Febeuaby 12, 1897.] 



SCIENCE. 



277 



as the minor premise, of course. But £ is ^4 is 

 a non sequitur, both a formal and a material 

 fallacy in the case. In fact, the instance is 

 simply the common one for puzzling school 

 boys. 



It either rains or it does not rain. 



It rains 



.•.It does not rain. 



The illusion is created by the failure to see that 

 the principle of disjunction is not fulfilled by 

 merely using the word ' not ' before rains in the 

 conclusion, when an additional negative is re- 

 quired by the dictum of this form of reasoning. 

 The ' not ' in this case is a part of the second 

 term in the disjunction 'not rains,' and hence, 

 when we follow the law of disjunctive inference, 

 we should get 'It does not not rain,' or by 

 double negatives 'It rains,' which is the true con- 

 clusion. So in Professor Jastrow's case. The 

 modus toUendo ponens requires us to affirm the 

 second term, which is 'not A,' and we get as 

 the true conclusion B is not A, instead of B is 

 A, which is a nonsequitur, as indicated. 



But now, that I find that the conclusion is the 

 same as the minor premise in the disjunctive 

 reasoning, I may raise the further question 

 whether there is not another material fallacy 

 somewhere, since disjunctively I might get B is 

 not A. In the instance before us this can be done, 

 and in disjunctive inference the only fallacy 

 that is most likely to occur is thepetitio principii. 

 The non sequitur will occur only when there is 

 also a formal fallacy in it. Now, after assuming 

 that A is B, it violates conversion to suppose 

 that BisA, and it is a contradiction to suppose 

 that B is not A. Hence with .4 is -B as our 

 premise, and B is either A or not A as the 

 other ; we have a petitio principii in the latter 

 case. We might say that the disjunction is in- 

 complete, which is possible if we assume that 

 A is B, and which would only result in making 

 the third alternative a particular proposition, 

 I or 0, with the formal fallacy mentioned in the 

 prosyllogism, a petitio principii in the disjunctive 

 syllogism, and a non sequitur in supposing that 

 .Bis^. 



James H. Hyslop. 



Columbia University, 



New York, January 15, 1897. 



SCIENTIFIC LITERATURE. 

 Higher Mathematics. A text-book for classical 

 and engineering colleges. Edited by Mans- 

 field Meeeiman, Professor of Civil Engi- 

 neering in Lehigh University, and Robeet 

 S. Woodwaed, Professor of Mechanics in 

 Columbia University. New York, John 

 Wiley & Sons. 1896. 8vo. Pp. xi+576. 

 The appearance of this rather unique volume- 

 is significant as a proof of the rapid develop- 

 ment of mathematical instruction in this coun- 

 try. It is designed for undergraduates who- 

 have mastered the elements of the diflfereutial 

 and integral calculus. After referring to the 

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 which, for several reasons, is worth quoting in. 

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 change of opinion has occurred as to the aims- 

 and methods of mathematical instruction. The 

 old ideas that mathematical studies should b& 

 pursued to discipline the mind, and that such 

 studies were ended when an elementary course 

 in the calculus had been covered, have for the 

 most part disappeared. In our best classical 

 and engineering colleges the elementary course 

 in calculus is now given in the sophomore year, 

 while lectures and seminary work in pure 

 mathematics are continued during the junior 

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 ing the existing demand for a suitable text ta 

 be used in such upper-class work that the edi- 

 tors enlisted the cooperation of the authors in 

 the task of bringing together the chapters of the 

 book. ' ' The following synopsis of the chapters 

 will give some idea of the contents of ' Higher 

 Mathematics:' I. ' The solution of equations, ' 

 by Mansfield Merriman (32 pp.); II. 'Deter- 

 minants,' by Lsenas GifiFord Weld (37 pp.) ; 

 III. 'Projective geometry,' by George Bruce 

 Halsted (37 pp.); IV. ' Hyperbolic functions,' 

 by James McMahon (62 pp.); V. 'Harmonic 

 functions,' by William E. Byerly (57 pp.) j VI. 

 'Functions of a complex variable,' by Thomas 

 S. Fiske (77 pp.); VII. ' Difierential equa- 

 tions,' by W. Woolsey Johnson (71 pp.) ; VIII. 

 'Grassmann's space analysis,' by Edward W. 



