirely misused well-known mathematical signs 

 in the expression -f S - P. Segner's formula is hardly 

 better, namely S< — P. Mr. MacCoU's notation, so 

 recently the subject of discussion in the Mathematical 

 Society, the Educational Times, and N.-vture, is at 

 least convenient, namely S : P', though, as I venture to 

 hold, only a disguised form of the equation S = S P'. 

 But this single page gives matter for endless study, and 

 Mr. Venn has conferred a great benefit upon logical stu- 

 dents in opening up the subject of logical symbolism and 

 logical method in its full extension, thus hastening the 

 time when some decision can be arrived at. 



There is, however, much that is novel in the volume- 

 No author, for instance, has carried th.e diagrammatic 

 representation of logical relations to anything like the 

 same extent and perfection as Mr. \'enn. Starting with 

 the well-known circular diagrams, attributed to Euler, 

 but traced back to earlier logicians, at any rate to Lange, 

 Mr. Venn has succeeded in representing, by interlacing 

 oval figures, the logical relations of four or even more 

 terms. Although opinions may differ as to the value of 

 the method, he has unquestionably worked out a complete 

 and consistent system of diagrammatic reasoning, which 

 carries the Eulerian idea to perfection. He has gone 

 even further and has converted his diagrams into a kind 

 of logical-diagram machine, which allows the elliptic 

 segments representing classes to be selected and rejected 

 mechanically. Of this remarkable device Mr. Venn 

 (p. 122) says that "it would do very completely all that 

 can be rationally expected of any logical machine. Cer- 

 tainly, as regards portability, nothing has been proposed 

 to equal it, so far as I know." The latter statement 

 may be certainly conceded, as the machine, though con- 

 structed needlessly large, is only five or six inches square, 

 and three inches deep. So far, however, as I can judge 

 from the somewhat brief and unexplicit description given 

 by Mr. Venn, I cannot see how his machine can perform 

 logical operations automatically. The selections of classes 

 have to be guided and judged lay the selector, and all that 

 the mechanical arrangements effect is to select a whole 

 class of elliptic segments at one movement of the fingers. 

 This mechanical diagram, then, is analogous, as Mr. 

 Venn remarks, to what has been described as " The Logical 

 Abacus," but I do not think it can be called mechanical 

 in the same degree as the logical machine. 



