186 



NOTES AND QUERIES. 



[No. 42. 



from the most ample list. Its professed object 

 was to disprove the phenomenon of motion ; but 

 its real one, to embarrass an opponent. It has 

 always attracted the attention of logicians ; and 

 even to them it has often proved embarrassing 

 enough. The difficulty does not lie in proving 

 that the conclusion is absurd, but in shoicing ivhei'e 

 the fallacy lies. From not knowing the precise 

 kind of information required by ISiwttjj, I am 

 unwilling to trespass on your valuable space by 

 any irrelevant discussion, and confine myself to 

 copying a very judicious note from Dr. Whateley's 

 Logic, 9th edit. p. 373. 



" This is one of the sophistical puzzles noticed by 

 Aldricb, but he is not happy in his attempt at a solu- 

 tion. He proposes to remove the difficulty by demon- 

 strating that in a certain given time, Achilles wonkl 

 overtake the tortoise ; as if any one had ever doubted 

 that. The very problem proposed, is to surmount the 

 difficulty of a seeming demonstration of a thing pal- 

 pably impossible ; to show that it is palpably impos- 

 sible, is no solution of the problem. 



" I have heard the present example adduced as a 

 proof that the pretensions of logic are futile, since (it was 

 said) the most perfect logical demonstration may lead 

 from true premises to an absurd conclusion. The re- 

 verse is the truth ; the example before us furnishes a 

 confirmation of the utility of an acquaintance with the 

 syllogistic form, in tcliick form the pretended demonstration 

 in question cannot be exhibited. An attempt to do so 

 will evince the utter want of connection between the 

 premises and the conclusion." 



"What the Archbishop says is true, and it dis- 

 poses of the question as one of " Formal Logic : " 

 but yet the form of the sophism is so plausible, 

 that "it imposes with equal force on the " common 

 sense" of all those who repose their conclusions 

 upon the operations of that faculty. With them 

 a ditFerent procedure is necessary ; and I suspect 

 that if any one of the most obstinate advocates of 

 tlie sufficiency of common sense for the "balancing 

 of evidence" were to attempt the explanation of a 

 hundred fallacies that could be presented to him, 

 he would be compelled to admit that a more 

 powerful and a more acciirate machine would be 

 of advantage to him in accomplishing his task. 

 This machine the syllogism supplies. 



The discussion of (jregory St. A'incent will be 

 found at pages 101-3. of his Opus Geometricum, 

 Antw., 1647, f(d. The principle is the same as 

 that which Aldrich afterwards gave, as above re- 

 ferred to by Dr. Whateley. I can only speak 

 from memory of the discussion of Leibnitz, not 

 having his works at hand ; but I am clear in this, 

 that his principle :igain is the same. ISiarip is in 

 error, however, in calling St. Vincent's " a i^eonie- 

 trical treatment" of it." He indeed uses lines to 

 represent the spaces passed over: and their dis- 

 cussion occurs in a chapter on what is univer.?ally 

 (but very absurdly) called " geometrical propor- 



tion." It is yet no more geometrical than our 

 school-day problem of the basket and the hundred 

 eggs in Francis Walkinghame. Mere names do 

 not bestow character, however much philosophers 

 as icell as legislators may think so. All attempts 

 of the kind have been, and must be, purely nu- 

 merical. T. S. D, 

 Shooter's Hill, August .S. 



Achilles and the Tortoise. — Your correspondent 

 will find references in the article " Zeno (of Elea)" 

 in the Penny Cyclopcedia. For Gregory St. Vin- 

 cent's treatment of the problem, see his Quadra- 

 tura Circuli, Antwerp, 1647, folio, p. 101., or let it 

 alone. I suspect that the second is the better refer- 

 ence. Zeno's paradox is best stated, without either 

 Achilles or tortoise, as follows : — No one can go 

 a mile ; for he must go over the first half, then 

 over half the remaining half, then over half the re- 

 maining quarter ; and so owfor ever. ]\Iany books 

 of logic, and many of algebra, give the answer to 

 those who cannot find it. M. 



Heplic^ ia ;;^tnor caurriCiS. 



''Barum" and " Sarum" (Vol. ii., p. 21.). — The 

 formation of the first of these words has not yet 

 been accounted for. I must premise my atteiupt 

 to supply an explanation by admitting that I was 

 not aware it was in common use as a contraction 

 for Barnstaple. I think it will be found that the 

 contracted ibrm of that name is more usually 

 " Berdest," " BarnsT." In trying further to con- 

 tract the word, the two last letters would be 

 onutted, and it would then be " Barii," with the 

 circumflex showing the omission of several letters. 

 Having reduced it to this state, an illiterate clerk 

 would easily misread the circumflex for the plain 

 stroke "-," expressing merely the omission of the 

 letter " m," and, perhaps ignorant of the name in- 

 tended, think it as well to write at full length 

 " Barum." J. Bx. 



Countess of Desmond (Vol. ii., p. 153.) — It is 

 stated in Turner's Sacred History., vol. iii. p. 283., 

 that the Countess of Desmond died in 1612, aged 

 145. This is, I presume, the correct date of her 

 decease, and not 1G26, as mentioned by your 

 querist K.; for in Lord Bacous History of Life 

 and Death, originally published in 1623, her death 

 is thus alluded to : — 



" The Irish, especially the Wild Irish, even at this 

 dav, live very long. Certainly they report that within 

 these few years the Countess of Desmond lived to a 

 liundred and forty years of age, and bred teeth three 

 times." 



Tiie manner of her death is recorded by Mr. 

 Crofton Croker, in his agreeable volume of Re- 

 searches in the South of L-eland, 4to. London, 1824. 



