730 



SCIENCE 



[N. S. .yoL. XLII. No. 1090 



the rise of the mathematical method, have, 

 each for himself, attacked its direct and in- 

 direct consequences. I shall not here stop to 

 point out how the very accuracy of exact sci- 

 ence gives better aim than the preceding state 

 of things could give. I shall call each of these 

 persons a paradoxer, and his system a paradox. 

 I use the word in the old sense : a paradox is 

 something which is apart from general opinion, 

 either in subject-matter, method or conclusion." 

 Further on in his introductory remarks De 

 Morgan adds : " After looking into books of 

 paradoxes for more than thirty years, and hold- 

 ing conversation with many persons who have 

 written them, and many who might have done 

 so, there is one point on which my mind is fully 

 made up. The manner in which a paradoxer 

 will show himself, as to sense or nonsense, will 

 not depend upon what he maintains, but upon 

 whether he has or has not made a sufficient 

 knowledge of what has been done by others, 

 especially as to the mode of doing it, a prelim- 

 inary to inventing knowledge for himself. 

 That a little knowledge is a dangerous thing 

 is one of the most fallacious of proverbs. A 

 person of small knowledge is in danger of try- 

 ing to make his little do the work of more; but 

 a person without any is in more danger of 

 making his no knowledge do the work of some." 

 How De Morgan would have enjoyed for his 

 collection the solution ( ?) of Fermat's problem 



by Miss , of the New York schools, 



whose name will not go down in history, pub- 

 lished by the staidest of New York evening 

 papers; this problem to solve, or prove not 

 solvable, a;" + 2/" =■ 2" in integers for n greater 

 than 2 has been the subject of many similar 

 solutions and the Wolfskehl prize of $25,000 

 has often been claimed and as often denied. 

 Without fear of contradiction we may say that 

 the final solution will be given by some able 

 student of number theory who is not ignorant 

 of " what has been done by others." Equally 

 would De Morgan have welcomed the high- 

 school boy's solution ( ?) of the trisection of an 

 angle, with ruler and compass, published only 

 three or four years ago in a journal devoted to 

 elementary science. Particularly, too, De 

 Morgan would have desired for his " Budget " 



something typical concerning our American 

 prodigies, whose names, we note, are found 

 more often in paragraphs than in monographs, 

 more often in headlines than in footnotes. 



How many works of to-day come within the 

 classification of paradoxical nonsense, foisted 

 upon the press by authors ignorant of " what 

 has been done by others " in the fields in which 

 these authors would instruct the public. 

 Among these " paradoxers " are scientists of 

 real fame in science, but without philosophy, 

 who wish to instruct philosophers in philos- 

 ophy, philosophers ignorant of the work of 

 Georg Cantor and Dedekind who wish to in- 

 struct mathematicians about the nature of the 

 number idea and the psychology of number, 

 school superintendents who are profoundly 

 ignorant of the fundamental ideas of arith- 

 metic who wish to write text-books on arith- 

 metic, old maids living in a two-room flat on 

 the fifteenth floor of a New York apartment 

 who wish to instruct the parents of the United 

 States on the art of bringing up a large family 

 of children, manufacturers successful in busi- 

 ness who yearn to instruct the world in philos- 

 ophy and science. These are modern para- 

 doxers of the nonsense type who need another 

 De Morgan to call attention to their folly. 



" All the men who are now called discoverers, 

 in every matter ruled by thought, have been 

 men versed in the minds of their predecessors, 

 and learned in what had been before them. 

 There is not one exception. I do not say that 

 every man has made direct acquaintance with 

 the whole of his mental ancestry; many have, 

 as I say, only known their grandfathers by the 

 report of their fathers. But even on this point 

 it is remarkable how many of the greatest 

 names in all departments of knowledge have 

 been real antiquaries in their several subjects. 



"... if any one will undertake to show a 

 person of little or no knowledge who has estab- 

 lished himself in a great matter of pure 

 thought, let him bring forward his man and 

 we shall see." 



Let every editor have a copy of these words 

 to enclose with rejected manuscripts which vio- 

 late the principles so sanely laid down by De 



