March 24, 1881] 



NATURE 



487 



yield true and simple results within the sphere of logic, 

 but it disclosed wonderful analogy between logical and 

 mathematical forms, to which De Morgan adverts in the 

 passage quoted above. All true progress in the philo- 

 sophy of those fundamental sciences depends upon ever 

 keeping in view the fundamental identity of the reasoning 

 processes, as depending on the process of substitution, 

 practised explicitly by algebraists for some two or three 

 centuries past, and implied in the geometrical reasoning 

 of Euclid. 



But Mr. MacCoU takes a backward step ; he S3ys he 

 can make a simpler notation by taking a : j3 instead of 

 my n = a/3. In regard to form there is absolutely no 

 novelty in the implication, for it is simply De Morgan's 

 X ) ) V, or the ancient Aristotelian proposition A is B. 

 It is true that Mr. MacCoU makes his terms consist of 

 assertions, so that all his assertions would appear to be 

 assertions about assertions — a needless comple.\ity,landing 

 us in the absurdity that a calculus of equivalent statements 

 has no means of exhibiting the statements themselves. 

 Mr. MacColl claims indeed considerable advantage for 

 his notation on the ground that in the syllogism (a : /3) 

 (/3 : y) : (a ; -y), the very same relation which connects a 

 with /3, and /3 with y, connects also the combined premises 

 (a: 3) (/3:y) with the conclusion a : y. He thinks that 

 my notation is very clumsy and roundabout, because, as 

 my propositions treat of things or qualities, I should have 

 to use words to express the inference of one proposition 

 from others. In that case Mr. MacColl must bring the 

 like charge of clumsiness against the whole body of 

 mathematicians, because their equations are between 

 things or their magnitudes, and they still use language 

 "hence," "therefore," &c., to express the fact that 

 certain equations lead to other equations. If there is 

 any mathematical sign to denote inference, it is rarely 

 used, unless it be the familiar '. " and . '., which are merely 

 shorthand signs. 



Mr. MacColl however, while pointing out the excellence 

 of his implications, objects to my statement that he rejects 

 equations in favour of implications on the ground that his 

 method admits of both forms : " As a matter of fact," he 

 says, " I employ both, sometimes even in the same 

 problem. In my first paper , . , I adopt the equational 

 form throughout ; in my second and third papers, which 

 relate entirely to questions of pure logic, I generally adopt 

 the implicational form, as the simplest and most effective; 

 while in my fourth paper, which treats of probability, I 

 mainly adopt the equational form." There is nothing 

 which I can see in this to contradict my objection that 

 Mr. MacColl rejects equations in favour of implications. 

 Mr. MacColl uses implications as "the simplest and 

 most effective," but he adopts the equational form, I 

 suppose, when he finds it indispensable ; if not, why does 

 he not hold to his simple and effective implication ? If 

 he finds one form best in logic and the other in mathe- 

 matics, then he is ante-Boolian, because it was the whole 

 point of Boole's labours to establish identity of method 

 in logic and mathematics. I have really no wish to 

 condemn Mr. MacCoU's calculus or to enter into con- 

 troversy with him, but in the interests of truth and 

 sound science I must assert my belief that his impU- 

 cation a : /3 is at the best but a shorthand rendering of 

 a = ali^ which is Boole's form adopted by me. I have not 

 said, and do not undertake to say, that Mr. MacCoU's for- 

 mula; are not concise and neat. But a shorthand notation is 

 bad if it obscures the real nature of the reasoning operation, 

 and the fact that Mr, MacColl always keeps the equation 

 in the background as a reserve method to call into opera- 

 tion when needed, shows to my mind that his methods 

 are mistaken in a philosophical point of view. The very 

 name of his method is " The Calculus of Equivalent 

 Statements," and the word equivalent sufficiently implies 

 that the equation is at the bottom of the matter. The 

 end of it all then is that a : /3 has one letter less in it than 



a = a 3, and to save the trouble of writing this one little 

 letter Mr. MacColl would have us obscure all the grand 

 and fertile analogies which Boole disclosed to the astonish- 

 ment of mathematicians in l8_|.7 and 1854. Mr. MacColl 

 says : "The question whether the implication a : 3 or its 

 equivalent the equation a = a'ji should be preferred in a 

 symbolical system of logic, must be decided on the broad 

 grounds of practical convenience," It is not however a 

 question of practical convenience, but of philosophical 

 truth which is at issue, and in thus playing fast arfd loose 

 with the equation, Mr, MacColl shows his entire want of 

 comprehension of what is involved in the Boolian reform 

 of logic. It may be added that were Mr. MacColl to 

 discard implications and use only the equations which he 

 admits are equivalent to them, there would be no formal 

 difference between his calculus and that modified form 

 of Boole's calculus which I proposed in 1S64, and have 

 been ever since engaged in developing, excepting indeed 

 Mr. MacCoU's unaccountable adoption of assertions as 

 terms. 



Perhaps it ought to be added that Boole, both in his 

 " Mathematical .-Xnalysis of Logic," and in his great 

 " Laws of Thought," introduces chapters on what he 

 calls "Secondary Propositions" or Hypotheticals, which 

 deal, like Mr. MacCoU's assertions, with the truth of 

 other assertions ; but nothing emerges from Boole's dis- 

 cussion of secondary propositions e.xcept that they obey 

 e.^actly the same formal laws as primary propositions, 

 and are of course expressed equationally, 



W, Stanley Jevons 



ILLUSTRA TIONS OFNE W OR RARE ANIMALS 

 IN THE ZOOLOGICAL SOCIETY'S LIVING 

 COLLECTION^ 



III. 



THE animals we now speak of are again inh.ibitants of 

 North-Eastern Asia— a country which, as before 

 remarked, has of late years produced a considerable 

 number of accessions to the list of Mammals, Both of 

 them also belong to the great group of Ruminants — which 

 is of special interest, as embracing all the animals upon 

 the tlesh of which civilised man principally subsists, 



6. The Japanese Goat-Antelope {Capricornis crispa). 

 For many years Siebold's "Fauna Japonica" was almost 

 our only authority on Japanese zoology. The Dutch, 

 having long had a monopoly of Japan, were enabled to 

 stock their great National Museum at Leyden with a host 

 of objects unknown to the other cabinets of Europe, but 

 of which their travellers and residents managed to obtain 

 specimens from various parts of the land where they only 

 were permitted to penetrate. The " Fauna Japonica," 

 although Japan is now open to all the world, still remains 

 the best work of reference on the mammals of Japan, In 

 it will be found the first description of the singular goat- 

 like antelope of which the Zoological Society have recently 

 obtained their first living example, drawn up by the cele- 

 brated naturalist Temminck, formerly director of the 

 Leyden Museum. Temminck named the animal Antelope 

 crispa, from the rough coat of hair which covers it, and 

 tells us that it inhabits the higher alps of the Japanese 

 Islands Nippon and Sikok, and is known to the Japanese 

 as the " Nik." But a more complete account of its habits 

 has lately been published by Capt, H. C. St, John in 

 his recentlv-issued " Notes and Sketches from the Wild 

 Coasts of Nipon," Capt, St. John tell us that the 

 Japanese chamois, as he calls it, "is a very difficult 

 animal to find, and to bag when found ; they keep to the 

 highest mountains, and to the highest and must rugged 

 pe'aks of these ranges. I have hunted them with the 

 natives, and with their dogs, and this often ; and yet only 

 once, although often close to the creatures, have I had a 



* Continued from p. 417. 



